SOME PRELIMINARY NOTES ON THE USE OF PRODUCTION FUNCTION
CONCEPTS IN RELATION TO LAND APPRAISAL
Farm land appraisal is generally a process whereby the net earnings of
land is capitalized and then adjusted for various aspects of the farm which
have not been previously taken into account in the earning value. The
adjustments, because they are very subjective in nature, cannot be described
in a theoretic framework. It is the evaluation of land on the basis of
net earnings to which this paper is directed.
The accepted process of arriving at earnings value is very simple.
Based on so called "typical'! management and organization for a given type
of farm, gross income is determined, expenses are deducted, (including
expenses for labor, management and interest on non-real estate investment
items) and the resulting net income figure is given as the earnings on the
land and other real estate of the farm. This process is used for either
an owner-operator or a landlord-tenant relationship. Considering an
owner-operator, all expenses involved in the farming operation are deducted.
In the landlord-tenant operation, only those expenses for which the land-
lord is normally held, plus taxes on the land are deducted. The part of
the farming expenses for which the landlord is held responsible, are normal-
ly determined from the typical type farm-lease for the area and type of farm
The error which results in arriving at imputed productivity or value
of land in this manner, is due to assuming that the productivity of all non-
land inputs for which costs are deducted is equal only to the amount of
their costs. That is, the price of each of the other inputs times the quantity
used is considered to be equal to its4productivity or the average value
product (AVP) times the quantity of the input used.
This would be the case only in a perfectly competitive industry and a
perfectly adjusted firm. For such a firm, marginal value product (MVP) =
marginal factor cost (MFC) = average factor cost, (AFC) = average value
product (AVP) which can occur only where AVP is at a maximum. This is common-
ly known as the beginning of stage II of the production function. Farms do
not usually operate exactly at this point. Rather they operate somewhere
to the right of this point or within stage II.
Assuming that the price of inputs is not a function of the quantity used,
MFC = AFC. If the optimum farm organization is within stage II rather than
at the beginning of stage II, then given a farm in optimum adjustment,
AFC=AVP. (Point A in figure 1.)
0o & A | T
Assuming the type of farm for which an appraisal is being made is typically
at optimum adjustment, then the farm in figure I will be operating with
inputs all at point A. At this point, the input in question has been charged
to the farm at a cost of OARM. However, also at this point the total
productivity of the input to the firm is equivalent to amount OASN. Thus,
the input has returned to the farm on amount MRSN over and above its cost
to the farm. Yet in the appraisal the farm will be charged only OARM leaving
the amount MRSN as imputed to the earnings of land.
For farms not optimally organized operation will be in the area between
B and A, (figure I). The same reasoning holds true, however, anywhere in
this area since AFC
Since the relationship for each and every input can be assumed to be
similar to that in figure I, each input adds more to the farm in product
than the farm is being charged. Thus, land which is receiving the residual
return)is actually being imputed a productivity greater than its actual produc-
tivity. That is, it is receiving not only its actual productivity but also
the productivity over and above the amount of cost for each and every input
the farm uses. This particular point is mentioned in an article by Blase
in the October, 1960 edition of Iowa Farm Science in an article titled,
"What Governs Farm Land Prices?". Mr. Blase states that new technology
in resources in agriculture have tended to reinforce the rise in land prices
in two ways. One of which is, "Because of accounting difficulties the
return from new technology in capital resources is often credited to land
Effect on Appraisals of Lending Institutions
Lending institutions normally appraise land as collateral by following
the above procedure. Because the resulting productivity of land is exaggerated,
the institution must follow some method of discounting this figure to make
the land a safe piece of collateral. Two methods are commonly employed fto
discounting this value.
The first procedure is to discount yields when initially determining the
gross income from a piece of land. Yields of farm crops in such a process
ar normally based on long time averages for counties or other geographic divisions.
In many, if not most instances, this figure is below that which could reasonably
be expected on the farm in question. In many cases it is exceedingly low
when considering the new technology which is available to the farmer. The
average yields have been based to a large extent on the absence of this new
technology, while in the future the new technology most certainly will be
in use. Thus, higher yields can very likely be expected than those which
have occurred over the past. Yet, because it is necessary in some way to
discount the productivity of the land, the average yields are still in common
Another method, and used sometimes in conjunction with the first, is to
loan only on:a certain percentage of the determined value of the land. Thus,
some institutions may lend only 80% or 65%, etc., of the value of any piece
of farm land determined by their method of appraisal.
The Need For Research
While the use of either or both of the above procedures does tend to
arrive at a reasonable estimate of the productivity of the land resource,
it does not leave a clear picture of how that productivity was determined.
If the actual productivity of various resources in a particular farm
situation could be determined, it would be helpful in arriving at the actual
productivity of the land resource in a logical manner.
It would be possible with the use of marginal analysis and continuous
production functions to take various types of farms of different sizes and
determine the production functions of different groups of inputs involved
in farming for each type of farm. Then, since appraisals are made on typical
usages, the input categories could each be evaluated at the geometric mean
for given land areas. The resulting values would serve as a guide in making
adjustments on the amount to deduct from earnings for each of the groups of
input categories. More accurate imputed values then could be determined for
the land resource, thus making appraisals of land more realistic.
Land Valuation Directly From A Production Function
Consider a group of homogeneous farms, one of which is to be appraised.
Each of these farms is the same type of farm, each hasAthe same investment
in capital and each has the same access to labor and management. The land is
similar in type and productivity,, however, the acreages in the farms vary.
A production function could be derived with land as the sole varying factor
of production. Consider Figure II having been derived from such a production
570 /moo \
The hundredth acre of land has a marginal value product of OA. It
would be profitable to pay no more than a price of OA for the hundredth
acre. If the price of land is OA., then a hundred acres would be purchased.
If the price were OB, only 90 acres would be purchased. Although the
average value product of a hundred acres is OB, one would not purchase
-a hundred acres at a price of OB. If the price of land is OB and a
hundred acres were purchased, the cost of the last 10 acres exceeds the
productivity of the last 10 acresA anx amount equal to triangle CDE. The
productivity of the last 10 acres is equivalent to the area lying under the
MVP curve between 90 and 100 or the integral of MVP from 90 to 100.
The AVP of a hundred acres is OB. The average product for the last 10 acres
then exceeds the marginal product by the triangle CDE. Thus, the average
value product over estimates the true productivity of the factor of
production where the elasticity of production is less than one.
If in valuing a hundred acres of land, the marginal value product
or OA is used, this places a proper value only on the last acre of land.
The total productivity of the land is the area lying under MVP from 0 tb
100 or the integral of MVP from 0 to 100. However, since the same price
must be paid for each acre it is necessary to determine the average value
productivity of each acre. Since the integral of the MVP is TVP the average
value of the productivity equals the AVP or total value product divided
by the number of units of input. AVP therefore, is a measure of the actual
productivity of each acre of land and would be the amount which should
be paid for the land or the amount at which the land should be valued.