Maximizing rate of return to owned capital
A third possible objective of the farmer may be to maximize the
rate of return (R) to his personal capital (K). This objective would
be most appropriate in cases where capital is the limiting factor.
The estimate of return would be based upon the expected profits in
the particular activity, and the rate of return would be the ratio of
expected profits to owned capital, that is,
r EDO .
Maximizing total profit
Unconstrained profit maximization^ is the income objective com
monly assumed by many analysts, yet, it may involve a high level of
risk for the farmer. Frequently the activities that yield the highest
profits are subject to the largest income fluctuations (either through
output or price instability). Pursuit of unconstrained maximum pro
fits is reasonable only for those farmers who are able to absorb the
losses which are incurred in a relatively large number of the produc
tion periods. Maximizing profits may be a long- or intermediate-range
goal over which time the annual or semester profits approximate the
Unconstrained maximization is used here to indicate the condition
in which land is the only limiting factor.
investment is completely without risk, but several investment oppor
tunities can be identified as risk-free for practical purposes. Alter
native earnings can be calculated from the rate of return (R) of the
alternative investment, and the sum of personal capital (K) committed
to the activity in which the loss was experienced. Foregone alter
native earnings are equal to R x K.
Negative prof i t.--Negat i ve profit (11^) is the difference between
total revenue and total cost, where costs are greater than revenue
(i.e., nÂ£ <0). This is the farmer's monetary loss--the loss of money
which he possessed at one time.
Penalty interest.--Penalty interest (l) is the increase in in
terest rates when the farmer fails to repay his initial loan within
the allotted time. Although the government supervised agricultural
loans carry low interest rates for the original loan period, late re
payment is frequently negotiated between the lending bank and the
borrower. The final agreement between these two parties often includes
a higher interest charge on the unpaid balance of the loan (C) than
was charged in the original transaction.
The total monetary cost of the loss (T ) incurred is the summation
of the above three elements, and can be expressed in equation form as,
T = RK n + Cl.
The total cost of the loss (j^) is a function of the amount of
owned (K) and borrowed (C) capital invested, and the magnitude of the
expected loss (n) associated with a particular activity or crop. A
rather good rule of thumb that can be applied is that the T will
generally be higher in those investments requiring high levels of
Table 12 gives a summary of regression coefficients, means, and other
Like sesame, sorghum is a new crop in the area and very few
farmers have more than two or three years of experience with it. There
were insufficient data in the sample to calculate effects of pesticide
and fertilizer from the regression equation.
The maximizing level of machinery and labor were calculated by
the simultaneous solution of their first derivative equations set equal
to zero while holding capital at its mean value. The use of labor is
substantially below the optimizing level, and it is quite possible
that it is also at a level corresponding to Region I of the production
function. Given that sorghum is a new crop and that the farmers are
not yet committed to it, there is much hesitation toward investing
large quantities of inputs in sorghum production. In many cases the
producers are searching for a low cost crop to be grown in rotation
with cotton, and,thus, are operating at very low levels of inputs.
Although the mean machinery use is above the indicated level to achieve
optimal output, it is considerably below the amount used in the other
crops of the area which indicates that there is an attempt to use
machinery at the lowest possible level, and this may be decreased
further as more experience is gained.
The marginal value products (MVP) of machinery, labor, and NCI
were calculated using the sample means, ICA's cost of production reports,
and the Fondo Financiero Agrario's cost of production studies which
serve as a guide to credit. In the input groups there was a wide range
of levels of application or use. The following discussion compares the
destroying or aiding in the realization of disasterous or bounteous
harvests are observed, more usually the variation is less drastic, and
the resulting effect on yield is less dramatic. The sensitivity to
weather differs among crops, and,therefore, must be an important con
sideration in selecting factor and crop combinations for areas which
are subject to a wide range of weather characteristics.
Yield can be greatly affected by diseases and pests. The increas
ing control possibilities have lessened the uncertainty surrounding
this source of variability. However, in countries in which the agri
cultural sector is in the modernization process, the decline in dangers
associated with plague incidence is a slow process and often new and
unexpected outbreaks are experienced. The adoption of new crops and
the introduction of crops into new regions is often followed by rapid
increases in pest and disease incidence in spite of the existence of
chemical and natural means of control.
The final aspect of yield uncertainty that will be mentioned is
that related to technological change. A crucial point often over
looked by developers is the extent of the uncertainty of the effects
of the introduction of new technology. The uncertainty inherent in
any major change in the existing system of agriculture must be a key
factor in the decisions concerning innovative practices.
The preceding points have been directed toward yield variability
with respect to quantity of output. Weather, pests and disease damage
the difference between the high and low reported yields was great.
This difference expressed as a ratio of higher to lower yields was:
cotton 3.33, rice 8.40, sesame 3.18, and sorghum 5.33. Farms with zero
yields were reported for each crop; however, these zero values were
not used for the present comparison.
CHAPTER I I I
CHARACTERISTICS OF THE GEOGRAPHIC REGION,
AND THE SAMPLE SURVEY
The area chosen for the present study lies at the eastern end of
the cotton region that stretches across most of the Northern Coastal
Zone of Colombia. The choice of this area was based upon the following
1. The region is characterized by widespread use of
machinery and capital inputs; thus there was the
opportunity to get input-output data on modern
2. The cotton zone is a relatively new agricultural
area, and no previous study had been made of
agriculture at the farm level.
3. There is an interest in Colombia in an evaluation
of opportunities for diversifying agriculture in
The area occupies portions of the departments of Cesar and Guajira
and is situated, on an alluvial plain lying between the Sierra Nevada
de Santa Marta and the Cordillera Oriental of the Andes Mountains. The
soils are largely medium textured loams, ranging from sandy to clay
Rice. Sesame, and Sorghum
On irrigated land rice is an excellent crop for the region.
Profit levels are higher and risk of failure is lower than for cotton.
The current technology is quite efficient and approaches the optimum
employment of inputs. The major limitation is the lack of irrigation
water in most of the region. To date, there is little or no informa
tion regarding the economic aspects of deep well irrigation, nor in
dications as to what effect large scale ground water use would have
on the region's water resources. A second factor which may limit the
significant expansion of rice, if water were to become available, is
its high capital requirements. Even with large sums of credit avail
able from various sources, the individual farmer is frequently required
to invest sizeable amounts of his own funds. For many farmers, suf
ficient capital is not available.
Sorghum and sesame are relatively new in the area. However,
experience in this region and in other regions shows that both crops
can supplement or be substituted for cotton. The principal advantages
of these crops are their low capital requirements and low risk.
Farmers with little capital can maximize profits with these two crops;
at the same time, these crops provide a risk-averting system of
production. If income objectives other than profit maximization are
considered, sorghum and sesame appear to be good alternatives due to
their low capital requirements, low risk, and high rate of return to
rice production profit per hectare declines rapidly. When rice finally
is forced out of the solutionat the low capital-medium machinery
levelcotton cannot compete with sorghum because it requires twice the
machinery and capital inputs while yielding only about 30 percent higher
profit. Sesame also enters the solution at the lowest levels of re
source use due to its very low capital requirement.
Solutions Without a Rice Activity
When rice production is eliminated as a possibilityfor land with
out irrigationcotton becomes the principal second semester crop at
the higher resource levels. It remains an important crop until the low
capital-medium machinery input level is reached. This is the same com
bination at which rice left the solution in the first program. Begin
ning at this level the solutions of the first and second programs are
the same, using low capital consuming sesame, and low capital and ma
chinery consuming sorghum to maximize profits. The profits in the
second program are considerably lower than those of the basic one,
particularly in the upper resource groups where rice is the major crop
in both semesters (Table 16).
Maximizing Returns to Owned Capital
The third program modifies the basic one by changing the objective
function from a profit to a rate of return function. The value to be
maximized is the rate of return to owned capi-tal J where owned capital
^Rates of net returns to owned capital for the four crops are;
Sg2 = .56
Table 16. Crop Combinations for Maximizing Profit at Selected Levels
of Capital and Machinery Inputs, Excluding Rice Production
Annual Rate of Return
to Owned Cap tal
aCapital is indicated by the first symbol and machinery by the
^C = Cotton, Sm = Sesame, Sg = Sorghum
1 = first semester 2 = second semester
Numbers in parentheses indicate the fraction of total land to be
planted in the specified crop.
Return to Owned
1 for Cotton,
Rice, Sesame, and
Rate of Return
to Owned Capital
Y = -108605.0 + 11028.9M 1071.82M2 + 33.56M3
+3191.1L 59.13L2 + O^L3 + 21.1 (NCl)
-0.0052 (NCl)2 + 799.7Fd
Y = yield of rice in kilograms per hectare
M = tractor hours per hectare (not including combine harvesting
t i me)
L = man hours of labor per hectare
NCI = expenditures on fertilizer, insecticide, herbicides, and
improved seed, in pesos
Fp = dummy variable for methoct of fertilizer application,
0 = hand application, 1 = mechanical application.
A summary of the findings is given in Table 10.
In contrast to cotton, it was indicated that there should be an
increase in the use of machinery. This result could be due to the
increased water retaining capacity of the soil brought about by the
changes in soil structure, principally compaction, during pre-planting
soil preparation. This effect would be especially significant during
the dry semester when water supplies are greatly decreased. The sample
data include observations from both semesters, thus water availability
may enter as a factor affecting yields and yield variance.
The mean input of labor in the sample was somewhat above the in
dicated yield maximizing and profit maximizing levels; thus the marginal
productivities were negative. The most important cause of high labor
input was hand application of fertilizer during the growing season.
The substitution of hand application for aerial application decreases
the productivity of fertilizer, as many areas receive small amounts of
Expected Yields and Prices in
for Cotton, Rice, Sesame, and
in the Present Study
Good, Normal, and Bad
Sorghum Based on Data
E[Yg] E[YnD ECYb:
e[p : e[p :
- kilog rams
Table 6. Ordinary Credit Available per Hectare Through the
Maximum Financing per Hectare
Small Farms Medium Size
aFinanceable costs are total costs excluding rent, interest,
insurance, and administration.
Source: Caja Agraria, 1970, unpublished data.
final program varies from the basic one in the objective function.
Rather than maximizing profit, this last program maximizes net return
to owned cap tal.
Solutions to each of the programs were calculated for eight
combinations of machinery and capital input levels. These levels
ranged from unlimited quantities of both inputs to levels below the
minimum per hectare requirements for any of the four crops. The levels
of machinery (in tractor hours per hectare) are based on estimates of
the power supply that would be available if the farmer were to possess
a large or a small tractor, or combinations of the two sizes.' The
capital allowances were made in agreement with potential credit, and
high to low personal capital resources.
Another limiting resource was the labor available for cotton
harvesting. The maximum amount of labor permitted corresponds to 93
percent of the amount that would be needed if the whole farm were planted
in cotton. This restriction is based upon the sample data and repre
sents the average harvest labor input (per kilogram of cotton) from the
farms in the lowest quintile of the sample, when ranked by this measure.
It was assumed that these farms had a scarcity of labor during this
period. The average in the lowest quintile was compared to the average
in the upper four quintiles, and it was observed that the former was
approximately 93 percent of the latter. The constraint on labor was
made in consideration of the region as a whole, rather than from the
standpoint of a single farm. If cotton were to be planted on all avail
able land in the second semester, then a shortage of labor would occur
^ In the linear programming problem capital refers to the total
cost of the activity, excluding the costs associated with farm buildings.
in the study area and the crops most consistent with these different
Maximize the Probability of Realizing a Selected Income Level
The minimum necessary income level chosen for the study area was
15,000 pesos per semester. This amount is one-half of the figure
generally given as an acceptable income, and enough to support an
average family for this short period of time. Table 20 gives the
number of hectares required to earn 15,000 pesos with the indicated
probability of attainment. The expected profits in Table 20 are taken
from Table 3^ in the appendix. These profit levels are the lowest
that were considered acceptable for application in the risk model.
r ~ - '
The probabilities of realizing these profits were calculated from data
given in Table 35 by summing the probability of occurrence of each
yield-price combination that produced an acceptable profit. If pro
duction in the first semester were sufficient to yield the 30,000 pesos
which satisfies the annual minimum necessary income, then this conser
vative approach could be abandoned and some income maximizing scheme
adopted. However, if the first semester crop is poor, the program used
in the first semester would be used again.
The analysis indicates that rice, sesame, and sorghum would each
require about 20 hectares to provide 15,000 pesos per semester with
close to an 80 percent chance of success. Sorghum offers the highest
probability of attaining the necessary income level. However, if the
farm is used for rice production, the probability of success for rice
is perhaps not sufficiently lower (.78 for rice versus .83 for sorghum)
to warrant 20 hectares of sorghum on an otherwise homogeneous crop
Three recommendations are made with regard to changes in credit
policy. First, consideration should be given to the establishment
of some form of loan insurance. This type of repayment guarantee
would undoubtably lessen the reluctance on the part of commercial
banks to extend credit to unknown borrowers, and to borrowers with
little collateral. Second, the government should examine the pos
sibility of creating a credit program for farm purchase. Presently,
the government sponsored programs allocate funds for land rental, but
not for farm purchase. A program of this type would decrease the
insecurity of the present tenant farmers, and would be in accord with
the current philosophy on land redistribution. Finally, crop asso
ciations similar to the existing ones for cotton and pice should be
encouraged to establish offices and credit programs in the area.
Such national associations already exist and, with the increasing
importance of sesame and sorghum, are needed in the area.
Indicated Factor Levels
The following summary shows the factor levels which would maximize
profit for each crop:
Profit maximization for
production with present practices and
3. The allocation of resources among alternative crops.
Based upon the results of the studies of the above questions,
recommendations are made with respect to the following items:
1. Credit policy.
2. Factor levels for specific crop production.
3. Farm organization to achieve selected income goals, namely:
(a) maximizing income, (b) maximizing return to owned capital,
(c) maximizing the probability of realizing a selected income
level, and (d) minimizing losses.
Plan of Presentation
The thesis is presented in seven chapters. In Chapter II a
general discussion of the approaches and analytical techniques is
presented. In addition, the types of risk and uncertainty encountered
in the agriculture found in the study area are defined, classified, and
discussed. Methodology is established that is used later to indicate
the risk revealed by investigation and discussed with relation to the
final crop combination recommendations.
Chapter III provides a brief overview of the agriculture in the
study area, and includes a discussion of the present situation with
respect to inputs and crops, current and potential problems, and the
relevant agricultural programs in operation or proposed. In the second
part of Chapter III data collection procedures and the specific problems
presented by the conditions in the area are discussed.
Capital availability is the subject of Chapter IV, in which a
discussion of the institutional sources of credit is given. The
conditions related to the acquisition of capital from these sources
of modernization. Further, it is probable that the resources on the
firm level are generally insufficient to permit the luxury of in
efficient use. That is, if the farmer has as one of his goals the
realization of a reasonably high return to inputs, he must seek the
activities which use his capital most efficiently. Thus, at both the
government and at the firm levels there is a need for indicators of
the relative productivity of capital among its alternative uses. With
out such indicators (which is generally the existing condition) govern
ment programs of technical assistance, credit, and infrastructural
investment are formulated and administered with little knowledge of
the amount of capital available and its potential and actual produc
tivity. Allocations are made on the assumption of a capital shortage
in all activities and more or less equal returns among alternative
investments. On the firm level apparent returns to investment govern
the choice of enterprises, and actual productivity of capital and
other inputs is largely unknown.
In part, due to a lack of data obtained from or describing on-farm
conditions, planners and policy-makers in the agricultural sector must
draw upon estimates based upon information either from external sources
or experimental results. The inadequacy of this type of information
has been noted by various authors (23; 36, p. 254). Heady has been
concerned with the problem of explaining the difference between theo
retical optima and actual outputs in the United States, a concern which
is appropriate in many developing countries today. Referring to the
U.S. agricultural situation following World War II Heady argued that:
More is known about the optimum than about the
extent and cause of the gap between the existing
and the optimum. Theory provides tools which
yield, is .667, and that it will be 600, or 1.20 of a normal yield,
is .333. The expected yield in a good year (Y ) is
E[Y ] = 500 [.667 (1.1) + .33 (1.2)]
= 500 [1.13]
The probability of having a good year is .15 (i.e. S/kO). Thus, the
expected yield at the beginning of each crop period is calculated as
E[Y] = P(Yg) (E[Yg]) + P(Yn) (E[Yn]) + P(Yb) (E[Yb])
= (.15) (565) + (.65) (500) + (.20) (375)
The above procedures can be repeated for lower and higher than normal
prices. At the farm level the probability of occurrence of any price
(P ) is considered independent of yield, thus the probability of a
combination of yield and price is the product of the separate proba
bilities. However, if the farm yield is correlated with the area
yield and the area production is sufficient to affect price, then there
may be an inverse correlation between farm yield and farm price. In
this three-level (low, normal, and high) model, when price is indepen
dent of yield, there are nine possible combinations of price and yield
(i.e., of gross income) and nine corresponding probabilities of the
occurrence of each combination (Table 3).
In a continuation of the above example, let the probability of
a normal price be .75. Then, the probabilities of the various combina
tions are: a low yield with a normal price .15 (i.e., .20 x .75), a
high yield with a normal price .11 (i.e., .15 x .75), etc.
Cost of Loss
Â£ + (C)(1)
free rate of
K = owned capital, pesos
Â£ = negative profit, pesos
I = penalty interest, pesos
C = borrowed capital, pesos
the effects are spread throughout the North coast cotton region.
Distribution problems are also encountered for domestically produced
seed. Transportation between storage facilities and local seed out
lets is frequently inadequate to meet the demands during the planting
season. The short planting season, with the optimal period lying be
tween 20 July and 20 August, increases the need for an adequate dis
tribution system, and world competition necessitates that Colombia
continue to use imported varieties of cotton in order to produce a
fiber consistent with demand.
The second aspect of input uncertainty relates to the appropri
ateness of modern inputs in developing countries and has been under
discussion for some time. By and large, this discussion has concerned
itself with the problems of transferring modern technology to the
developing agricultural sectors (16; 38; 24). Due to several factors
such as climate, light, and soilsoften it has been found that rec
ommended practices and products have not given expected results, even
to the point where losses have been incurred by farmers who adopted
the recommendations. Furtherand this is usually more a matter of
degree of success rather than a success or failure situationrecom
mendations from the research organizations in the developing countries
themselves have often not yielded the increases in production indicated
by experimental results (8; 23). There are often very large differences
between the experimental yields and those realized under actual farming
conditions. A good indication of the "productivity gap" in Colombia
has been given by Lopera and Hildebrand (23); a gap which should em
phasize the large degree of uncertainty surrounding even the adoption
of inputs which have been developed and .tested within the country in
which they are to be used.
KEY TO ABBREVIATIONS
ASOCESARAsociacin de Algodoneros del Cesar.
Caja Agraria (or Caja)Caja de Crdito Agrario, Industrial y Minero.
CORAL--CorporacÂ¡on de Algodoneros del Litoral.
FEDEALGODONFederacin Nacional de Algodoneros.
FEDEARROZFederacin Nacional de Arroceros.
FFAFondo Financiero Agrario.
ICAInstituto Colombiano Agropecuario.
IDEMAInstituto Nacional del Mercadeo.
IFAInstituto de Fomento Algodonero.
INC0RA--Insti tuto Colombiano de Reforma Agraria.
All monetary figures are given in Colombian pesos; one peso =
approximately U.S. $0.05^ at the time of this study (1970-71).
indicated by the regression analysis, higher pesticide costs associated
with lowered yields.
An examination of the doses used on the sample farms revealed
that the above explanation could well be applicable in many instances.
In the case of the two most widely and often used insecticides, Toxafeno
DDT and Methyl Parathion, it was observed that over 60 percent and 75
percent, respectively, of the applications were below ICA recommended
levels. With respect to Toxafeno DDT almost two-thirds of the cases of
low dosage had application levels of only 50 percent of the recommended
level, and for Methyl Parathion the percentage was only slightly higher.
The inverse relationship between expenditures on insecticide and
crop production has a second possible explanation. The use of chemical
control not only affects the pests at which it is directed, but also
affects, and possibly to a greater extent, the parasites and predators
of the insect pests. That is to say, insecticides are very successful
in decreasing the biological or natural controls of the insect popula
tions. There is a tremendous decrease in the incidence of pest deaths
due to natural causes in areas which are under heavy or frequent insec
ticide applications. It is estimated that much of the initial control
of cotton pests could be accomplished through biological control, or
a combination of biological and chemical control at costs substantially
below present ones (7).
Several conditions or practices related to spraying cotton in the
The constant movement of predators and parasites in search of
victims and hosts increases the probability that they will be exposed
to areas in which insecticide was applied. In addition, many of the
beneficial creatures move through the upper regions of the plants
which increases their exposure to the toxic chemicals.
are lower in the developing countries partly due to
the characteristically poor communication network
for transmitting information concerning new tech
niques, research findings, weather and market con
ditions (10, pp. 251 -3)-
Sources of Risk and Uncertainty
There are several possible causes of "loss" as well as various
resources and outcomes which can be gambled in a risky situation.
It appears that three distinct aspects in the study of risk and un
certainty will be useful in clarifying and organizing the subject.
First is the identification of the sources. For present purposes
this is done by discussing three sources: inputs, prices, and yields.
These sources are by no means exhaustive, nor mutally exclusive.
However, since a principal objective of this study is to arrive at
conclusions which can be implemented into actual farm decision-making
practices, these three source areas are chosen on the basis of their
relative importance, identifiabi1ity, and measurability.
Following the identification of the risk elements one is faced
with the task of their measurement. This necessarily must be done in
part on a subjective basis, firstly due to a lack of available data,
and secondly because it is the perception of risk by the farmer which
is usually the important element in his decision-making. More objective
measures can also be introduced, but they must be used in a manner which
is consistent with the realities of the decision-making process.
Finally, based on the quantifications of the risk elements, a
risk model can be constructed. Risk models may be either of a predic
tive type or a prescriptive type. For the purposes of this study, the
CHAPTER I I
Regression, Production Functions, and Linear Programming
Positive vs. Normative Analysis
By normative we refer to the course of action which
ought to be taken...when (a) the end or objective
takes a particular form and (b) the conditions and
restraints....are of a particular form....the term
pos iti ve is used...to describe analyses which ex
plain phenomena as they exist...(14. pp. 8-9).
Production function (via regression) analysis is of the positive
Â£ ** r if
category. Once the coefficients have been estimated by means of re
gression analysis, the calculated function describes how the changes in
inputs affect output within the existing organization of production.
That is, the production function equation defines the relationships
between input and output under the particular system of production in
Similarly, the predictive aspect of the production function is
positive in nature. Using the production function one can predict the
effect on output of changes in the independent variables. Given the
specified functional relationship one can estimate what would or will
be the results if certain actions are taken. Yet, although one is
dealing with future results, the answers obtained are based upon the
assumption that the existing firm structure will not be changed. The
accuracy of the predictions depends upon the accuracy of the model
is the total investment less that portion which has been borrowed.
Maximizing this rate of return under the conditions which are generally
found in the study zone (i.e., the farmer's own funds are fixed in
amount at the beginning of the production period, and this period is
of a fixed length) also maximizes net returns to total capital invested
in the activity (6, p. 62).
Under conditions in which capital, not land, is the limiting
factor of production, maximization of the rate of return to capital is
a more logical goal. With the objective function in these terms the
programming solution indicates that the low capital using crops will
yield a rate of return between .54 and .64 over the considered range
of inputs. However, it should be noted that per hectare profits are
considerably lower than in the previous programs at all but the lowest
levels of resource use.
In maximizing the rate of return, only sesame and sorghum enter
the solutions (Table 17). Although rice was also included as a poten
tial crop, its high capital requirements excluded it in spite of high
profits per hectare. Similarly, the high capital requirements for
cotton cause the rate of return to capital to be lower than in the
case of sorghum, even though the net income per hectare is considerably
higher. The annual rates of return for rice and cotton are .40 and .47,
Comparison of Profit and Rate of Return Maximizing Solutions
With sufficient capital, farming in the study zone is unrestricted
as to which of the four crops, and in what combinations, one is able to
Thus, at harvest time farmers face monopsonistic, or at best oligop-
sonistic, situations. Prices depend greatly upon the particular con
ditions of the local market; thus, the stage is set for potentially
wide price variations. To ameliorate the effects of large price
fluctuations conditioned by variations in production, and most impor
tantly the low prices associated with "good" years, one cannot turn to
the various methods usually employed in the developed countries.
Insurance and price supports are rare. Adequate storage is often not
available and the farmers have an immediate need for money to begin
preparations for the new cropping period and to repay the loans from
the previous one. Loan periods usually correspond to the production
marketing time of the particular crop, with severe penalties for
deliquency in repayment.
In any particular selling period one encounters wide price varia
tions from one market to another. The variations usually are not as
great as annual variations within a given region. It is very difficult
to predict what the prices in a distant market may be if one can only
base his expectations on local conditions. With the inadequate commu
nications found among regions, the producers must frequently resort to
guesswork concerning outside market conditions. When selling to buyers
who function on a national scale (a good example in Colombia is PURINA
in the grain market which pays nearly 35 percent more for sorghum than
local Cesar buyers) higher prices are offset by uncertain transporta
tion costs associated with shipping relatively long distances and in
small quantity.' The earnings thus associated with the crops are often
not sufficient to compensate for the risks involved in producing them,
especially when levels of income are quite low, and farmers can hardly
afford a loss in any year.
Figure 3.Rice; Supply and Demand for Capital per Hectare
MVP per Peso
5,500 Quantity of Capital
Figure 2.--Cotton: Supply and Demand for Capital per Hectare
Table 11. Production Function and Sample Means for Sesame
To Maxi mize
Significantly different from zero at a =.05.
aSignificantly different from zero at a =.10.
INPUT USE AND PRODUCTIVITY IN THE STUDY REGION
A necessary consideration when one is estimating production
functions by means of regression analysis is the selection of the
variables. Generally, due to the large number of inputs into the pro
duction process, it is impossible to include in a computationally
feasible model all elements which affect output. Thus the matter of
combining individual inputs into input classes is encountered by the
When approaching this matter of input aggregation two elements
should be considered. First, from a practical standpoint how much
aggregation is necessary? Data collection as well as computational
problems will frequently require that there be some grouping of inputs.
The second element focuses on the criteria used to form input classes.
In these criteria the purpose and objective of the analysis, and the
nature of the inputs, should be considered.
When combined optimally, inputs that are perfect complements should
be combined as well as those which are perfect substitutes (32; 4, pp.
137-^5; 15, pp. 215~7) However, perfect complements and perfect
substitutes are encountered infrequently in farm sample data. Under
conditions where less than these perfect relationships are found,
The population had to be constructed from records of credit, technical
assistance, and sale of seed. In the case of sesame where ICA was
directly responsible for the distribution of improved seed, the lists
were probably more complete than for sorghum. The total population
for sorghum and sesame were 37 and 32 growers, respectively, and the
final sample sizes were 18 producers of sorghum (49 percent of the
estimated population) and 21 for sesame (64 percent of the estimated
population). Both crops are in an experimental stage for many of the
growers, thus out of the small populations several farms were eliminated
because they were less than 10 hectares.
LIST OF FIGURES
1. Maximizing the Probability of Realizing a
Selected Income Level 30
2. Cotton: Supply and Demand for Capital per
3. Rice: Supply and Demand for Capital per
4. Sesame: Supply and Demand for Capital per
5. Sorghum: Supply and Demand for Capital per
6. Cotton: Supply and Demand for NCI per
7. Rice: Supply and Demand for NCI per
indicate that profits and rate of return would be maximized with com
binations of sesame and sorghum. In both of the preceding risk avoid
ing models sesame and sorghum again appeared. It is interesting to
note, then, that for farmers with very limited capital resources,
rice and cotton would be neither the income maximizing nor the risk
minimizing crops. By adopting other crops (e.g., sesame or sorghum),
these farmers would be able to secure themselves against loss with a
rather high degree of confidence, and also maximize profits.
Table 7. Fondo Financiero Agrario Financing for Cotton, Rice, Sesame, and Sorghum
Costs 100% Financed
FFA Total FFA Total Portion of Costs
Costs Financed at Cost/ha. Credit/ha. Covered by
Less Than 100% Estimates Credit
Application of fertilizer
technical assistance, and
Application of fertilizer, Purchase of fertilizer,
insecticide, fungicide, insecticide, fungi-
and herbicide, cide and herbicide. 6,500
seed purchase, and
seed purchase, and
Table 28. Continued
Return over cost
cultural sector. Two methods are employed to accomplish this end.
Agricultural bonds are sold by the Caja Agraria to the commercial banks
which are compelled to purchase an amount in proportion to their assets.
The second source of money for the Caja is the difference between the
obligations to the agricultural sector and the amount actually loaned
to it by the commercial banks. This difference must be invested in
development bonds. The proceeds from both classes of bonds are then
loaned to the agricultural sector by the Caja Agraria.
As the sole recipient of funds requisitioned for agricultural
development loans, the Caja Agraria is responsible for allocating what
constitutes the government's major capital contribution, albeit indirect,
to the agricultural sector. The Caja Agraria must grant all loans
applied for by those farmers qualifying under the definitions of small
or medium farms, except for those from farmers who have proved, in
previous experience with Caja Agraria, to be unacceptable credit risks.
A comparative note
The major differences between the ordinary credit of the commercial
banks and the Caja Agraria can be traced to the objectives of each. As
stated earlier, the loans to agriculture by the commercial banks are
made as competitive investments. The aim of the Caja Agraria, however,
is to provide the loan recipients with opportunities to invest in
agricultural activities which would be unavailable otherwise. Fre
quently, these farmers would not qualify for or would find it very
difficult to obtain credit from other sources.
The average amount of credit per loan (see Table 5) is many times
greater for the commercial banks than for the Caja Agraria. This dif
ference clearly implies one of three situations: the average farm size
At the point of production or importation control can be exercised
rather effectively as there are only a few sources of the inputs. How
ever at subsequent points in the distribution system the problem of
quality supervision becomes more critical and more difficult. As
distributors at the various "break-down" points become responsible for
mixing and packaging, the opportunity for contamination, dilution, and
misrepresentation greatly increases. Thus, vigilance is necessary
during all phases of production and distribution of inputs to the
farmer, and inadequate control at any point is sufficient to prevent
the buyer from receiving the expected quality of the input.
Results of the analyses of samples taken by ICA in 1970 are given
in Table 1. These results are not encouraging when one considers that
fertilizers and pesticides are essential to the success of the major
segment of the agricultural sector in the study zone. The high pro
portion of poor quality ratings for fertilizer samples throws much
doubt on the real effects to be expected from this input. The per
centage of substandard pesticides was not as high as was the percentage
of fertilizer samples. However, it should be noted that nearly one-
half of the pesticide samples taken had not been tested. It becomes
rather obvious that the quality of inputs could be, and perhaps is
already, a serious problem for the farmer.
Prices of products and inputs
In a market where there is very limited guarantee of prices, sub
sidies, or output control, price fluctuation is a major cause of un
certainty with respect to farm income (26, pp. 52-6). Price uncertainty
manifests itself in input prices as well as in product prices.
See Heady (12, pp. 460-4) for tables on price variability in
the United States.
Linear programming is applicable in the study as a tool for de
termining optimum crop combinations and for determining the value of
limiting inputs. This method of analysis indicates which crops and
how much of each crop should be produced to achieve the income goals
of the farmer. Some of the inputs into the model are modifications
of the present levels of inputs or of the yields currently obtained.
These modifications are especially useful in the cases of sesame and
sorghum for which experience in the study area is quite limited and
the data available are from a very small sample. Data from other
similar agricultural areas are used to modify the data from the study
Evaluating Input Contribution
The basic measure of the contribution of an input to the produc
tion process in production function analysis is its marginal physical
productivity (MPP) The partial derivative of the production function
with respect to input X. (equation 2-1) is the MPP of this input.
w. HPPÂ¡ <2-')
Based on equation (2-1), the monetary value of the change can be
easily calculated. This value, the marginal value product (MVP), is
the marginal physical product .multiplied by the price of the output
(Py) > and indicates the change in income brought about by the change
in the use of input X.. Profit (net income) can be maximized by equat
ing the MVP to the input price (PvÂ¡) and this point is referred to
as the optimal level of XÂ¡. The optimal level of each input can be
obtained by the simultaneous solution of the set of equations of the
1. Alcaraz, V. H., "Problemas Entomolgicos del Algodn en Colombia."
Paper prepared for V Reunion Latinoamericana del Fitotecnica.
Instituto National de Technologia Agropecuaria, Argentina,
2. Baker, C. B., "Limited Capital as a Restraint on Agricultural
Development," in Economic Development of Agriculture. Iowa
State University Center for Agricultural and Economic Develop
ment, Ames, Iowa State University Press, 1965:118-131.
3. Banco de^la Repblica (Colombia), El Mercado Burstil. Bolsa de
Bogota, Bogota, Colombia, November, 1969.
4. Bradford, Lawrence Allen and Glenn L. Johnson, Farm Management
Analysis. New York, John Wiley and Sons,1953.
5. Caja de Crdito Agrario, Industrial y Minero, Carta Agraria, No.
244, Bogot, Colombia, November, 1970.
6. Carlson, Sune, A Study on the Pure Theory of Production. New York,
Augustus M. Kelley, 1965.
7. Dangond, Teodora Daza and Hernn Alearas Vieco, Control Supervisado
de las Plagas del Algodonero, Gi,rardot, Colombia, Federacin
Nacional de Algodoneros, Comisin Mixta Tolima Sur, October,
8. Davidson, B. R., B. R. Martin and R. G. Mauldon, "The Application
of Experimental Research to Farm Production," Journal of Farm
Economies. 49:900-907, November, 1967.
9. Dos Santos, Teatonio, "The Changing Structure of Farm Investment
in Latin America," in Latin America: Reform or Revolution,
ed. James Petras and Maurice Zeitlan, Greenwich, Fawcett
10. Gittinger, J. Price, "Planning Characteristics of Low-Income Agri
culture," in Economic Development of Tropical Agriculture,
ed. W. W. McPherson, Gainesville, University of Florida Press,
11. Grunig, James, "The Minifundio Problem in Colombia: Development
Alternatives," Inter-American Economic Affairs, 23:3-23,
or 150-day periods. Purchase procedures differ between fertilizer
and other inputs. When buying fertilizer the farmer must pay 40 per
cent of the value in cash and may obtain the remainder on credit. The
interest charges are approximately 6.6, 8.2, and 9.7 percent for 90-,
120-, and 150-day loans, respectively. The charges on loans for pesti
cides are higher; however, no initial payment is required.
The commercial suppliers of inputs perform a very limited role
in the credit programs of the study region. Because of a previous
high incidence of non-repayment of debts, there is much reluctance to
allow credit purchases. The major sources of credit purchases in the
past were the large producers and distributors, including Shell, Esso,
and Proficol (a Colombian firm). Present credit from these suppliers
is now restricted largely to previous borrowers. The terms and interest
rates were not obtained in that the credit is provided on a personal and
Conclusions Regarding Institutional Credit Supply
The consensus among policy-makers and public officials is that
the supply of credit in the study zone is adequate to achieve the major
objectives of increasing output by modernizing production techniques
and expanding crop area. The loans provided through the public agencies
are meant to supplement the personal capital of the farmer and not to
replace it. Here, however, lies a major shortcoming of the system.
Private capital is in fact being withdrawn from the agricultural sector
and borrowed funds substituted.
The publicly controlled or sponsored loan programs do not impose
any criteria of need on the part of the borrower; thus, both wealthy
and, MP = = b
. (AP) (P ) = AVP = (MP) (P ) = MVP.
AVP = MVP =r(1+Â¡) + Â¡ + 1.
The shadow prices and MVPs of capital for cotton, rice, sesame, and
sorghum are summarized in Table 24.
The derived demand functions are discontinuous step functions.
The discontinuities result from discrete quantities of capital being
used in the linear program; it is for these specified levels that the
shadow prices are given. The functions all demonstrate the expected
relationship between MVP and quantity of capital; decreasing marginal
productivity is indicated as larger amounts of the input are used.
Although the shadow prices for capita] differ slightly between
semesters, the MVP from only one of the semesters was chosen to derive
the demand curve with respect to each crop. In no case, however, would
the choice of one semester over the other affect the general outcome
of the supply and demand analysis.
At the point where total capital requirement--total cost of pro-
duction is reached, the MVP-1 is equal to the interest rate. At
higher levels of capital, when it ceases to be a scarce resource, the
MVP is not meaningful in a programming framework. The contribution of
the input beyond this point is assumed to be zero.
Demand Derived from Regression Analysis
The demand for the non-traditional cash inputs was derived for
These costs were rounded-off from-the costs calculated in the
marginal value product of each input by crop and by source of data
(i.e., sample, ICA, and Fondo Financiero Agrario). Table 13 gives the
marginal value products by inputs, crops, and data sources.
Machinery is generally over-used in cotton. Under the present
system of production in the area most farms have specialized in only
one crop per semester, thus, the errors in machinery allocation cannot
be rectified by correcting the proportions of total hours given to each
crop. Rather, it is a question of increasing or decreasing the use of
machinery in each semester on the particular crop as indicated by the
MVPs (Table 13).
Perhaps the major reason for the misuse of machinery is the lack
of knowledge of the effects of mechanization on output. In the absence
of data on machinery use, the questions of soil preparation and cultiva
tion will continue to be answered by guesswork, and trial and error.
The absence of knowledge concerning this phase of production is further
implied by the wide range of machinery recommendations and use among
the professional workers and among the farmers. The large difference
between the optimal use and recommended use with respect to sorghum
and sesame primarily stems from the lack of experience in the area with
these crops. Recommendations are generally based upon the practices
found in other regions of the country.
Generally, the MVPs for labor display the fluctuations between
negative and positive quantities that were seen with respect to machinery
(Table 13). The MVP of labor as calculated from the sample is the only
positive labor MVP among the three calculated for cotton. This result
is due to the labor shortage in the study area which does not exist in
the cotton zone from which the ICA data were derived, nor is it accounted
Risk and Crop Choice
After establishing the probabilities associated with yields and
prices, the selection of a crop or crop combination is governed, in
large part, by the farmer's income objectives. Objectives can vary
from conservative loss minimization and income stabilization programs
to the more speculative goal of profit maximization. In the following
section, four income goals and the appropriate action needed to realize
these goals are discussed. The four goals are:
1. Maximizing the probability of realizing a selected income
2. Minimizing expected losses.
3. Maximizing rate of return to owned capital.
Maximizing the probability of realizing
a selected income level
The level of income to be considered here lies somewhere between
subsistence and the level of living to which the farmer is accustomed.
The objective is to stabilize the lower limit of annual income. The
basic idea of the approach to a risk situation is to guarantee with
a high degree of probability that the farmer will earn the money
necessary to provide adequately for himself and his family. With
sufficient land the farmer may undertake two distinct programs, one,
the guarantee of minimum income, and, two, production according to
some other income goal.
Figure 1 illustrates the results of adopting the alternative of
stabilizing the lower income limit. The income level selected as the
minimum acceptable income is n In order to achieve this level of
Comparison of Profit and Rate of Return
Maximizing Solutions 91
Shadow Prices 93
Comparison of the Linear Programming and
Regression Results 96
Alternative Objective Criteria and
Resulting Crop Selection . 97
Maximize the Probability of Realizing a
Selected Income Level 98
Minimizing Expected Losses 99
Maximizing Rate of Return to Owned
Maximize Profit 101
A Further Note on the Results of the Linear
SUPPLY AND DEMAND FOR CAPITAL AND CREDIT 105
The Supply Function 105
The Demand Functions 106
Demand Derived from the Programming
Demand Derived from Regression Analysis .... 108
Relation Between Supply and Program Derived
Demand for Capital 110
Relation of Supply and Regression Derived
Demand for NCI 115
Conclusions Regarding Credit Supply and Demand . 119
CHAPTER V I I
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 122
Input Productivities 123
Adequacy and Allocation of Credit 124
Rice, Sesame, and Sorghum 127
Credit Policies 128
Indicated Factor Levels 128
Table 27. Continued
Return over cost
and are subjected to tariffs of varying magnitudes depending upon the
priority given to them. As the quantity of total imports increases,
the general level of tariffs may also be increased in an effort to
curb the real and potential trade imbalance. Unless specifically
excluded, the rise in tariffs would be evidenced in the price of
In the initial stages of development, domestic production of
modern inputs is also associated with high prices (unless perhaps the
industry is subsidized). The developing countries are often forced to
import raw materials, thus facing a situation similar to the one de
scribed above. In addition, these new industries do not enjoy the
economies of scale which may be present in the developed countries
which are producing for a large market, nor can they benefit from the
technical advancement that industry in general exhibits in the advanced
A further reason for rising prices over time is that production
and importation do not keep pace with demand. Due to the bottlenecks
encountered in the limited capacity of the sources of inputs, demand
is frequently seen to increase faster than supply. An eventual sta
bilization or even decrease in price must wait until the industries
have achieved the economies of scale associated with adequate market
size and complementary industrial development.
Weather conditions are most likely to be the major cause of yield
variability.'* Although instances of extreme weather conditions either
In the study sample which
includes yields over a three-crop period,
ticular crop (e.g., fertilizer in sesame production), and in other
cases the quantities and qualities of the input were too uniform among
farms to significantly contribute to the explanation of yield variation
(e.g., improved cottonseed).
The combination or aggregation of these non-traditional inputs
into one input group was done in an attempt to compare the productivity
of this class of inputs with other input classes. The major disadvan
tage of this aggregation is that information with respect to the indi
vidual items in the group is not given. However, for purposes of the
present study, it was considered more important that the analysis
indicate the productivity of the cash input group, and at what levels
it should be used.
The results of the analysis indicate the productivity of the NCI
input as it is used in the area. The aggregate NCI input is defined
by the components as combined in present practices, that is, by the
combination of pesticide, herbicide, fertilizer, and seed prevalent
in the region.
For each of the four crops included in the study, coefficients for
production functions were derived by means of multiple regression.
Linear programming was used to determine the combination of crops that
would maximize net returns to capital with the existing resource use
The production function chosen for each crop was selected from
several functions having alternative forms and independent variables.
In the.prelimrnary analyses, linear, quadratic, and cubic forms of the
aggregation must be somewhat arbitrary but these relationships are the
Definition and Measurement of Inputs
The three basic input classes used in the regression analysis are
machinery, labor, and non-traditional cash inputs (NCI). The machinery
variable is measured in tractor hours and sums the time spent in tractor
powered operations associated with crop production. Other types of
machinery time, for example combine harvesting, are not included in
the machinery variable. Combining is not entered as part of total
machine time as over 90 percent of the combining is done on a contract
basis and is not controlled by the individual farmer. The labor input
is measured in man hours, and is net of machinery operator time. It
was felt that including both machine time and operator time artifically
creates two variables where only one input unit exists; that is, these
two inputs are perfect complements.
The last major class of variables is termed non-traditional cash
inputs (NCI). These inputs include pesticide, herbicide, fertilizer,
and improved seed. In the final forms of the production functions in
this study the composition of the NCI variable differs among the crops
1. Cotton--ferti1izer, herbicide, and insecticide.
2. RiceFertilizer, herbicide, pesticide, and improved seed.
3. Sesameimproved seed only, denoted by S.
4. Sorghumno NCI variable is included.
The decision as to which inputs to include as regression variables was
made for each crop based upon actual use. In some cases an input was
omitted because it was not generally used in the production of the par-
(production function) and the accuracy and adequacy of the observa
tions used in the estimates of the coefficients.
Linear programming is a normative tool of analysis. Using ob
served or derived input-output coefficients and prices, the solution
obtained is that which best satisfies the objectives and constraints
of a contrived problem. The solution indicates the action which should
be taken to achieve a stated goal, and does not necessarily describe
the practices which are presently being followed in the study area.
The output indicated by linear programming is that which represents
the optimal utilization of the resources available, combined according
to the relationships specified by the coefficients. Thus, linear
programming is used to indicate a reorganization of production and
resource use in order to realize the given objective. Numerous factors
may cause this normative model to differ from actual conditions, and
the value of it lies in its use as a guide toward efficiently employ
ing resources in achieving specified ends.
A Note of Comparison
A basic difference between regression analysis and linear program
ming was discussed in the preceding section comparing positive and
normative analysis. Briefly, it should be remembered that production
function analysis, using coefficients derived by regression analysis,
can be used to solve the maximization (minimization) problem under
existing conditions, that is, under the existing organization of pro
duction. The solution given is in the context of, and in accordance
with, the actual structure of the production process. The use of
linear programming in the maximization or minimization problem permits
A third factor which creates an element of price uncertainty is
the low degree of quality control of output and the relative indiffer
ence to quality by the buyers. Grading is often done after several
farmers' crops have been combined, resulting in an averaging of the
overall quality, which is an obvious disadvantage to the producer of
high grade output. Thus, even if one were to control fairly carefully
the quality of his own production, there is no guarantee that it will
be judged consistently by buyers from one period to the next. A
companion problem in this quality-price relationship is the degree of
quality control in production, and will be discussed briefly in the
section on yield uncertainty.
Input price. Prices of inputs are generally more stable than
product prices. Certainly one does not usually face the possibility
of fluctuations in both directions. At the time of purchase and use
the prices of inputs are known. However, it is often the case in the
developing countries that the prices of modern inputs are constantly
increasing, a condition which would be most critical to growers of
long-term crops, but also important to those farmers wishing to plan
rotation patterns and crop substitutions.
In the initial stages of modernizing the agricultural sector, the
source of inputs is usually importation from foreign manufacturers.
The price is thus higher than in the country of origin due to extra
transport and marketing costs. In addition, these agricultural inputs
must compete with other classes of imports for limited foreign exchange
S-his practice is especially prevalent in the case of cotton.
There is little premium for high grade fiber in that the cotton from
different farms is combined before grade and price determinations are
Table 1. Results of ICA's Input Quality Tests in Colombia
1 i zer
aCorrect denotes that sample contained 3% of the indicated level
^Incorrect denotes that the amounts or concentrations of the rel
evant ingredients were not within the acceptable range established by
Sample was termed unacceptable for various reasons among which
were that the material was not that which was claimed to be sampled
or improper packaging rendered the sample untestable.
Product price.Large price variations occur among farms in a
geographic zone during the same semester, and from one cropping period
to another on any given farm. At the time inputs are purchased and
allocated to production, the farmer is likely to have very little basis
for estimating what the price of the output will be. Due to the general
ignorance of alternative market opportunities, relatively small scale
of production, and high transport costs, the local market or buyers of
a particular crop are the only outlets considered by most producers.
3|n the study sample which includes prices over a two-crop period,
the difference between the high and low reported prices was great.
This difference, expressed as a ratio of higher to lower price was:
cotton 1.46, rice 1.54, sesame 1.58, and sorghum 1.44.
is grown either on a year-round basis or is double-cropped, with plant
ings in April and September, and harvestings in July and December and
Sorghum and sesame are just beginning to emerge as important crops
in Cesar. The high production costs of cotton in the last two or three
years, and the high risk in growing cotton,have led many farmers to
shift from cotton, usually to sorghum, or to plant a crop in the "dead"
season, after the cotton harvest. Sesame is the primary crop used in
rotation with cotton in the interior of the country; yet its adoption
is not widespread in Cesar-Guajira. It has a low capital requirement,
high resistance to drought, ready markets, and a short growing season.
Most sorghum is sold to IDEMA in the local area. But, because of
IDEMA's low prices and stringent quality requirements, several producers
sell to PURINA in Barranqui11 a. PURINA's prices are considerably higher
(300 to 400 pesos per ton), but transportation costs absorb most of
this difference in price. However, PURINA does not impose strict
quality requirements, thus acceptance of the product is nearly always
Sesame is sold to buyers from Barranqui11a at the farm, and the
buyers pay their own transportation costs. The demand for both sorghum
and sesame is greater than the amount which can be presently supplied,
and it is likely that the importance of both crops will be increased
in the future.
Focus of the Survey
The present study focuses on commercial agriculture and is limited
3. Mechanical cotton pickers should be brought into the
operations on the experiment stations and the results care
fully compared with those from hand picking. Possibly
mechanical harvesters could be used to supplement hand labor
to enable production to be increased in the zone, and also
preserve employment for the permanent labor force in the
4. More varied and in depth experiments should be run with crops
other than cotton. These crops include, but are not limited
to, sorghum, sesame, soybeans, peanuts, and perhaps some
annual fruit crops (e.g., melons and tomatoes). This work
should emphasize the search for varieties best suited to
the area and wel1-designed, complete experiments regarding
all phases of production (e.g., machinery, seed, fertilizer,
weed control, pesticides, and harvesting techniques). An
important objective should be to find crops which would be
most successful in rotation with cotton, which would enable
cotton growers to utilize their fixed resources (e.g., land,
machinery, and permanent labor) during the entire year.
Table 18. Programmed Annual Rate of Return per Peso to Owned Capital
Resource Level Rice Included Rice Excluded of Return
Table 15. Crop Combinations for Maximizing Profit at Selected Levels
of Capital and Machinery Inputs, with Rice Included
ng Annual Profit
Annual Rate of Return
to Owned Capital
indicated by the
first symbol and
machinery by the
bC = Cotton, R= Rice, Sm = Sesame, Sg = Sorghum
1 = first semester 2 = second semester
Numbers in parentheses indicate the fraction of total land to be
planted in the specified crop.
explain the optimum scale of operations and combi
nation of resources in general. ...obviously,
there is some important and sound reasoning in the
minds of farmers for not attaining this optimum
even though it be what the most profitable farm is
doing. ...numerous forces condition the use of re
sources on farms and explain this gap. ...produc
tion economics research should probe further in ex
ploring this gap as reflected on individual farms.
Only then will attempts to bring about the most ef
ficient use of farm resources be entirely realistic.
Individual farmers can be better advised. But as
important is the fact that a base will be laid for
altering customs, institutions and programs which
condition the efficiency of farm production (13,
The last-mentioned benefit of determining the actual on-farm pro
ductivities of inputs, that of serving as a guide for large scale
changes, is primarily related to government action which would be based
upon information gathered at the farm level. With the governments of
the developing countries playing key roles in the development process,
it is imperative that they be supplied with this type of realistic
data (33, p. 133; 36, p. 254).
The major objective of this study is to calculate the productivity
of the agricultural inputs used in the study areaan area located at
the eastern end of the cotton region that stretches across most of the
Northern Coastal Zone of Colombia. Special interest is given to the
productivity of the non-traditional inputs and the variable capital
invested in selected enterprises. In light of the results of the pro
ductivity determinations three further questions are considered:
1. The adequacy and allocation of credit supply.
2. The efficiency of the input mix and levels for cotton, rice,
sesame and sorghum.
If the sesame farmer could obtain a commercial bank loan then
he could meet the total costs of production with borrowed capital
(Fig. 4). The FFA provides more than one-half of the total costs
at an interest rate of 14 percent. On the remainder of the capital,
borrowed from the commercial banking system, MVP would exceed the 24
percent interest charge.
As in the case of sesame, credit could be used to completely
finance the sorghum crop (Fig. 5). The 14 percent FFA rate and the
24 percent commercial bank rate of interest are below the .26 MVP
of capital at 2,700 pesos, the total cost of sorghum production.
Relation of Supply and Regression
Derived Demand for NCI
The step supply function is used again; however, the NCI demand
functions are continuous and based upon the MVPs from regression
analysis. Only cotton and rice are considered because NCI could not
be incorporated into the production functions of sesame and sorghum.
Approximately 1,000 pesos are available from the cotton federa
tions at 6 percent interest. This credit is extended for the purchase
of the non-traditiona1 cash inputs. This horizontal supply function
intersects the demand function at a quantity of approximately 950 pesos
of NCI; thus, this single credit source provides adequate capital for
the purchase of NCI (Fig. 6).
combination of crops would maximize profit and that double-cropping
would increase annual profits.
If one were to assume that all rice growers had no capital re
strictions (at least within the range of the costs of the four crops)
it would pay them to produce rice exclusively. However, the irrigation
requirement allows this crop pattern to be applied only to a small
portion of the land in the zone. Farmers on non-irrigated land must
look to crops other than rice as production alternatives. In the pro
gram without the rice growing activity cotton dominates the second
semester when capital and machinery are not limiting, but it is not
planted on 100 percent of the land due to the labor restriction. How
ever, once constraints are placed on capital, cotton quickly declines
in importance, and at the low levels it disappears.
Based on the MVPs from the production function analysis the in
dication is that resources other than labor should be taken out of
cotton production and used for other crops. With the exception of
machinery the MVPs of the inputs in sorghum and sesame have high
positive values. A reasonable reaction to these indicators would be
to shift these inputs out of cotton and to either diversify during
semesters, or to introduce a rotation crop in the first semester if
the farmer were opposed to abandoning cotton completely.
Alternative Objective Criteria and
Resulting Crop Selection
In the final section of Chapter II, four income objectives were
discussed. When these criteria were applied to the data from the study
area the crops which best satisfied them varied among the four alter
native objectives. The following discussion outlines the conditions
produce. Profits per hectare are the highest for rice production and
the .41 annual return to capital is competitive with most non-agricul-
tural investments. In the areas where irrigation is not feasible, for
either physical or economic reasons, cotton performs a similar role as
rice, with somewhat lower profits per hectare, but higher returns to
capital. On farms where land is the limiting input these crops would
maximize profits for the farm.
With capital rather than land as the restricting input, the max
imization of return to capital investment, not per hectare profit,
should be the primary goal. The farmer with low capital resources
maximizes profits by maximizing the rate of return to his capital. In
Table 18 the rates of return calculated for resource levels in each
program are presented and profits per hectare are summarized in Table
19. Only in the low capital levels do the profit maximizing and rate
of return maximizing solutions coincide. The most obvious points in
dicated by these results are that there is no justification for planting
cotton when capital supply is at these levels, and that there is a
definite difference among optimum cropping patterns for the different
resource situations. These differences are rarely recognized in the
present recommendations made to farmers in the study area.
The shadow price derived from linear programming is the counter
part of the marginal value product derived from production function
Even the problem of water shortage can be solved with well irri
gation. Preliminary results of an INCORA study in the area indicate
that there is sufficient ground water to irrigate much of the zone.
Cost studies, however, are still in process.
Table 31. Estimated Total Costs of Production for Cotton, Rice,
Sesame, and Sorghum, by Source, 1970
Crop Caja Agraria ICA FFA (present study)
pesos per hectare
aThe Schwartz estimates are for the study zone; the other three
sources are based on national cost calculations.
able inputs. This situation is well illustrated by the way in which
funds were allocated among the non-traditionl cash inputs. Although
there was sufficient total credit available to purchase these inputs,
an over-use of pesticides and an under-use of fertilizers were in
A second problem in credit distribution was the inaccessabi1ity
of commercial bank loans for some farmers. Discrimination against
operators of smaller farms and farmers with limited loan collateral
prevented otherwise available funds from circulating.
In spite of some distribution problems it appears that the crop
associations, commercial banks, and government supervised credit pro
grams can provide adequate credit for most operators. It is not the
purpose of the credit institutions, with the exception of commercial
banks in some cases, to provide complete financing for farmers.
Rather, the funds provided are viewed as supplements to the farmers'
own capital, and often for the purpose of encouraging the use of
The conclusions are grouped under two headings, those dealing
with cotton and those dealing with the other three crops.
After examining the various aspects of cotton production it is
obvious that there were many farmers for whom growing cotton could not
be justified from an economic standpoint. Those farmers who have in
sufficient personal capital resources and limited access to credit are
not in a position to continue with this high risk crop, especially
Sources of Short
Up to 24
Comme re i a1
than 10 has.,
use of improved
seed and tech
Comme re i a 1
than 10 has.,
use of improved
seed and tech
7 to 9
Use of improved
seed and tech
Table 30. Continued
Admi n i stration
Return over costs
Total hours 50.86 5-63
two inputs. In view of the heavy emphasis on pesticide application
there may be a mi sal location of credit between fertilizer and pesticide.
If the fertilizer response levels are in Stage I of the production
function as indicated in this study, additional financing should be
given for purchase of fertilizer rather than for pesticides. The
reallocation of credit within the present amount used to purchase
modern inputs would yield positive MVPs.
The second possible cause for the negative MVPs of NCI stems
from the Fondo Financiero's aim to increase the use of modern inputs
in Colombian agriculture. To achieve this goal the incentives to adopt
the inputs are made as enticing as possible, and a major strategy is
to provide a large measure of help for the farmer who wants to raise
his level of technology. Among the inputs and activities for crop
production, the cash inputs are invariably those financed at levels
between 70 and 100 percent of their cost by the Fondo Financiero Agrario.
In its desire to introduce and perpetuate the application of capital
inputs the FFA has possibly over-allocated its funds to these factors.
Crop Prof itabi1ity^
Based on the production functions derived from the sample data,
^Profit was calculated by subtracting costs from gross income.
All costs were included except the fixed costs of buildings and con
structions, and entrepreneurial costs. It was felt that the rent cost
included the costs of buildings and constructions. (Generally these
fixed costs are quite low on a per hectare basis.) Nearly one-half of
the farmers were short-term tenants and it was felt that the landlords
established a rent charge which would include a return to their invest
ment in constructions. Since the same rent cost was charged to owners
for purposes of land valuation in the study, it can be assumed that this
rent would also include fixed costs. Although the cost of the entrepre
neur (or decision maker) was not subtracted to calculate profit, a cost
was included for administration which covers the "in-the-field" mana
gerial costs. This charge was a standard amount per hectare.
valid in that many farmers are denied loans by the banks. However,
it is impossible to determine a priori what proportion of farmers
have access to this credit source. For the individual farm, the credit
standing of the farmer must be known in order to determine the amount
that he can borrow and the interest rate that is charged by the com
Table 17. Crop Combinations for Maximizing the Rate of Returns to Owned
Capital at Selected Levels of Capital and Machinery Inputs
Annual Rate of Return
to Owned Capital
aCapital is indicated by the first symbol and machinery by the
bC = Cotton, R = Rice, Sm = Sesame, Sg = Sorghum
1 = first semester 2 = second semester
Numbers in parentheses indicate the fraction of total land to be
planted in the specified crop.
Table 3. Probabilities of Yield-Price Combinations
- P(Y.) P(Py.)
i = 1,2,3
j = 1,2,3
and 1 = high
2 = normal
3 = low
The expected value of gross (and net) income can be determined
using the calculated probabilities of low, normal, and high yields
and prices, and the expected value of each yield and price. Using
the notation from Table 3, the following equations express the expected
income (ECnD) for a crop,
+ P2| (E[Yn:ELPyg3) + P22 (E^HeLf^) + P23 (ECYn3EEPybD)
+ P3, (E[YbJE[Py 3) + P32 (E[Yb]E[Pyn]) + P33 (ECYb:E[Pyb]).
Expected profit (EDO) would be
EDO = E[N] Cost.
Unless a separate study is made on input supply, indications of the
adequacy of supply must be obtained from subjective sources. These
sources are principally opinions and estimates of suppliers and users
of the inputs. In the present study no attempt is made to quantify
the availability of inputs. However, the problem was encountered in
the study region.
The problem of availability in the study zone was observed par
ticularly with respect to insecticides and cottonseed. For insecticides
the problem was one of timeliness of local delivery and application,
whereas for cottonseed there were delays in importation and regional
distribution. Locally, defined as the Cesar-Guajira major cotton
areas, specific insecticides were frequently difficult to obtain on
short notice and subsequently substitutes were employed. The problem
of shortages is amplified by the poor network of communications which
decreases the probability of locating the needed insecticide in time
for it to be used effectively.
There is often difficulty in contracting for spraying when needed,
when this need arises suddenly. This difficulty is partly due to the
tight schedules of the fumigation companies during the growing season,
and partly a result of pest problems occurring simultaneously on
several farms in the stricken area.
All distribution of improved cottonseed is coordinated and con
trolled by the Instituto Colombiano Agropecuario (ICA). In recent
years serious shortages have been experienced due to problems of
importation or inadequate initial purchases from foreign dealers
(principally in the United States). The importation difficulties have
generally been associated with clearing the seed through customs, and
Credit from Input Suppliers
In addition to the credit offered through the banking facilities,
the commercial sector acts as an important source of capital. The
principal agents for this type of credit are the associations of cotton
growers and of rice growers, and to an extent the merchants dealing
in agricultural inputs.
Three cotton associations operate in the study zone, the Federacin
Nacional de Algodoneros (FEDEALGODON), Corporacin de Algodoneros del
Litoral (CORAL), and the Asociacin de Algodoneros del Cesar (ASOCESAR).
Each of these associations performs several services for its members,
one of which is providing credit in the form of deferred payments for
purchased inputs. Fertilizers, pesticides, herbicides, and several
other types of inputs may be bought on credit through these organiza
tions, and payment made after the crop has been sold. The cost of the
loan is paid in the form of higher prices for the inputs when bought on
credit than for those paid for at the time of purchase. The charge is
approximately 4.6 percent for CORAL and 6.4 percent for FEDEALGODON.
It is estimated that the average member obtains 1,000 pesos of credit
per hectare per year, which is in addition to the amount received
through the banking system. In the case of FFA credit, the 2,500 pesos
allowance for a hectare of cotton would be raised to 3,500 pesos total
credit. The lower interest charges of the cotton associations, coupled
with prices which are lower than local retail prices, enable the credit
users to enjoy a cost advantage over nonmembers.
The Federacin Nacional de Arroceros (FEDEARR0Z) functions for the
rice growers in much the same way that the cotton associations serve
the cotton farmers. Credit for input purchases is offered for 90-.120-,
prescriptive model is formulated as it appears that the present system
of exploitation in the study area would benefit from changes that may
be indicated by such a model.
Input availability, appropriateness, and quality
Especially in the agriculture of developing countries risk and
uncertainty surrounding input use, and,in particular, "non-traditional11
input use, are of primary importance (34, pp. 145-6; 25, Chapter 13).
The decision to adopt new inputs (and in the sense of input into the
whole agricultural production process this includes new plants, new
varieties, different practices, etc.) must be made in view of the
risks associated with them (26, p. 47). Three areas of risk or uncer
tainty surrounding the employment of modern inputs in developing coun
tries are the availability, appropriateness, and quality of these in
The availability of inputs in agriculture is critical with respect
to the physical quantities in which they are made available as well as
the timeliness with which they are delivered (27, p. 32). The subse
quent increases in the uncertainty and risk which is associated with
a greater use of modern inputs are often ignored by advocates of mod
ernization (12, pp. 44-5). The problem of availability is difficult
to pinpoint in that deficiencies of supply and timeliness manifest
themselves in much the same way, yet the solution to each is quite
different. Both conditions are evidenced by a lack of inputs at a
critical time in the cropping season. However, the pure supply short
age is due to production or importation factors, and the problem of
timeliness of delivery is a communication and transportation problem.
The question of the measurement of availability is likewise confounded.
15 percent of their year end cash on hand to loans in the agricultural
sector, which includes crops, livestock, and fisheries. Depending
upon the investment, the period of the loan varies from one to five
years with a maximum interest rate of 9 percent. The significant
difference between these loans and FFA loans is that the private sector
(i.e., the commercial banks) makes the choice as to who receives the
loans. There is no control by any public agency. The vast majority
of Law 26 money goes to finance the livestock industry. It plays a
relatively minor role in financing short-term crop production. Table 5
indicates the percent of total credit composed of Law 26 loans, and
only a small part of the indicated contribution is to crops.
Summary of Available Bank Credit
Bank credit in Colombia is available under several different
programs. Those discussed here are the main sources of short-term
credit for crop production. For the study area in particular there
appears to be no important shortage in the lending capacity for the
agriculture of the zone. The interest rates are low when compared with
the average rate of return in crop production of 30 to 40 percent.
From the banking side this return is also acceptable. The FFA re
discounted loans pay 22.7 percent on own capital, and banks can charge
up to 24 percent for ordinary loans. Even the Law 26 interest rate of
9 percent is not very far from returns in some alternative invest
ments. In 1969 an average return on bonds was 11 percent and on stocks
on the Bogota*exchange it was 9.7 percent (3).
Based on sample data.
For use in two of the approaches to risk which will follow, the
probabilities will be those which quantify the occurrence of yields
and prices which fall short of (in bad years) or exceed (in good years)
their normal, or modal, values by some specified percentage. That is,
the frequencies are noted with which values above or below the normal
values of yield and product price are observed. These non-normal
values, grouped by percentile intervals, express the magnitudes by
which the observed values differ from the normal values. The proba
bilities of experiencing values above and below the normal value for
the activity are calculated.
In the example which follows the probability of a low and a high
yield is calculated, as well as the expected value of yield in any
a given year (Table 2). Based on these data the probability of having
a low yield is .20 (i.e., 8/40). G iven that a bad year will occur
the following probabilities can be calculated describing the magnitude
of yield loss: \
1. Probability of realizing .90 (i.e., 450/500) of a normal crop
2. Probability of realizing .80 (i.e., 400/500) is .375.
3. Probability of realizing .70 (i.e., 350/500) is .25.
4. Probability of realizing .40 (i.e., 200/500) is .125.
The expected value of yield in a bad year (Y^) is
E[Yb] = 500 C-25(.90) + .375(.80) + .25(.70) + .125(.4o)D
= 500 C.75]
Similarly, the expected yield in good years can be calculated. Given
a good year the probability that yield will be 550, or 1.10 of a normal
Bank Credit in
mi 1. pesos
Ca j a
Comme re i a 1
Sources: Superintendencia Bancaria, Fondo Financiero Agrario, and
Caja Agraria, unpublished data.
A different, yet important, conclusion implied by the profit
levels is that the ICA recommendations give rather poor results. For
cotton they yield lower profits than do present practices (sample mean),
and they are substantially below the optimum. The low profit based on
ICA recommendations in sesame may not be entirely realistic since ICA
recommends weed and insect control which do not enter into the regres
sion equation; these inputs could have considerable effect on yields.
There were inadequate data from the sampled farms to permit pesticides
to be entered as a variable.
In general, there is a wide gap separating the potential and actual
profitability of the four crops. Even under the existing cropping
systems profits could be increased.
Linear Programming Analysis
The basic program included all four crops, and employed the input-
output data obtained in the sample (see enterprise budgets given in
Tables 27 through 30 in the appendix). Two additional programs were
calculated using identical input-output coefficients, but with a varia
tion in the number of activities in one and a different objective func
tion in another. The results show the optimum crop combinations under
the present systems of production. The second program differs from
the first in that rice has been deleted as an activity. This variation
was made to conform with the conditions found in some parts of the study
area. Generally, irrigation is available for all of the land on a farm,
or for none at all. Thus, to prevent rice from entering into the solu
tion when dealing with farms without irrigation, as is the case on the
vast majority of farms, this second program was run. The third and
This dissertation was submitted to the Dean of the College of Agri
culture and to the Graduate Council, and was accepted as partial ful
fillment of the requirements for the degree of Doctor of Philosophy.
Dean, Graduate School
arbitrary. The very small units were excluded in that they were either
subsistence farms, or because they had production and institutional
characteristics peculiar to small units. Extremely large farms were
also omitted from the study in the belief that these farms did not
typify the majority of the commercial farms in the area, and most
absenteeism was encountered on units of this size. In addition,
regardless of the outcome of this study, it would be unrealistic at
this time to recommend a re-organization of farm holdings in favor of
the extremely large farms. Such a recommendation would be directly
contrary to the present policy goals being voiced by the National
Government which advocates increased land redistribution and frag
mentation. Public policy-makers would reject any program which
called for greatly increasing farm size and concentration of ownership.
The range for the sample of cotton farms was established at 25 to
500 hectares, and for all other farms the samples were limited to units
with more than 10 hectares. The latter restriction has no upper bound,
but there were no sorghum or sesame plantings of over 150 hectares.
For rice, farm size makes no significant difference in production
methods used or in yield per hectare.
Data were collected in the study zone through personal interviews
that were recorded on a prepared questionnaire. The subjects of the
For example, sorghum farms under 15 hectares and other farms
under 10 hectares are not eligible for FFA financed loans (see Chapter
IV), and, therefore,often do not employ techniques which characterize
commercial farms in the area. For FFA financed loans improved seed
and technical assistance are obligatory.
per loan is much smaller for the Caja, the average loan per land unit
is larger for the commercial banks, or both conditions exist simulta
neously. Based upon the allowable financing per hectare for the Caja
Agraria (Table 6) it can be deduced that the national average for farm
size per loan is between one and two hectares, whereas that for the
commercial banks would be more nearly between 10 and 15 hectares.
Fondo Financiero Agrario
The Fondo Financiero (FFA) was created in 1966 by the Colombian
Monetary Board to finance commercial agriculture and to regulate and
increase production of short-term (less than one year) food and indus
trial crops, encourage the increased use of modern inputs, and raise
the amount of private investment in the agricultural sector (29, p. 20)
The commercial banks and the Caja Agraria are obligated to contrib
ute to this fund based upon a percentage of their cash holdings. The
money is then used as counterpart funds to bank and Caja loans in the
proportion of 65 percent FFA to 35 percent bank or Caja participation.
The interest rate charged to the borrower for use of credit under the
FFA system is 12 to 14 percent. However, the return to the bank or
Caja Agraria on its own money is nearly 23 percent.
Because of the lack of data regarding average farm size per loan
this rough estimate has been used. The great disperity between the
values for each source of credit allows one to gain insight into the
nature of each in spite of the lack of precision of measurement.
The interest charge is 13 percent less 0.5 percent for adminis
tration costs. Thus, the banks receive 12.5 percent net interest on
the total loan. However, the participation of the bank is 35 percent
of the loan value, with the remaining 65 percent being rediscounted
through the Fondo, with a rediscount charge of 7 percent. The return
then to the bank on its contribution is nearly 23 percent. This can
be seen more clearly in the following example: Let 100 pesos be the
Table 9. Production Function and Sample Means for Cotton
(NCI)2 -0.0011a 0.0009
(NCI)3 -2.2x107a 1.8xl0~7
""Significantly different from zero at a =.01.
aSignificantly different from zero at a =.20.
Table 34. Estimated Profits3 at Various Yield and Product Price Combinations
Pesos per Hectare
R i ce
aBased on calculations from study data.
independent variables and interaction terms were tested. The selection
of the final equation for each crop was based upon the extent to which
it was believed to describe observed conditions in the area, and upon
statistical indicators of significance. The statistical criteria in-
eluded the students "t" values for individual variables, and R values
for the function as a whole.
Generally the level of significance of the regression coefficients
was a =.05 or lower. However, several variables were included in the
final production functions for which the coefficients were significant
at the a =.20 or a =.25 levels. These latter levels were considered
acceptable given the nature of the data used. The data were obtained
by interviews and were based on recall, not written records. The sizes
of the samples were small and this may have contributed to the lower
confidence levels for a number of coefficients. Also, it is believed
that these results would provide useful guidance in any future investi
gation and experimentation.
The following production function was derived for cotton:
Y = -3266.82 + 253.10 Hp 25.00 Mp2 + 23.92 L .038 L2 + 1.812 (NCI)
-.0011 (NCI)2 + .00000022 (NCI)3
Y = yield of seedcotton in kilograms per hectare
Mp = tractor hours per hectare in soil preparation (pre-planting)
L = hours of labor per hectare
NCI = value of fertilizer and insecticide per hectare, in pesos.
In Table 9 the values derived from this equation and the mean value of
each input based upon sample data are summarized.
and poor farmers are eligible for loans. Control over the use of funds
is ineffective and much of the credit is actually used in agricultural
activities other than those specified in the credit agreement, or is
invested outside of the agricultural sector altogether. This misuse
and escape of funds leads to an apparent, and sometimes real, shortage
of capital in agriculture. Attempts are made to remedy the supposed
shortage by increasing the credit supply, which, in turn, induces more
private capital to be withdrawn. These spirals of public credit (upward
spiral) and private capital (downward spiral) invested in agriculture
create a highly speculative atmosphere in the agriculture of the study
area where the farmers are largely risking borrowed money obtained at
relatively low interest rates.
On the part of government there is often a lack of physical cap
ital resources that are necessary for the implementation of programs
for agricultural development. Public investment in or support of
various agricultural activities must be limited and priorities must be
established to guide the use of available funds. A second problem
arises in the financing of "modernization" due to the demand for
foreign-produced inputs. The nearly universal lack of adequate foreign
exchange in developing countries restricts the importation of capital
inputs. Similarly, borrowing on a governmental level to support agri
cultural programs can be limited by the foreign exchange imbalance
unless provisions are made for repayment in local currency or export
Finally, foreign private investment as a source of capital to
meet investment needs in agriculture is, except for a few specialized
export crops, an unpromising basis upon which to build a program of
agricultural development. The foreign private investor is reluctant
to assume the risks and uncertainties associated with production for
the internal market which is often small, complex, and poorly organized
(31, pp. 24, 82-9). In addition, the growing negative attitudes toward
private investment which are encountered in many developing countries
are another obstacle to the entrance of capital from foreign sources.
Thus, the expansion of the supply of private investment to fill the
needs of the domestic agricultural sector is highly unlikely (9, pp.
In light of the foregoing discussion it can be inferred that there
is a strong possibility that the capital resources available for agri
cultural development will be inadequate to support the desired program
Figure 6. Cotton: Supply and Demand for NCI per Hectare
Table 27. Cotton: Estimated per Hectare Costs, Returns, and Input Use
Total Revenue: Cotton
Operations and Variable
Urea (46% N)
Methyl Parathion (48%)
production function. These corroborating findings from ICA and from
farm data imply that fertilizer is being underemployed, both in exper-
Â¡mental work and on commercial farms.
The analysis indicates that the current quantities of pesticides
being used are decreasing yields and greatly increasing costs. Pes
ticides and their applications account for approximately 20 percent of
the total costs of cotton production. In the sample of 59 farms these
costs ranged up to 2,400 pesos per hectareto more than 40 percent of
the average costs of production per hectare.
The decrease in yield associated with increases in the level of
pesticide application is difficult to understand. Two possible, and
reasonable, explanations for this phenomenon were encountered. Ento
mologists in ICA expressed the belief that the applications of insec
ticide at lower than recommended dosage could be a possible cause of
the negative relationship between pesticide expenditures and cotton
yields. Low level applications would not destroy the insect pests as
completely as desired, even though they would reduce the population.
The remaining pests would continue to destroy the crop. The two un
favorable results of this situation would be that a greater number of
applications of insecticide would be required, and that there would be
a nearly continuous destruction of plants due to the failure to destroy
the pest population. The symptoms of this condition would be those
^The average levels of fertilizer application were:
Kqs. per hectare
Lbs. per acre
Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
INPUT PRODUCTIVITY IN AGRICULTURE
ON THE NORTH COAST OF COLOMBIA
Chairman: Dr. W. W. McPherson
Major Department: Agricultural Economics
The objectives of this study were to estimate input productivities,
efficiency of input allocations, and to relate the supply of capital to
Regression analysis and linear programming were used to estimate
the marginal productivities of three classes of inputsmachinery,
labor, and non-traditional cash inputs (including fertilizer, pesti
cide, herbicide, and improved seed) in the cotton zone on the North
Coast of Colombia. Data obtained in farm interviews were used to
derive production functions for cotton, rice, sesame, and sorghum.
A survey was made of the institutional credit system in the area with
respect to the amount of credit available, lending terms, and interest
rates. Using supply and demand functions for capital funds, a range
was estimated for each crop within which financing crop production
through borrowing would be economical.
Results of the regression analysis show that the input levels in
the study zone were not optimal. In Colombian pesos, the MVPs for
machinery, labor, and cash inputs at the mean levels of use were: for
cotton, -37.7, 26.3, and -0.07; for rice, 124.5, -261.6, and -0.77;
for sesame, -140.4, 10.6, and 117.1; and for sorghum, -100.8, and
xi i i
INSTITUTIONAL SYSTEMS OF CAPITAL
AND CREDIT SUPPLY
The purpose of the work reported in this chapter is to provide
a description of the supply of credit and inputs to farmers, and to
determine the ways in which credit agencies can influence the amount
and forms of capital that the farmers use. In the study area borrowed
funds and credit purchases provide a large part of the funds used to
purchase and apply farm inputs. A discussion of the availability of
credit will serve to complement the findings concerning input produc
tivities. In a later chapter the calculated productivities of inputs
are considered in light of the potential supply of credit for financ
ing their acquisition and use.
Commercial Banks and the Caja Agraria^
The major institutional sources of short and medium term agricul
tural credit in the study area and in all of Colombia are the commer
cial banks and the Caja Agraria. The commercial banks are privately
controlled, whereas the Caja Agraria is a quasi-public entity in which
the Colombian Governmerrt is the major shareholder. By dint of this
quasi-public standing, the Caja Agraria's role is somewhat different
than that of the other banks. However, the credit extended by both the
The Caja de Crdito Agrario, Industrial, y Minero.
primarily in cattle production, the income realized from these opera
tions is much less than that received from crop production. In 1967
income in the department of Cesar was generated as follows (28, p. 6 ) :
Percent of income
The agricultural entrepreneurs of the Cesar and lower Guajira
region can be grouped into three major classes: owner-operators,
renter-operators, absentee landlords. Absenteeism is most prevalent
in cattle enterprises, although many of the larger cotton and rice
producers reside in one of the major coastal cities or even as far
from the area as BogoteT. The major consequence of the absenteeism
appears to be that much of the land in the larger holdings is under
utilized in low earning cattle production.
On the crop producing farms in the area the major portion of the
land is rented. The percentage of the land operated by owners appears
to vary appreciably among crops, but because of the incomplete listing
of farmers the true situation can only be approximated. Usually the
^Distribution of farms by tenure class is as follows:
Source of data
(FEDEALG0D0N and CORAL)
(STUDY SAMPLE and ICA)
(STUDY SAMPLE and ICA)
Figure 4.Sesame: Supply and Demand for Capital per Hectare
to production units within a specified acreage range. It was believed
that a study of Colombian agriculture should concentrate on either
commercial or subsistence agriculture due to differences in their dis
tinctive characteristics. Commercial agriculture was chosen for this
study. The deciding factors in selecting the commercial segment were:
1. The study is to be primarily on a microeconomic level
with some final discussion given to policy questions
suggested by the analysis. Studies of subsistence
agriculture must be greatly concerned with political
and social institutions, and macroeconomic aspects
must necessarily share at least an equal role with
2. It was believed that the application of any useful
findings of the study would be made faster in the
commercial segment due to the more change oriented
nature of this segment and the lesser need for insti
3. The accepted formula for the shift from traditional
to modern agriculture relies heavily on the use of
capital inputs, and the extensive use of these in
puts in the commercial sector provides an opportunity
to measure their productivity.
The choice of farm size^ to be included in the study was somewhat
^Farm size here refers to the size of the area planted to a single
crop. Thus a 200 hectare unit can consist of 100 hectares of cotton
and 100 hectares of rice with each 100 hectares counted as a farm.
income with a high probability, Xm units of land are planted in a low
risk crop or crop combination in the first semester (or in the crop
season if there is only one). The remainder of the available land
(X-Xm) can then be put into a higher risk, but higher mean earning,
crop in order to maximize profit (or other goals can be pursued, such
as maximizing return to capital). Assuming constant net returns per
unit of land, profit is a linear function of land. In Figure 1, the
two-stage combination of stabilizing an income floor and maximizing
profit, for example on X land units, is given by OAB with profits
given by nr* If one were to maximize profits on the entire X units
of land, the expected value of profits would be nmx* The difference
in expected earnings between the two activities is equal to nmx nr>
which is the expected annual or semestral cost of the security given
by the lower risk option.
Minimizing expected losses
A second possible income goal of farmers, and also a conservative
response to the risks in agriculture, is to minimize the expected value
of loss in bad years. Losses occur when the farmer fails to earn the
opportunity cost of his owned capital, and the monetary costs of the
loss consist of three components. These three components are the
alternative earnings foregone by not investing in another activity,
the amount of money actually lost, i.e., negative profits, and the
penalty interest incurred on the borrowed funds in the investment.
Foregone.alternatiye earnings.The activity in which a farmer
sustains a loss is usually only one of many available investment oppor
tunities. For simplicity the alternative investment of importance will
be that which yields the highest risk-free return. Admittedly no
profit functions were evaluated for each of the four crops at the input
levels given by ICA, the Fondo Financiero Agrario, and the mean, the
output maximizing, and the profit maximizing levels from the sample.
Table 14 gives the profits corresponding to these crops and levels of
inputs. The most striking feature of the results is that neither the
mean (actual use), ICA, nor Fondo Financiero Agrario levels approached
the potential profits at the optimum, with the exception of the Fondo
Financiero Agrario for sorghum. The heavy emphasis on cotton seems
justified when viewed from the potential profit aspect, but much less
so for profits presently being achieved.
Table 14. Profit per Hectare for Cotton, Rice, Sesame, and Sorghum
Using Calculated and Recommended Input Levels
Crop Mean Output Profit ICA FFA
For those farmers who are seeking alternatives to cotton, or who
are considering the possibility of supplementing cotton with a first
semester crop, both sesame and sorghum present encouraging indications.
Their low costs and competitive profit rates reflect characteristics
which are being sought by these farmers*
LIST OF TABLES
1. Results of ICA's Input Quality Tests in
2. Hypothetical Probabilities of Yield 26
3. Probabilities of Yield-Price Combinations 28
4. Area Planted and Production of Cotton, Rice,
Sesame, and Sorghum in Cesar 1966-1969 38
5. Sources of Short Term Agricultural Credit
in Colombia 48
6. Ordinary Credit Available per Hectare Through
the Caja Agraria 51
7. Fondo Financiero Agrario Financing for Cotton,
Rice, Sesame, and Sorghum 58
8. Bank Credit in Cesar, 1969 58
9. Production Function and Sample Means for
10. Production Function and Sample Means for
11. Production Function and Sample Means for
12. Production Function and Sample Means for
13. Marginal Value Product (MVP) of Machinery,
Labor and NCI at Three Levels of
Resource Use 81
14. Profit per Hectare for Cotton, Rice,
Sesame, and Sorghum Using Calculated
and Recommended Input Levels 84
v i i i
The amount of cotton removed from the field is related to the size of
the picking force which can decrease the length of the harvesting period
and the chances of loss due to rain damage or to the fiber falling from
A second use of labor which may also help to explain the high
marginal productivity is hand cultivation or weed control. After the
emergence of the cotton plant, herbicides are not used in weed control,
and two to four hand cultivations are the major means of weed control
during most of the growing period. These hand methods of weed control
could have a significant positive effect on yields.
The marginal returns to NCI (fertilizer and pesticide) were nega
tive at the mean level of use. A regression analysis in which fertil
izer and pesticides were entered as separate variables indicated that
this negative result was due almost entirely to pesticide use, as
cotton showed virtually no response to fertilizer at the level of ap
plication observed. The problem of low level fertilizer use in cotton
production stems, in large part, from ICA recommendations. A recent
analysis of experimental data indicated, tentatively at least, that the
quantities of fertilizer applied in ICA test-plots were producing in
Region I of the production function, and that additional amounts would
greatly increase output. In many instances the levels were even too
low to have reached the point of increasing returns and the production
surface was essentially flat over the range of observations. Similarly,
the results of the analysis of fertilizer use in the study zone showed
a very weak positive response which was, from a practical standpoint,
linear. When fertilizer was later included in the regression equation
as a cubic expression the mean level of use fell in Region I of the
for by the Fondo Financiero Agrario when estimates are made for nation
The MVPs for NCI indicated by the sample are closely related to
the amount of credit which can be obtained for the particular crop.
That is, as the percentage of production costs which can be financed by
borrowing increases, so does the relative use of these inputs. For
sesame approximately 54 percent of the costs can be obtained easily
through institutional sources. The basic amount of financing (i.e.,
from the FFA or the Caja Agraria) is 57 percent for rice, but this
does not include the credit which can be received for buying cash in
puts from the Rice Federation. The percentage for cotton is at least
64, excluding some of the minor sources of credit. It appears, then,
that the farmer is more likely to invest borrowed funds, which he can
obtain at relatively low interest rates, rather than his own capital
for which the opportunity costs are higher.
The MVPs for NCI based upon the allowances of the Fondo Financiero
Agrario are all negative. The high levels of inputs recommended (or
at least approved) by this major credit source can be explained in two
ways. First, there is constant pressure on the credit agencies from
the organized farm groups, in this case the National Cotton and Rice
Federations, to increase the amount of credit extended to their members.
Increased credit quotas for these crops can be justified only when the
production activities for which they are to be spent are shown, and
when they are justified by rising costs or changes in recommended inputs
or input levels. The most variable portion of production costs for
cotton and rice is the amount spent on fertilizer and pesticide. Thus,
the increases in credit allowances are most easily allocated to these
Table 12. Production Function and Sample Means for Sorghum
L2 6.122* 2.8135
L3 -0.040* 0.0178
(M)(L) -8.439a 5.4109
Significantly different from zero at a =.05.
aSignificantly different from zero at a =.10.
fled, or imported seed used by nearly 100 percent of the cotton growers
in the area. The original plan provided for a 10 percent sample with
each stratification represented in proportion to its percentage fre
quency in the population. Due to the fact that a number of farm
operations contained more than one crop, the final sample included
about 12 percent of all cotton farms, and consisted of a total of 59
Neither the method for drawing the sample nor the results of the
sample itself were nearly as satisfactory for the other three crops
(rice, sorghum, and sesame) as they were for cotton. The lists from
which the samples were drawn were not as complete for these crops,
nor was there so large a population from which to draw. The National
Rice Federation (FEDEARROZ) provided a list of all its members, and
records of technical assistance firms and the Caja Agraria (an entity
which provides much of the credit to the growers) were consulted to
compile a frame from which to select the sample of rice farmers to be
interviewed. Unfortunately the last two sources added little to the
first, and only a total of 44 farms were identified. The high per
centage of tenants in rice farming resulted in not being able to
locate many of the growers of the previous years. Similarly, absentee
ism contributed to the reduced number of farmers actually available
for questioning. The final size of the sample interviewed was only 17
farmers; yet this number represented 39 percent of the total number of
rice farms contained in the lists from which the sample was drawn.
Similar circumstances surrounded the sampling of the sorghum and
sesame producers. Both crops are very new to the area, consequently
there are no federations or associations which represent the growers.
The author wishes to express his appreciation to Dr. W. W.
McPherson, Chairman of the Supervisory Committee, for his help in
all phases of graduate study including this dissertation research.
Appreciation is also extended to the other members of the Committee,
Dr. F. H. Tyner, Dr. J. E. Reynolds, and Dr. I. J. Goffman.
The author is greatly indebted to Dr. P. E. Hildebrand for his
supervision and assistance during-the research period in Colombia.
A debt of gratitude is owed to Dr. Chris 0. Andrew, Dr. James L.
Driscoll, and the University of Nebraska Colombia Mission for assis
tance and support.
Appreciation is also extended to the professional personnel and
staff of the Instituto Colombiano Agropecuario, especially to Mr.
Raphael Samper A., Director, Department of Agricultural Economics, ICA.
The author is grateful to the Agricultural Economics Department
and Center for Tropical Agriculture of the University of Florida, and
to the Instituto Colombiano Agropecuario for providing financial aid
and research facilities.
The author would like to thank Miss Linda Di Duonni for patiently
typing many pages of rough draft, Mrs. Lillian Ingenlath for typing
the final copy, and Mr. T. L. Brooks for the graphics.
The author's children, Chris and Eric, must be thanked for suffer
ing their father's neglect throughout the study period. However, the
greatest debt is due the author's wife, Betsy, for cheerfully spending
are examined, and the existing institutional arrangements with respect
to capital supply and the effects of these arrangements on capital use
The analyses of data collected in the study area are presented in
Chapter V. The results of the regression, production function, and
linear programming analyses are given and discussed. The central
theme of the chapter is concerned with the comparison of capital pro
ductivity among inputs for each product and among products for each
input. The value of the results of the normative linear programming
analysis is discussed in light of existing conditions and future
In Chapter VI, the results of the supply and demand for credit
and capital are synthesized. Finally, in Chapter VII, the results
are summarized, and the major conclusions and recommendations indicated
by the study are presented.
Table 23. Gross Income, Cost, and Expected Profits per Semester for
Cotton, Rice, Sesame, and Sorghum
aGross income = N.
inflation. Coincidentally, I also was given a value of .10. This
amount represents the difference between the interest rate (14 percent)
charged for the major portion of agricultural loans and the maximum
legal rate (24 percent) that commercial banks are permitted to charge.
Using the maximum difference will bias the choice of loss minimizing
crops toward low capital consuming ones.
As seen in the T column in Table 21 sorqhum and sesame have the
smallest expected total cost of loss. If a farmer were to adopt these
crops he would greatly decrease the potential loss encountered in any
Maximizing Rate of Return to Owned Capital^^
The rate of return data for the four crops in the study area are
summarized in Table 22. Sesame is the crop indicated for those farmers
who wish to maximize return to their capital, and sorghum is the crop
for which the rate is the second highest.
The final income objective to be considered is profit maximization.
Rice is the crop which earns maximum profits, if irrigated land is
available (Table 23). On non-irrigated land first semester sorghum
and second semester cotton would be the profit maximizing combination.
A Further Note on the Results
of the Linear Programs
For low levels of capital availability the programming solutions
of credit available
is the difference between total cost and the amount
from FFA and cotton association credit sources.
Figure 1.Maximizing the Probability of Realizing
a Selected Income Level
Crop Combinations to Achieve Selected
Income Goals 129
Suggestions for Further Investigation 130
LITERATURE CITED 147
BIOGRAPHICAL SKETCH 150
loams, which are for the most part well to moderately drained. Gen
erally, the soil pH ranges from 6.5 to 8.0, although there are some
areas with high alkalinity where salinity is encountered (19). Annual
rainfall varies rather widely within the region, from an average high
of 1290.0 mm in the south, to an average low of 782 mm in the north
eastern corner of the study area. There is a wet-dry seasonal pre
cipitation pattern throughout the region. There is an eight-to nine-
months season, from April to December, that is predominantly a rainy
period. April and October are the two riionths of highest rainfall.
There is a short dry period in June and July, which permits the har
vesting of first semester crops. The period from the second half of
December to the middle of March constitutes the dry season, during
which average monthly precipitation is less than 10.0 mm.'
The cotton zone of Cesar and lower Guajira is highly mechanized
and modern agricultural inputs are used extensively. These inputs
include improved or certified seeds, chemical fertilizers, pesticides,
and herbicides. Most of the area is devoted to commercial agriculture,
and the important cropscotton, rice, sorghum, and sesameare grown
on medium-to large-size farms. Of the more than 1.5 million hectares
of farmland in Cesar, only 7.2 percent is operated in units of less
than 30 hectares (30, p. 10). Although many of the largest farms are
Precipitation data were taken from records provided by various
agencies, including INC0RA and IFA.
Average size by crop is as follows: (a) cotton 120 has.
(FEDEALG0D0N and CORAL); (b) rice 40 has. (FEDEARROZ); (c) sorghum
40 has. (ICA); (d) sesame 30 has. (ICA).
Table 25. MVP of Non-Traditional Cash Inputs for Cotton
Input Level MVP-1
Table 26. MVP of Non-Traditional Cash Inputs for Rice
Input Level MVP-1
Table 2. Hypothetical Probabilities of Yield
Normal or modal (Y )
Low or below normal:
High or above normal:
Total or mean
on some farms. By restricting the portion of the area planted in cot
ton it was felt that a more realistic situation could be programmed.
The Basic Program
The objective function of the basic program was to maximize
profit. Estimates of profits per hectare for cotton, rice, sesame,
and sorghum are as follows:
Crop and semester
R i ce
The following are the per hectare machinery and capital levels used in
thousands of pesos
The solutions are given in Table
15. The numbers
following the crop
symbols indicate the proportion of the total farm which should be
planted in the particular crop. The net profit per hectare per year
for the crop combination is given.
With unlimited capital resources rice planted on the total farm
would maximize profits. However, due to its high capital requirements,
this proportion quickly decreases as capital restrictions are imposed.
Sorghum's low cost and moderate profit allow it to occupy the area with
drawn from rice production, but with the decrease in area devoted to
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interviews were the farm owners, tenants, and farm administrators with
at least five years experience on the present farm. The five-year
minimum was imposed on the assumption that data given by memory recall
often represent averages over a period of years, or quantities which
represent norms. If the administrator had worked for different employers
on various farms there would be a strong likelihood that his response
would be a blending of these recent experiences on several farms.
The basic purpose of the questionnaire was to obtain detailed
production data which included all operations from pre-planting soil
preparation to marketing the final output. These data were obtained
on an individual crop basis for all crops that the farmer had grown
during the two semesters prior to the interview. This cross sectional
information was used in the regression and linear programming models.
A final section of the questionnaire was designed to obtain time
series data on crop yields and prices over the last 10 years. The
farmers were asked to compare past harvests and prices to what was
considered normal yields and prices. From this information, frequency
distributions were calculated for output and prices, and probabilities
were assigned for the occurrence of each particular value.
The sampling technique used for selecting cotton farms was a
stratified random sample. The stratification was made on farm location
and there were four size groupings represented25 to 50, 51 to 100,
101 to 200, and 201 to 500 hectares. The frame used for sampling was
the list of cotton producers from the Instituto Colombiano AgropecurarÂ¡o
(ICA). These records provided a very acceptable listing as ICA must
approve any farmer before he is allowed to purchase the improved, certi-
Table 7. Continued
Costs 100% Financed
Costs Financed at
Less Than 100%
Portion of Costs
Application of fertilizer
purchase of fertilizer,
seed and insecticide,
technical assistance, and
Source: Fondo Financiero Agrario, 1970, unpublished data.
It is indicated by the regression analysis that there is an over
use of machinery in soil preparation. The average use is above the
maximization level, thus the farmers are actually lowering yields, as
well as incurring unnecessary expenses. Two possible causes of the
negative effect of machinery have been hypothesized. The first is that
excess preparation is harmful to the soil structure, and with its dete
rioration yields are adversely affected. Deterioration of the struc
ture is usually in the form of compaction which disrupts normal drain
age, airflow, and root growth. The second possibility relates to the
techniques of performing the various preparatory operations. It has
been observed that in the course of pre-planting preparation the natural
drainage of the fields is often interrupted by the irregular surface
which is created.' When the rainy period resumes, large pools of
standing water collect and cause serious damage to (sometimes killing)
the cotton plants.
Average use of labor in the area is well below the indicated
maximizing level. This may reflect the fact that during the two months
of the cotton harvest there is a shortage of labor in Cesar. It has
been estimated that up to 20 percent of the cotton produced in the area
is not harvested due to this shortage. This figure is probably an
exaggeration of the problem.
The labor variable used in the cotton production function includes
harvest labor. It was felt that the quantity bf labor used during
harvesting had an important effect on the realized yield of the product.
^This possibility was suggested by a member of the Agricultural
Engineering section of the University of Nebraska1s Colombia Mission
who is conducting research on farm machinery use in the study area.
FFA (Table 7), but there is no predetermined maximum on the total
amount of credit that may be extended to any one farm.^
Credit from the FFA is available in only 16 geographic regions of
Colombia, in two of which (Cesar and the Lower Guajira) lies the study
zone. The cotton zone in these two regions characterizes precisely
the conditions in which the FFA was designed to work. Here the FFA
plays a much more important role than in the country as a whole, as
is illustrated in Table 8. Credit from ordinary bank loans and through
FFA replace that extended elsewhere under the Caja Agraria ordinary
Interestingly, in a country presumed to be short of agricultural
capital, the money programmed under the FFA is not completely utilized:
Loans granted as percentage
of loan money allocated to
It is generally believed that the quantity of credit being offered via
the FFA, for the purposes intended, is sufficient, and for some crops
an over-supply exists due to the restrictions which disqualify a large
number of farmers for FFA credit (29).
Law 26 of 1959
Law 26 states that commercial banks must commit the equivalent of
"For the Caja Agraria there is a 300,000 peso maximum, but this
is a Caja Agraria, not a FFA, regulation.
32. Probabilities of the Occurrence of Good,
Normal and Bad Yields and Prices for Cotton,
Rice, Sesame and Sorghum in the Study Zone .... 142
33. Expected Yields and Prices in Good, Normal,
and Bad Years for Cotton, Rice, Sesame, and
Sorghum Based on Data Collected in the Present
34. Estimated Profits at Various Yield and Product
Price Combinations 144
35. Probabilities of the Occurrence of Combinations
of Good, Normal, and Bad Yields and Prices
for Cotton, Rice, Sesame, and Sorghum 145
36. Linear Programming Matrix for Profit Maximiza
tion Solution, Rice Included 146
Input levels per hectare
levels were calculated
from sample data.
For sesame and
sorghum the sample did not provide sufficient information for making
estimates of total NCI use. For sesame only the seed component of NCI
is used and for sorghum the NCI coefficient could not be estimated
from available data. The tractor hours for cotton are for soil pre
paration operations only. The levels of inputs given above would
maximize profit under the existing production techniques. There
remains the question of determining the levels of the component inputs
of the class, especially with respect to cotton. However, if the
operations are well planned, these levels can in large part be deter
mined. Certainly expenditures on herbicides, fertilizers, and seed
can be closely estimated, and barring unusual conditions so can the
costs of pest control.
Crop Combinations to Achieve Selected Income Goals
Not all farmers have identical income goals. The following
summary presents four of the many alternative income objectives that
any farmer might have, and indicates the enterprise combination which
would enable him to best achieve each objective:
Due to data restrictions crop possibilities considered here
limited to cotton, rice, sesame, and sorghum.
SUPPLY AND DEMAND FOR CAPITAL AND CREDIT1
One important question facing the developing countries concerns
financing modernization or commercialization in agriculture. In this
chapter the supply of capital from institutional credit sources and
the demand for capital for use on farms in the study zone are examined.
Demand is considered both as a demand for capital to finance total
production costs, and to finance the cost of the non-traditional cash
inputs. Demand for total capital is derived from the linear programming
solutions, and the demand for NCI capital is derived from the results
of the regression analysis.
After considering the supply and demand relationships a brief
discussion of the adequacy of capital supply in the study area is
The Supply Function
The supply function for credit is a step function reflecting the
amounts of credit which are available at various rates of interest.
The three sources of credit included are the FFA, commercial banks, and
crop associations. In the case of the commercial banks the assumption
was made that the maximum interest rate is charged on all loans. The
The discussion that follows is based on revenues and costs per
one to introduce coefficients derived from various sources, which
gives a greater degree of flexibility to this phase of the analysis.
In linear programming the input-output coefficients are inputs
into the model. That is to say, they are postulated by the investi
gator according to the purposes of the study. This enables one to
choose among several sources of data for the programming coefficients
(e.g., those derived by regression analysis of experimental and actual
farm data, those provided by technicians, or those derived from any
combination of these sources), and permits programming to deal with
techniques, inputs, and products that may differ from actual farm
experiencean important advantage over production function analysis
when dealing with questions of change. In production function and
regression analysis, however, these coefficients are determined by
the data. They describe the input-output relationships in the study
population. This aspect of the two methods of analysis is closely
related to their positive and normative characteristics.
Applications in This Study
Both production function and linear programming procedures are
appropriate for use in this study. Because of the lack of information
with respect to present production methods, regression analysis is
used to determine input-output relationships under existing farming
conditions. Further, the production functions derived are used to
evaluate the productivities of the inputs and to estimate the effects
of changes in input levels. Based on the results of regression analysis,
production functions are used to make comparisons of the productivity
of different inputs with respect to one crop and among several alter
Table 19. Programmed Annual Profits per Hectare
Resource Level Rice Included Rice Excluded of Return
Quantitative expression of the use, and effects of using, inap
propriate inputs would be a very difficult task. Examples, however,
were seen in the study area, especially with regard to recommended
seed varieties of sorghum and sesame. The sorghum variety which was
recommended by ICA for the area was ICA-PAL which was developed by ICA
at their experiment station in Palmira in the Cauca Valley. This
variety did not prove to be well suited to the Cesar-Guajira zone.
The lower one-quarter to one-third of the head of the plant remained
surrounded by vegetation, and during the final months of growth and
ripening, rain water trapped in this bowl around the grain, causing it
to rot, resulting in a loss of 25 to 33 percent of the crop.
In the case of sesame several of the recommended varieties were
found to be highly susceptible to a disease which was difficult or
impossible to control. Until new resistant varieties were introduced
the chances of yield losses due to diseases were extremely high.
The final aspect of input risk and uncertainty to be discussed is
with respect to the quality of inputs. This question arises partly
from a lack of initial control over production and importation, and
partly from problems occurring in distribution and application. The
implication of low quality inputs are obvious and need not be discussed.
Clearly if the users of the inputs cannot have confidence in the product
being used, the uncertainty of the outcome resulting from its use is
increased. By sampling and testing the inputs in the various stages
of the production-distribution process this phase of input uncertainty
can be measured and presented in a quantitative expression of risk.
The ability to detect and control quality deficiencies decreases
as the input approaches the stage of actual application (18, pp. 17~20).
amount of credit per hectare which can be obtained from the FFA and
the crop associations is limited. The maximum that can be borrowed
from the FFA is established by law and varies among crops. The limits
on loans from the crop associations are taken from estimates of the
amount frequently borrowed by members. As this credit can be applied
only to NCI the quantity required does have this approximate limit.
The Demand Functions
Demand functions were derived for total capital used in the pro
duction process, and for the non-traditional cash inputs. The first
function is by crop and is based upon data taken from the linear pro
gramming solutions. The second function is also by crop, but only for
cotton and rice, and is derived from the regression analysis. In both
cases demand is considered to be a function of the MVP of the respective
input. In order to scale the MVP to the equivalent of the interest
rate, the quantity MVP-1 is used to derive the demand function. The
total cost of capital is equal to 1+i; however, the net cost of capital
is equal to the interest rate (i). The equilibrium point between
supply and demand for capital is where MVP=l+i, or, in terms of interest
rate alone, where MVP-1=i.
Demand Derived from the Programming Solutions
The MVP of an input can be approximated by using the shadow prices
in the programming solution. The shadow prices given represent the
addition to profit that would be gained by using an additional unit
of capital, that is, one peso. The shadow prices were calculated using
capital input coefficients and a profit function which includes interest
Two sources of credit can be used to obtain the necessary funds
for the NCI in rice. These sources are 1,500 pesos at 9 percent in
terest from FEDEARROZ, and 2,950 pesos at 14 percent interest from
FFA (Fig. 7).
Conclusions Regarding Credit Supply and Demand
In light of the foregoing results it can be judged that the
institutional credit system is adequate for present needs of farmers
in the area. This conclusion is particularly true in the case of the
non-traditional cash inputs for the two major crops in the region--
cotton and rice. At least the major portion of total required capital
is available for each crop at interest rates that are less than its
MVP, and for sorghum and sesame total financing may be justified.
Three points should be kept in mind when considering these
results. First, although 24 percent is the maximum legal interest
rate on commercial bank loans, in many cases the rate actually charged
may be less. Additional funds would be available if these rates fell
below the MVP of capital at the given level of use. Second, the
regulations of the FFA state that the credit available under this
program is net of credit obtained from other sources. Thus, if
strictly enforced, this rule would decrease the funds from FFA when
additional sources of credit are used. However, from a practical
standpoint the regulation may be ignored for the present, as it is not
enforced in the study region. Finally, the above discussion assumes
that any farmer can obtain commercial bank credit if he is willing to
pay the 24 percent interest rate. This .assumption is not completely
for each input,
yield the optimal
MVP = P .
MVPx2 = Px2
Thus the simultaneous solution of equation (2-2)
levels of the XÂ¡ through Xn inputs.
Linear programming does not allow for the estimation of the mar
ginal value of an input while all other inputs are held constant.
Rather, the shadow prices which are given by the program indicate the
increase in profit (when the objective function is a profit function)
if the supply of the scarce resource is increased by one unit. A
scarce resource is one for which the supply has been completely ex
hausted in the program solution. The shadow price represents the
monetary value of the increase in output using the additional unit of
the scarce input in combination with the corresponding quantities of
the other inputs.
Risk and Uncertainty
The distinction between risk and uncertainty is that the former
can be quantified in terms of probabilities. The probabilities of
outcomes or occurrences in a risk situation are measurable; whereas,
in the case of uncertainty they cannot be meaningfully measured (20,
pp. 19-21, 197-233). When outcomes can be expressed in terms of prob
abilities, decision makers then may be able to compensate or allow
Al.3, respectively. Data were not available for cash inputs for
sorghum. Thus for cotton, machinery was used excessively, additional
labor inputs would have been profitable, and for the aggregate of non-
traditional cash inputs the mean level was very near the optimum. For
rice, machinery was under-used while the labor input exceeded the opti
mum level and non-trad itiona1 cash inputs were very near the optimum
level. For sesame, machinery was used excessively, while the inputs
of labor were below the optimum level, and non-traditional cash inputs
were near optimum level. In sorghum production, machinery was used
excessively, while the labor input was below the optimum level.
Input prices in Colombian pesos were: machinery, 44.00 per hour;
labor, 3.75 per hour; and cash inputs, 1.08 per peso.
Optimum cropping systems were developed for four different income
objectives, with risk taken into account.
Results of this study indicate that there are sufficient credit
resources in the area to provide financing for a high percentage of
production costs. The major problem with respect to credit is its
inaccessabi 1ity to some types of farmers. However, through the fa
cilities of government initiated programs and the crop associations,
nearly all farmers can borrow at least 50 percent of their production
hectares in crops in Cesar in 1969 nearly 60 thousand were planted in
crops not found in significant quantities in the study area. Thus,
instead of the 56.4 percent of cultivated land in the study area being
used to produce the four major crops, at least 82 percent is planted
in cotton, rice, sorghum, and sesame.
Cotton is the principal crop of the region, and the area is the
single most important cotton zone in Colombia. Cotton is planted in
July and August and harvested in December to February. Modern tech
nology is used in production. Farm operations are highly mechanized,
with the exception of harvesting. Until the 1970-71 harvest, picking
was done entirely by hand. For the 1970-71 harvest a few mechanical
pickers were imported (one was used in the study zone), but results
of this trial are not yet available.
All cotton is ginned in the immediate area, and sold through the
various cotton federations in the area at prices which are controlled
by IDEMA. Until the 1968-69 crop, costs of production were the lowest
in the country. However, due to the rapid rise of insect populations
the pest control costs have nearly doubled, thus destroying much of
the advantage that cotton producers in this area enjoyed.
In the absence of well irrigation, paddy rice growing is limited
to those areas which have access to a continuous supply of surface
water. Rice is the most mechanized crop in the region, and even much
of the fertilizer is applied by airplanes rattier than by the hand
methods used in much of the rest of the country. The product is sold
locally, principally to mills in Valledupar. On the larger farms, rice
6These federations are: FEDEALG0D0N, CORAL, and ASOCESAR.
loans are not designated prior to the lending period, which means that
all ordinary credit from the commercial banks is awarded by evaluating
each loan with respect to the other opportunities which are available
at the time.
The quantity of credit received under the ordinary credit program
of the Caja Agraria represents over 70 percent of the total value of
institutional loans in agriculture. The population served by this
type of loan is comprised of farmers with small-(total capital value
of less than 300,000 pesos) and mediurn-(cap tal value between 300,000
and 1.5 million pesos) sized farms. The maximum amount of credit per
hectare is fixed, as is the overall maximum per semester which can be
given to any one farmer. The maximum amount per hectare is based
upon the calculated variable costs for the particular crop (Table 6),
and the allowable financing is set at 90 percent of these costs for
small farms and at 70 percent for medium farms.
In addition to funds derived from its regular banking practices,
the Caja Agraria receives money from contributions required by law,
from the commercial banks for use in financing agricultural development.
Basically, these regulations stipulate that a certain percentage of the
several classes of funds which are controlled by commercial banks (e.g.,
savings, cash on hand, etc.) must be invested, via loans, in the agri-
100,000 pesos is the maximum loan which is not earmarked for
specific purposes. In addition, the farmer is eligible for 100,000
pesos to be spent on improved seed, and 100,000 pesos worth of inputs
purchased directly from the Caja Agraria (i.e., credit in kind).
Table 29. Continued
Return over costs
Table 30. Sorghum: Estimated per Hectare Costs, Returns, and Input Use
Total Revenue: Sorghum
Operations and Variable
Fert 1 1 i zer
App11 cat 1 on
Appl1 cat 1 on
Cult!vat 1 on
Table 29. Sesame: Estimated per Hectare Costs, Returns, and Input Use
Total Revenue: Sesame
Operations and Variable
Methyl Pa rath ion
Cutting & piling
the area contribute to the high cost and decreased yields which are
explained by the reasons given above (1, pp. 173-9):
1. Insecticide application is frequently ordered by the
agronomist giving technical assistance before the in
sect population is sufficiently great to actually
cause significant plant damage.
2. Often whole farms or crop areas are sprayed when the
infestation is in fact localized.
3. Attention is not given to optimal times for spraying,
thus it is much less effective than could be expected.
Spraying is done during the day when many pests have
migrated to the lower sections of the plant, and,
hence, escape much of the insecticide applied. Most
spraying should be done during the morning and late
afternoon feeding periods.
4. The wrong chemicals are prescribed, or the prescribed
ones are not available.
5. Attempts are made to destroy the insects after they
have reached stages in their life cycles in which
they are little affected by the pesticides.
6. Highly toxic, broad spectrum insecticides are used
when less toxic, more specific ones would work as
well with less damage to the beneficial fauna in
R i ce
The following production function for rice was estimated:
Table 5. Extended
Portion of Total
Size per Loan
per Loan, I969
Up to one
Up to 5 years
Excluding coffee and livestock.
Source: Superintendencia Bancaria, Fondo Financiero Agrario,
and Caja Agraria, unpublished data.
cotton and rice using the MVPs from the production functions. These
functions are continuous and negatively sloping. Both the demand
function for cotton and that for rice are essentially linear in the
relevant range of input quantity indicating that the MVP's are decreas
ing at a nearly constant rate.
A summary of the MVPs is given in Tables 25 and 26.
Relation Between Supply and Program
Derived Demand for Capital
The demand and supply functions relate the MVP of capital to its
supply prices, that is to the interest rate in relation to quantity.
The quantity at which the MVP curve intersects the supply curve is the
profit maximizing level of input use. However, in the present case
both of these functions are step functions, and a unique equilibrium
point may not be indicated. Yet, for each crop, with the exception of
rice, the question regarding an equilibrium level of capital is answered.
For cotton, there is a level of capital for which it is clearly in
dicated that the price (i) is greater than the MVP. Using this simple,
and perhaps somewhat naive, decision criterion borrowing should not
take place beyond this level. In the case of both sesame and sorghum
the MVP remains greater than the price of capital throughout the rele
vant range of capital use. Thus, although supply and demand analysis
does not determine an equilibrium point, it solves the problem as to
the level of capital use by showing that financing 100 percent of the
production costs through borrowing is economically justifiable.
For rice the supply and demand analysis, as used with cotton,
sesame, and sorghum, does not provide a clearcut answer concerning the
use of borrowed capital. There is no overlap between the supply and
demand functions, and the equilibrium level for borrowed capital is
indeterminate given the derived curves. From a practical viewpoint,
however, the probability of having one's entire rice crop financed
through loans is quite small. The portion of total costs falling
within the indeterminate range in question would most likely come from
owned capital. The amount represents only 20 percent of the total
capital input into the rice crop.
The financing of cotton production should probably not be done
from borrowed funds exclusively. Given the sources of credit available
to the cotton grower only 3,500 psos should be borrowed under the
existing institutional framework. The return to capital at a level
greater than 3,500 pesos is less than the 24 percent interest charge
on commercial bank loans (Fig. 2). Therefore, the difference between
the 5,500 peso cost of production and this 3,500 pesos must come from
owned capital. The sources of the 3,500 pesos are FEDEALG0D0N1,000
pesos at 6 percent interest, and FFA2,500 pesos at 14 percent interest.
R i ce
Analysis of the capita] supply and demand functions indicates that
the farmer could profitably borrow at least 4,900 pesos (FEDEARROZ
1,500 pesos at 9 percent, and FFA--3,400 pesos at 14 percent). The
discontinuity in the demand function from 4,900 to 6,200 pesos prevents
one from determining the point in this 1,300 peso range at which borrow
ing from commercial banks at 24 percent interest would be profitable
(Fig. 3). If the MVP falls below .24 before 6,200 pesos are invested,
then some of the production costs would have to be met by using owned
Negative profit 32
Penalty interest 32
Maximizing rate of return to owned
Maximizing total profit 33
CHAPTER I I I
CHARACTERISTICS OF THE GEOGRAPHIC REGION, AND THE
SAMPLE SURVEY 34
The Region 34
Physical Characteristics 34
Agricultural Patterns 35
Sample Survey 40
Focus of the Survey 40
Sampling Method 43
INSTITUTIONAL SYSTEMS OF CAPITAL AND CREDIT SUPPLY ... 46
Commercial Banks and the Caja Agraria 46
Ordinary Credit 47
Commercial banks 47
Caja Agraria 50
A comparative note 52
Fondo Financiero Agrario 53
Law 26 of 1959 55
Summary of Available Bank Credit 59
Credit from Input Suppliers 60
Conclusions Regarding Institutional Credit Supply 61
INPUT USE AND PRODUCTIVITY IN THE STUDY REGION 63
Input Characteristics 63
Input Aggregation 63
Definition and Measurement of Inputs 64
Regression Analysis 65
Cotton '. 66
Input Productivities 78
Crop Profitability 83
Linear Programming Analysis 85
The Basic Program 87
Solutions Without a Rice Activity 89
Maximizing Returns to Owned Capital 89
commercial banks and the Caja is acquired from private funds, and the
government does not contribute funds directly to either's regular
In many ways, the channeling of capital through these major credit
sources is very similar; thus they are discussed on a parallel basis,
noting the relevant differences. A summary of the characteristics of
the various types of loans available is given in Table 5.
The ordinary credit offered by the commercial banks and the Caja
Agraria is distinguished from the other two types of bank credit by
the lack of specific requirements with which the borrower must comply.
Ordinary credit is given at the discretion and under the control of
the lending agent. This source of credit is the most important supply
of agricultural credit in Colombia and in the study area. For the
country as a whole, ordinary credit accounts for about 75 percent of
all agricultural credit (through formal or institutional channels),
and for more than 50 percent in the study area.
The ordinary credit given by the commercial banking system repre
sents approximately 10 percent of the institutional credit for the
agricultural sector. The terms of repayment and the required security
for the loan are determined by the individual banks. Interest rates
are controlled by the government to the extent that a 2 percent per
month (24 percent per year) maximum is imposed. As private investment
ventures the ordinary loans of the commercial banks must compete with
alternative loan opportunities with respect to risk and return. These
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
W. W. McPherson, Chairman
- Graduate Research Professor of
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Associate Professor of Agricultural
Economics and Assistant Dean,
College of Agriculture
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.
aj n. iyner, jr
Associate Professorof Agricultural
Table 35. Probabilities of the Occurrence of Combinations3 of Good, Normal, and Bad Yields
and Prices for Cotton, Rice, Sesame, and Sorghum
Cotton Ri ce
P[Y] assumed independent of P dPyll; g = good, n = normal, and b
The allocation of capital within the agricultural sector of a
developing nation is, or should be, of primary concern to those who
are formulating or implementing development policy. The critical
nature of the use of capital is in large part created by its shortage
as an input in the development process, and by the widespread demand
and need for capital inputs to escape from what is now commonly called
"traditional" agriculture (2, p. 18).
A scarcity of capital may present barriers at various levels of
potential investment (37, PP- 83-6). At one level is the shortage of
investment capability on the part of a large portion of the agricul
tural entrepreneurs. This shortage is aggravated by the reluctance to
commit substantial portions of available capital to agricultural activ
ities (17, p. 2; 11, p. 42; 22, p. 999; 34, p. 7) and the inefficient
use of resources employed in agriculture, which reduces the "effective"
capital in this sector. That is, while the quantity of capital invested
in agriculture may be at one level, its productive effect may be at a
lower level which creates an apparent shortage as an excessive amount
of capital inputs is required to achieve a given level of output.
There is also the question of intersectoral allocation of capital
which must be considered by planners. However, this subject is not
and Input Use
r i ce
Urea (46% N)
The coefficients, means and derived values for sesame are summarized
in Table 11.
The experience with sesame in the study area is very limited.
Most of the farmers interviewed had grown this crop for only one or
two years and they were still in an exploratory stage in which they
were looking for the best combination and levels of inputs. The re
gression analysis is based on present practices, and it should be kept
in mind that the current production practices may be changed as addi
tional experience is gained. Fertilizer, herbicides, and insecticides
were not usually applied, and very low levels were used in the few
cases in which they were applied. Within the existing system of pro
duction only the machine input varied greatly from the optimal level
of use. The maximizing level that was estimated for seed indicates a
high return to improved seed varieties. There were seven varieties of
seed found in the sample of 21 observations. However, the quantity of
seed in kilograms per hectare was quite uniform among farms. The
implication with respect to seed is that the higher cost seed (imported
or domestic) produces higher yields than the ordinary domestic seed.
The following production function was selected for sorghum:
Y = 1141.82 + 1475.55M 106.34m2 231.05L
+ 6.12L2 0.040L3 8.44(M)(L)
Y = yield in kilograms per hectare
M = tractor hours per hectare
L = man hours per hectare
Table 4. Area Planted and Production of Cotton, Rice, Sesame, and
Sorghum in Cesar 1966-1969
Percent of Colombia
Percent of Colombia
1 ,000 Tons
Percent of Colombia
Percent of Colombia
Source: Caja Agraria
. Carta Aq
244, Nov. 1970,
costs. To express the shadow prices, or marginal rates of return,
as the MVP of capital the following transformation was made.
R = revenue
C = total production cost exclusive of interest (that is, all
inputs expressed in terms of an aggregate capital input)
i = interest rate
SP = r = shadow price or net rate of return,
R C(l+i) = SP = r (6-0
Equation (6-1) expresses the rate of return to capital with
interest costs included, as calculated in the linear programming solu
tion. By simplifying and combining terms (Equations 6-2 through 6-4)
AVP can be expressed in terms of the shadow price, or rate of return.
This value for AVP does not have interest costs included.
R_ 1 = r (6-2)
R_ = r + 1 (6-3)
R = AVP = (r+1) (1 + 0 = r( 1 + 0 + i + 1 (6-4)
In a linear production function which passes through the origin
the MVP = AVP of an input.
Let Y = bX
thus, AP = Y = b
In this case, shadow price may be considered as a net rate of
return- in that it represents the increase in profita net value per
unit of input.
Table 24. Shadow Prices and MVPs of Capital
R i ce
R i ce
l\Q LC pCl
r e so
i n the
12. Heady, Earl 0., Economics of Agricultural Production and Resource
Use, New York, Prentice-Hall, 1952.
13. Heady, Earl 0.,"elementary Models in Farm Production Economics
Research.11 Journal of Farm Economics. 30:201-225, May, 1948.
14. Heady, Earl 0. and Wilfred Candler, Linear Programming Methods,
Ames, Iowa State University Press, 1958.
15. Heady, Earl 0. and John L. Dillon, Agricultural Production Functions.
Ames, Iowa State University Press, 1961.
16. Herdt, Robert W. and John Mel lor, "The Contrasting Response of
Rice to Nitrogen: India and the United States," Journal of
Farm Economics. 46:150-160, February, 1964.
17. Hildebrand, Peter E., "Input Supply Risk," Instituto Colombiano
Agropecuario, Departamento de Economa Agrcola, Bogota,
Colombia, 1969 (mimeographed).
18. Instituto Colombiano Agropecuario, Insumos Agropecuarios, Division
de Control y Supervision de Insumos, Boletn Informativo No. 1,
Bogota, Colombia, 1970.
19. Instituto Geogrfico Agustn Codazzi, Estudios de Suelos para Cada-
stros; Municipios de Valledupar, Codazzi y Robles, Bogot,
20. Knight, Frank H., Risk, Uncertainty and Profit, Boston, Houghton
Mifflin Company, 1921.
21. Lindsey, Morris M., Effect of Harvesting Conditions on Cotton
Quality in the Yazoo-Mississippi Delta, Mississippi State Agri
cultural Experiment Station, Bulletin 95, Starkville, August,
22. Long, Millard F., "Why Peasant Farmers Borrow." American Journal
of Agricultural Economics, 50:991-1008, November, 1968.
23. Lopera, Jorge and Peter E. Hildebrand, La Brecha in la Productividad
Agrcola en Colombi a, Insti tuto Colombiano Agropecuario, ^Departa
mento de Economa Agrcola, Boletn Tcnico No. 1, Bogota,
24. McPherson, W. W. and Bruce Johnston, "Distinctive Features of
Agricultural Development in the Tropics," in Agricultural
Development and Economic Growth, ed. Herman M. Southworth and
Bruce Johnston, Ithaca, Cornell University Press, 1967:184-230.
25. Mellor, John, Economics of Agricultural Development, Ithaca,
Cornell University Press, 1966.
Table 36. Linear Programming Matrix for Profit Maximization Solution, Rice Included
bln 1 ,000 pesos.
weekends and holidays preparing data for analysis, but above all
for providing constant encouragement during the study and a source
of moral rejuvenation during the inevitable "dark hours."
Figure 7.--Rice: Supply and Demand for NCI per Hectare
Table 20. Area Needed to Earn 15,000 Pesos in One Semester and the
Probability of Success8
E Qf] per Hectare at
Given Probability Level
See appendix for probabilities.
With the required area producing the relatively low risk crop to
guarantee, as much as possible, the minimum necessary income, the
remainder of the farm could be used for the crops which maximize profit
or rate of return.
Minimizing Expected Losses^^
There was a wide range in the expected value of the losses among
the crops in the study, with the highest losses in the high cost crops.
In Table 21 the values of the loss components and the magnitude of the
total cost of the loss (T ) are given.
The value for R (i.e., .10) which was chosen was based on the
approximate rate of return on short term government development bonds.
It was believed that this alternative could be considered risk-free,
and the short term (6 months) of investment minimizes the loss due to
Symbols are defined
Unlike the ordinary credit discussed earlier, FFA credit carries
certain stipulations which must be met to qualify for the loans.
These stipulations are that the farm be greater than a given minimum
size, the farmer use improved seed, the farmer use technical assistance
from an approved agronomist, and that the farm be mechanizable. Each
loan must be approved by the FFA, which provides some measure of guar
antee that these conditions will be met. Payment of the loan is in
two installments; the first installment, 60 percent of the total loan,
is paid to the farmer before planting, and the second installment is
paid approximately six weeks after planting, when it is verified that
the farmer has fulfilled the seed and technical assistance requirements.
The purpose of FFA credit is to supplement the capital of the
farmer, and specifically to provide additional capital to be spent on
modern inputsespecially improved seed, pesticides and fertilizer.
Thus, the loan covers only 40 to 60 percent of total variable costs
of production, with the major portion allocated for these specific
inputs and advanced techniques of cultivation. The amount of credit
available per hectare is determined from cost calculations made by the
amount loaned by a commercial bank. It would receive 12.50 pesos net
return through interest charges. Upon rediscounting 65 pesos with the
Fondo, and paying 7 percent, the bank remains with 7.95 pesos which is
22.7 percent of its 35 pesos commitment.
$100.00 original loan
12.50 net interest
received by bank
65.00 amount rediscounted
x .07 rediscount rate
$ 4.55 rediscount charge
$ 7.95 interest earnings net
of rediscount charge
$ 7.95 = .227 return to bank's
Mel lor, John, "The Subsistence Farmer in Traditional Economics,"
in Subsistence Agriculture and Economic Development, ed.
Clifton R. Wharton, Jr., Chicago, Aldine Publishing Company,
27. Millikan, Max F. and David Hapgood, eds., No Easy Harvest. Boston,
Little, Brown and Co., 1967.
28. Ministerio de Agricultura, Fuentes Internas de Financimiento a
Entidades Crediticias nel Sector Agropecuario, Serie: Instru
mentos de Poltica Agraria, No. 2, Bogota, Colombia, July, 1968.
29. Ministerio de Agricultura, Informe Final de las Comisiones Sobre
Insumos Agropecuarios, Bogot, Colombia, December, I968.
30. Ministerio de Agricultura, Problemas de Desarollo en Cesar, Bogot,
31. Nurkse, Ragnar, Problems of Capital Formation in Underdeveloped
Countries, New York, Oxford University Press, 1953.
32. Plaxico, James S., "Problems of Factor-Product Aggregation in Cobb-
Douglas Value Productivity Analyses," Journal of Farm Economics.
37:664-675, November, 1955.
33. Rogers, Everett, "Motivations, Values, and Attitudes of Subsistence
Farmers: Toward a Subculture of Peasantry," in Subsistence
Agriculture and Economic Development, ed. Clifton R. Wharton,
Jr., Chicago, Aldine Publishing Co., 1969:111-135.
34. Rojas, Gentil, Productividad de Recoursos en la Agricultura del
Valle de Cuaca. Universidad del Valle, Cali, Colombia, I967.
35. Schultz, Theodore W., Transforming Traditional Agriculture. New
Haven, Yale University Press, 1964.
36. Simon, Herbert, "Theories of Decision Making in Economics and
Behavorial Science," American Economic Review. 49:253-283,
37. Viner, Jacob, "Barriers to Economic Development," in Development
and Society, ed. David E. Novack and Robert Lekachman, New
York, St. Martin's Press, 1964:81-90.
Welsch, Delane E., "Response to Economic Incentive by Abakalili
Rice Farmers in Eastern Nigeria," Journal of Farm Economics.
47:900-914, November, 1965.
rental contracts are for one year or one cropping period. The effect
of having more than 50 percent of the land in major crops cultivated
by tenants with short-term contracts is difficult to estimate. Based
upon the sample data, correlation coefficients were calculated between
tenure and yield for each of the four crops in the study, but no
significant correlation was identified. The absence of correlation
may possibly be explained by the homogeneity of production practices
followed throughout the area due to an almost universal use of tech
nical assistance. The effect of tenure on the use of well irrigation,
development of improved pastures, and on the intensity of land use
remains an important, unanswered question.
The four major crops grown in the study area are cotton, rice,
sorghum, and sesame. The area planted in cotton and rice occupies
approximately 80 to 90 percent of the land which is commercially
farmed, and production of these two crops accounts for nearly 90 percent
of the value of commercial crops. Sorghum and sesame have appeared in
recent years as alternative crops to cotton, or to be grown in rotation
with cotton.' Table 4 shows the relation of the production of cotton,
rice, sesame, and sorghum in Cesar to the total production of these
four crops in Colombia.
Although the Cesar-Colombia relationships can be easily read from
Table 4, the importance of the four major crops within the study area
cannot be appreciated without realizing that of the 192.1 thousand
Calculations of percentages are based on information from various
'From 1966 and 1969 the area planted in cotton, rice, sesame, or
sorghum ranged from 49.2 to 56.4 percent of total crops in Cesar.
under the existing system of one crop of cotton per year. The analysis
shows that these farmers could stabilize income and decrease the
chances of a loss as well as increase profits if other crops were
For those cotton growers who elect to continue producing this
crop, the analysis indicates that changes in their farming practices
would decrease costs, and increase yields and profits. Paramount
among the possible changes are those with respect to fertilizer and
pesticides. Indications, although as yet inconclusive, are that
fertilizer is being under-used. The bases for levels of application
were taken from ICA's recommendations which appear to come from in
The use of pesticides was such that costs were needlessly in
creased and yields were decreased. This result was probably due to an
excessive number of applications, improper timing, use of broad spectrum
pesticides, or low concentration of active ingredients.
The excessive use of machinery had a similar effect on costs,
yields, and profits as described above in the case of pesticides.
Decreased tractor time, presumably in the number of diskings, would
have a positive effect on yields.
Finally, the problem of the harvest labor shortage is critical
if this region is to continue or to increase its present emphasis on
cotton. It appears that this shortage cannot be greatly reduced by
a supply of temporary labor from other agricultural areas and from
urban centers as has been done, with limited success, in the past.
Mechanical pickers were introduced recently but, as yet, there is
little information with regard to the economics of their use.
analysis. The shadow price indicates the amount by which profit would
be increased with the addition of one unit of the resource which has
been exhausted. In the basic program both machinery and capital were
completely used in all but the first resource combination level. Be
ginning at the high level of capital (4,600 pesos per hectare) the
shadow prices were .104 pesos and .094 pesos for the first and second
semester, respectively. That is, if one peso of additional capital
were introduced into the program profit would be increased by these
amounts. When capital was reduced to the low level (2,300 pesos per
hectare) the shadow prices increased to .243 pesos and .302 pesos for
the first and second semesters. In the program without the rice activ
ity the shadow prices at the low level of capital input were .243 pesos
and .276 pesos. The estimate for the second semester was lower here
than in the basic program because sorghum was substituted for cotton
rather than for rice, and cotton produced a lower profit per hectare
Comparison of the Linear Programming
and Regression Results
Both the programming and regression results are based upon exist
ing conditions. However, enterprise combinations currently on farms
differ from those indicated to be most profitable by the programming
solutions. In the study region nearly 90 percent of the farms are
devoted solely to cotton, and this crop was grown in only one semester
of the year. The program solutions, on the other hand, indicate that a
^Capital here refers to total cash cost of the crop, excluding
costs associated with buildings.
Crop Combinations for Maximizing Profit
at Selected Levels of Capital and Machinery
Inputs, with Rice Included
Crop Combinations for Maximizing Profit
at Selected Levels of Capital and Machinery
Inputs, Excluding Rice Production
Crop Combinations for Maximizing the Rate of
Returns to Owned Capital at Selected Levels
of Capital and Machinery Inputs
Programmed Annual Rate of Return per Peso
to Owned Capital
Programmed Annual Profits per Hectare
Area Needed to Earn 15,000 Pesos in One
Semester and the Probability of Success . .
Total Cost of Loss
Return to Owned Capital for Cotton, Rice,
Sesame, and Sorghum '
Gross Income, Cost, and Expected Profits
per Semester for Cotton, Rice, Sesame
Shadow Prices and MVPs of Capital
MVP of Non-Traditional Cash Inputs for
MVP of Non-Traditional Cash Inputs for
Cotton: Estimated per Hectare Costs,
Returns, and Input Use
Rice: Estimated per Hectare Costs,
Returns, and Input Use
Sesame: Estimated per Hectare Costs,
Returns, and Input Use
Sorghum: Estimated per Hectare Costs,
Returns, and Input Use
Estimated Total Costs of Production for
Cotton, Rice, Sesame, and Sorghum, by
Source, 1970 141
can greatly affect the quality of the product as well. Cotton is
especially susceptible to quality changes. One study showed a signi
ficant correlation between rainfall (days of rain and measurable rain
fall) and quality of cotton produced. A positive correlation was
observed between rainy conditions and amount of ginning waste, and
negative correlations occurred between rainy conditions and cotton
grade as well as staple length (21, pp. 20-22). The grain crops are
also affected adversely by excessive moisture during the harvest
period. Excessive moisture content of the grain results in a lower
grade and price (with a likelihood of being rejected by some buyers).
The effects of pests and disease on quality of output are perhaps
even more obvious. Partly destroyed crops, crops infested with insects
and other pests, and disease-damaged products clearly suffer losses in
quality. Of the 15 to 20 percent toll on total crop output taken by
pests and diseases an important part can be attributed to quality
rather than quantity loss.
In the preceding section several sources of risk and uncertainty
were enumerated, some of which can be quantified and many of which can
not. The problem considered here is that of quantifying the risk
element in such a way that it can be applied in a risk model. It
appears that the risks encountered in each of the intermediate stages
or phases of production can be expressed in summary or in aggregate
terms using measures of risk with respect to the final product, that
is, physical output and product price. In this case it appears that
the best approach to risk measurement is to consider the probabilities
associated with the profits and losses of the activities involved.
Table 10. Production Function and Sample Means for Rice
"Significantly different from zero at a =.05.
Significantly different from zero at a =.10.
^Significantly different from zero at a =.25.
Relevance of Risk and Uncertainty
The elements of risk and uncertainty in agriculture have a much
greater effect on decision-making in the developing, and poorer,
countries than in the advanced countries where various means of re
ducing or coping with risk and uncertainty have been developed. There
are several circumstances which account for this situation:
1. Many of the farmers in developing countries cannot
afford, or withstand, a production failure or a
financial loss for even one production period, thus
they avoid entering into activities with which they
have little experience or personal knowledge (35, p.
167; 4, P. 405).
2. The types of changes which yield the greatest in
creases in return are often characterized by a high
degree of variability in results, and require a rel
atively large increase in expenses (12, p. 445).
These changes often require an increase in cash
capital inputs rather than in land or labor.
3. There is much less opportunity to shift risk in de
veloping countries (e.g., through insurance or price
support programs). Also the chances of being able
to diminish or eliminate risk and uncertainty are
lower in developing countries where inputs which
alter the agricultural environmentsuch as irriga
tion, fertilizer, and pesticides--are not as readily
4. The level of knowledge and control and the extent of
information services regarding agricultural production
MVP per Peso
Figure 5.Sorghum: Supply and Demand for Capital per Hectare
Quantity of Capital
i n Pesos
Machinery and tractor
Labor (L), hour
R i ce
Given that machinery, labor, and NCI unit prices were 44.00, 3.75, and
1.08 pesos, respectively, it is evident that actual mean input levels
in several of the input-crop cases differed substantially from esti
mated optimum levels. For each of the four crops there was at least
one input over-used and one input under-used. This misuse of inputs
resulted in profits that were below maximum levels.
The MVPs also indicate that the allocation of inputs among crops
was far from optimum in the event that two or more of these crops were
grown simultaneously. For example, shifting machinery time from sesame
to rice, and NCI from rice to sesame would move the MVPs in the
direction of equality, if these two crops were grown simultaneously.
Adequacy and Allocation of Credit
Supply and demand analysis indicated that there was generally a
sufficient quantity of production credit available in the area. In
many instances loans were available to cover the total amount of
operating capital required for crop production. A major problem lies
in the distribution and use of this credit. The excessive use of some
inputs prevented portions of the loans from being spent on more profit-
here. The product prices per kilogram for cotton, rice, sesame, and
sorghum were 3-70, 1.60, 4.60, and 1.20 pesos, respectively.
Table 13. Marginal Value Product (MVP) of Machinery, Labor and NCI at Three Levels of Resource Use
MVP of Machinery with Price = MVP of Labor with Price = MVP of NCIa with Price =
44.00, and Input Quantity 3.75 and Input Quantity 1.08 and Input Quantity
Given: Given: Given:
by at sample
and insecticide expenditures;
machinery input includes
only pre-planting soil
CHAPTER VI I
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
The area chosen for this study lies in the cotton belt on the
Northern Coastal Zone of Colombia. With the exception of small pockets
of irrigated rice land, cotton dominates agricultural activity, and
this region is the largest single cotton producing area in the country.
Other crops in the region which were found in quantities to warrant
inclusion in the study were rice (on irrigated land), sesame, and
The major objective of this study was to estimate the productiv
ities of the agricultural inputs used in the study area. Based upon
these productivities and additional information developed in this
study, further analyses dealt with three matters:
1. The efficiency of the input mix and levels in the production
of cotton, rice, sesame, and sorghum.
2. The allocation of resources among alternative crops.
3. The adequacy and allocation of credit.
Finally, recommendations were made with respect to the following items:
1. Credit policy.
2. Input levels for production of specified crops.
3. Crop combinations to achieve selected income goals: (a)
maximizing income, (b) maximizing return to owned capital,
(c) maximizing the probability of realizing selected in
come levels, and (d) minimizing losses.
An examination of the institutional supply of credit and capital
inputs showed that the largest share of capital was obtained through
joint .programs of the commercial banks and the government, where the
latter performed a supervisory role. Non-traditional cash inputs (her
bicide, improved seed, fertilizer, and pesticide) were often obtained
through government controlled outlets, and from privately organized
crop associations in the cases of cotton and rice. Information on
credit and capital supply was obtained from the agencies that supplied
Input-output data were obtained from a sample of farmers in the
area by means of personal interviews. Multiple regression and linear
programming techniques were employed to derive production functions,
input productivities, and optimal input and output levels and combina
tions. In addition, probabilities of expected yields, prices, and
profits were calculated and applied in simple risk-avoidance decision
models. The analysis was concerned with determining the most efficient
use of resources consistent with selected income goals of farmers.
The marginal value productivities of tractor and machinery use
(M), labor (L), and non-traditional cash inputs (NCI) were calculated
from crop production functions. These values were as follows:'
Only the MVPs at the sample mean input levels are summarized
TABLE OF CONTENTS
ACKNOWLEDGMENTS Â¡ Â¡
LIST OF TABLES vi Â¡ i
LIST OF FIGURES xi
KEY TO ABBREVIATIONS xi i
The Problem 1
Plan of Presentation 5
Regression, Production Functions, and Linear
Positive vs. Normative Analysis 7
A Note of Comparison 8
Applications in This Study 9
Evaluating Input Contribution 10
Risk and Uncertainty 11
Relevance of Risk and Uncertainty 12
Sources of Risk and Uncertainty 13
Input availability, appropriateness,
and qual i ty 14
Prices of products and inputs 18
Product price 19
Input price 21
Yield uncertainty 22
Ri sk Measurement 24
Risk and Crop Choice 29
Maximizing the probability of realizing
a selected income level
. Minimizing expected losses
Foregone alternative earnings ....
Probabilities of the Occurrence of Good, Normal and Bad
Yields3 and Prices3 for Cotton, Rice, Sesame and Sorghum
in the Study Zone
1 (Y) and
product price (P ) are classified into three levels
n = normal,
g = good (g > 1. In) ,
b = bad (b < ,9n) .
ob j ective
Indicated crop or
Maximize profit (a) Rice on irrigated land
(b) Sorghum in first semester and
cotton in second semester, if
irrigation is not available
Maximize return to
owned capital Sesame in both semesters
Maximize probability of
realizing a selected income Sorghum for the semesters in which
(In this case 15,000 pesos this is the objective
Minimizing losses Sorghum
Suggestions for Further Investigation
On the government owned and operated experiment stations in the
study zone much work could be done with cotton and other crops.
1. Experiments should be conducted with cotton to determine
the relationship between quantity and timeliness in the
use of pesticides. This would include:
a. determining permissable levels of pest populations
before spraying is done;
b. working with biological control of pests;
c. using spot or local spraying techniques;
d. determining optimal hours of the day in which to spray
e. experimenting with products which are pest specific
(i.e., those which cause minimum damage to the natural
2. Fertilizer response tests should be broadened to encompass
a wider range of applied levels, especially in the upper
limits of the amounts used (particularly for cotton and
Input Productivity in Agriculture
on the North Coast of Colombia
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
fertilizer which produce less rice than areas uniformally fertilized.
The dummy variable for fertilizer application substantiates this con
clusion. The regression equation indicates that the yield associated
with mechanical fertilizer application was 800 kilograms higher than
when hand application was used (800 is 18 percent of the mean yield on
farms in the sample). The mean levels of inputs were relatively close
to the optimal levels as calculated from the regression coefficients.
The rather long experience of rice growers in the region, and in
similar areas in the country, undoubtedly contributed to this condition.
The production function calculated for sesame is:
Y = -40805.0 259. IT + 11711.7M 1491 MZ + 58.6M3 + 215.1L
-1.43L2 + .0029L3 29.645S -575S2 + 2.52(M)(L) + 9.4(H)(S)
-202.7D, + 299.6D2
Y = yield in kilograms per hectare
T = tenure (0 = owner, 1 = tenant)
M = hours of tractor use per hectare
L = hours of labor per hectare
S = expenditures on seed per hectare
Dj = dummy variable for municipio (town) of San Juan (1 if farm
in San Juan; 0 otherwise)
D2 = dummy variable for municipio of Becerril (1 if farm in
Bercerril; 0 otherwise).
e third municipio is Codazzi.