ETHNOGRAPHIC LINEAR PROGRAMMING:
LIMITED-RESOURCE, FAMILY-FARM HOUSEHOLD MODELS
Peter E. Hildebrand
A Linear Program (LP) is a mathematical "optimizing" procedure that has been used at
least a half century to maximize or minimize an objective, subject to a set of constraints.
Mathematically it looks like the following:
Max (or Min): I = EjCjXj where j = 1 .. n
Subject to: YiAijXj <= Ri where i = 1 ... m
And Xi >= 0
Where II is the objective to be minimized or maximized, Cj is the cost (debit) or returns
(credit) of each of the n activities Xi, Aij is the input or output coefficient for each
activity j and resource or constraint i, and Ri is the set of m constraints or restrictions.
Current models are easily solved on spreadsheets such as Excel or Quattro Pro.
Agricultural economists began using LP models in the 1950s to model farms to show
farm managers how they could better allocate their resources and thereby improve profit.'
These models were normative in nature; the modelers anticipated telling farmers what
they "ought to do" when the solutions to the models differed from what the farmers
"were" doing, which was usually the case.
ETHNOGRAPHIC LINEAR PROGRAMMING (ELP) MODELS
Ethnographic linear programming models are a means of quantifying ethnographic
(largely qualitative) data and are both descriptive and analytic. Rather than following
normative theories of how farm households "ought to be" structured (based on traditional
economic assumptions of how firms operate), ELPs are based on ethnographic
descriptions of how households "are" structured. The linear programming optimization
process is a proxy method for solving the resource allocation problems farmers solve
using their own particular cognitive processes. The descriptive ELP models are
developed 1) to help researchers or other development workers understand the
complexity and diversity of these systems, which are first a home rather than a business,
and ultimately 2) to simulate the systems. Once the simulations are validated, the models
are used analytically to assess ex ante differential adoption or rejection of potential
technologies or the potential differential impacts on households of proposed
infrastructure or policy changes. Because limited-resource, family-farm households are
highly diverse, it is necessary that the ELP be amenable to incorporating and maintaining
this diversity in analyses, but at the same time allow users to aggregate results to
community or higher levels or scales.
Ethnographic skills require anthropological capabilities and participatory methods of
persons who are also knowledgeable about the biological processes of farming. This
combined knowledge base is combined in the economic methodology long called linear
programming. The result is Ethnographic Linear Programming.
CREATING AN ETHNOGRAPHIC LINEAR PROGRAM (ELP) MODEL FOR
LIMITED-RESOURCE, FAMILY-FARM HOUSEHOLDS
The first step in creating an ELP model is to define the livelihood system for the area that
the model will represent. The livelihood system is the full range of existing activities
(X3s) available to the households of the area and from which each household chooses its
livelihood strategies. The basic ELP matrix includes all the activities in the livelihood
A Sondeo offarmers and others in the area can obtain the information
rapidly and efficiently.
Production or input and output coefficients for each of the activities (Aijs) will generally
be quite standard within an area. The amount of time required to prepare, plant or weed
an acre or hectare of a crop and who in the household is involved (is it a man's job, a
woman's job) will be very similar. However, the same operation may be different for
different kinds of soil and should be recognized. If different kinds of soil are managed
differently and produce different yields each should be a separate activity.
Yields that can be "counted on"
One of the most difficult things to ascertain is the yield that farmers 'count on' for their
basic food crops. It is conventional to ascertain and use "usual" or "average" yields when
analyzing farm systems. Even though this seems logical to most people working with
small-scale farm households, it is not the measure of productivity that will provide good
descriptions of these households.
Farmers cannot depend on "average" yields; they know that often (perhaps half the time
or one year in two) yields will be below "average." For basic food crops, they need to
calculate area to plant based on a yield level that will occur with much higher frequency
than 'half the time.' They may, for example, want to plant a large enough area that they
can feed the household nine years out often or even 19 years out of 20. The yield level
that meets one of these criteria will be much lower than the average yield. This lower
yield level is what farmers can "count on" most of the time. Because this is the yield
level farmers use for planning how much to plant, this is the level that must be used in the
ethnographic linear program model."
These input/output coefficients usually can be obtained using a focus
group or with in-depth interviews of, perhaps, three farmers.
The above provides the information for the basic input/output matrix, which will be
common to most households in the area. Constraints (land area, labor availability,
consumption requirements, cash needs) and goals (provide minimum food needs for the
household, maximize discretionary cash, minimize male labor, maximize production of a
basic food crop) are highly diverse from farm to farm even in a relatively homogeneous
area and depend to a large extent on household composition. So after the information for
the basic matrix is collected, it is necessary to begin being specific.
Perhaps the most efficient means of constructing the complete ELP model is to select a
willing household whose farming practices reflect those in the basic matrix and model
that specific household. The process is to obtain information from the household
members individually and as a group on all the relevant constraints. This must be
specific enough to identify 1) who eats how much of each kind of food; 2) who can use
cash from various sources; 3) what are the necessary cash expenses for the household; 4)
when during the year must cash expenses be made, and who is responsible for each"; 5)
what each member of the household does; and 6) how much time is spent doing it, on a
monthly" basis. Seasonal cash accounting is critical and must include remittances from
persons who work off the farm whether or not in residence. Frank discussions with the
household members may be necessary to elicit 7) household goals.
The complete descriptive model of a specific household can be constructed
and modified as these discussions are going on.
Often inconsistencies can be spotted when the model is infeasible or the solution is
inconsistent with what is known or described.
Testing and validating the household model
When the ELP model adequately' describes the first household, a second specific
household should be modeled.
Considerably less time will be required in interviewing this second
household (and any subsequent households) than was requiredfrom the
The composition of this second household should be different from the first, but still its
farming practices should be similar to those in the basic matrix. If the first ELP
adequately reflects the type of livelihood system being modeled, changes in the model
should only require changing the household composition. This, of course would change
household consumption requirements, cash needs and labor availability. Land area may
need to be changed if the second household is larger and has more labor resources than
the first. The solution to this ELP model should be close to what this second household
actually does. Again, this is a subjective call.
A limited number of additional households of diverse compositions should also be
modeled in this process of testing and validation. The model can be considered to be
validated when it "adequately" simulates or describes each of these diverse households.
DATA FOR ETHNOGRAPHIC LINEAR PROGRAMMING MODELS:
KIND AND SOURCES
For a household
Age, sex and relationship of all persons of the household (those who contribute to
or receive something from the grouping of persons associated with a domicile
whether or not they reside in the domicile).
Who in the household contributes to each of the household's production and
reproduction activities on a seasonal, quarterly or monthly basis.
How much time does each of them contribute to each of these activities during
Seasonal cash needs: for what, in what amounts and from what sources. These
should include non-discretionary amounts for such things as education, clothes,
gifts, etc. Also need to know how much cash is needed at the beginning of the
cropping season by each member of the hearth hold (persons who normally are
physically present or reside in the domicile) responsible for having it available.
Off-farm sources and remittances from persons not living in the domicile should
Usual food consumption of persons in the hearth hold (persons who normally are
physically present or reside in the domicile). Should include seasonal differences.
Sources of the food: whether purchased, hunted, gathered, or produced and usual
amounts from each source. Special foods for infants and young children, if any.
Useful to know how food is prepared.
Amount of land available for each kind of use (upland, lowland, irrigated land,
pasture, bush, fallow, orchard, forest, etc.).
Separately for each annual crop or crop association the household pursues and on
a per unit of land area basis:
o Labor required during each period, disaggregated by gender (usually
sufficient: male and female children, male and female adolescents, male
and female adults)
o Inputs required, source and cost
o Amount produced of each usable product "
o Seasonal farm gate price of each kind of product sold "'
Separately for each perennial crop or crop association the household pursues and
on aper unit of land area basis orperplant basis, if appropriate:
Labor required during each period, disaggregated by gender
Inputs required, source and cost
Amount produced of each usable product
Farm gate price of each kind of product sold
Year before the crop produces VI
For each kind of animal activity the household pursues and on aper animal basis:
o Labor required for each activity during each period, disaggregated by
Inputs required, source and cost
Amount produced of each usable product
Farm gate price of each kind of product sold
Death loss, birth rate, weaning rate, etc.
Forest, bush or body of water
For each activity (hunting, gathering, fishing, etc.) the household pursues:
o Labor required during each period, disaggregated by gender
o Inputs required, source and cost
o Amount produced of each usable product
o Farm gate price of each kind of product sold
For a community
Each of the different kinds of constraints vary quite widely by household within a
community, but the main source of these variations is household composition. Using
input tables in conjunction with a linear program matrix, household composition can be
changed easily and these changes can be tied to changes in labor availability, cash
requirements and food needs. In some situations land area is also a function of household
composition. More often, however, this is an independent constraint. When land area is
an independent constraint, and if whole farms are on different types of land, then
sampling will be necessary to estimate number of farms on each. If each farm has several
types of land then a range of area or farm size must be determined.
Usually in a community there will be quite a lot of homogeneity in the way the different
activities are done (except, of course, farmers who use tractors will be different from
those who use animal traction, and these will be different from those who use only
manual practices). Those who farm manually will usually do things in quite a similar
fashion and most of this kind of farmer will be "representative" of the others. Those who
use animal traction likewise will do things alike. For this reason, it is not usually
necessary to have a large sample in order to obtain reliable data. Averages are of little
use, so sampling to obtain specific confidence levels is not necessary. A few case studies
within each type of farm (manual, animal traction, tractor, for example) should provide
Care must be taken to assure that all units are completely understood.
What is a working day? Is it 4 hours, 6, 7 or 8? Does it vary depending on whether a
person is working his or her own land rather than as a laborer for another farmer? Is food
included when wages are paid? At what age do boys begin working in the fields or with
livestock? How much time do they spend in these tasks when in school and when not?
At what age do girls begin helping with household chores? How much time do they
spend in these tasks when in school and when not?
What unit of land area are farmers using? What is the size of this area? Does it vary
from one area to another? Does it vary from one task to another?
'See, for example, 1) Heady, E.O. and W. Candler. 1958. Linear Programming Methods. Iowa State
College Press, Ames. 2) Hildebrand, P.E. 1959. Farm organization and resource fixity: modifications of
the linear programming model. PhD dissertation, Michigan State University, East Lansing.
"The "counted on" yield would be used to provide for household consumption. The difference between
"average" yield and "counted on" yield can be incorporated in the model by "selling" the difference at
harvest time. Because the price is usually lower at harvest, the cash could also be transferred to a later
period if not needed at harvest and its value could be increased.
SThis must include the amount of cash reserve necessary to begin the next cropping cycle.
v Other seasonal periods can be used. During the most critical and labor-scarce periods such as when
planting or weeding, shorter periods may be necessary.
v The term "adequately" is subjective. The model should reflect the correct strategies (that is, the correct
activities of the modeled household). The magnitude of each activity should be relatively close to what the
actual household does but it should not be expected that they would be exact. Exactly meeting the
magnitude often means that an artificial constraint has been built into the model. If that was necessary for
the model to describe the household then one or more constraints are usually missing or the magnitude of
an input/output coefficient is incorrect. More discussions with the members of the household will be
" See end note ii.
" Market prices, even in local markets, are not appropriate unless these are prices paid to farmers and cost
of getting the product to market (if any) is deducted. Prices in different seasons are important as well.
" Increasing yields in the first years of production are usual and must be estimated. It is not sufficient to
estimate only yields when in full production.