ENERGY-RELATED INPUT DEMAND BY CROP PRODUCERS

ergy price, four crop prices, and the risk-aversion
coefficient.

Changes in the price of petroleum and other fossil
fuels affect the prices of several of the inputs used by
crop producers (diesel fuel, propane, chemicals, fer-
tilizer). Diesel fuel price serves as a proxy for the prices
of fossil fuels. The levels chosen for this input are $.50,
$1.00, $2.00, $3.00, and $4.00 per gallon. The prices
chosen for the energy-based inputs (shown in Table 1)
reflect an assumption that the ratios of energy-based
input prices to diesel fuel price will remain at approx-
imately the values which existed during the 1970s. This
assumption precludes isolating the separate effects of
individual energy-based input prices, but allows for a
more complete treatment of output price changes. This
permits a more realistic design since input prices tend
to move together more than crop prices do. If input
prices had been treated independently as well, 625
times as many solutions would have been required.

It is assumed that the farmer faces neither price nor
quantity risks for petroleum-related inputs. This as-
sumption is not completely valid. The amounts of har-
vest inputs, such as propane for crop drying, diesel fuel,
and so forth, depend partly on crop yields. The harvest
costs are not always known with complete certainty at
planting time. Ignoring these minor price and quantity
risk components for energy-based inputs simplifies the
analysis. Only the exρected-net-retums vector has to
be modified when energy-related prices are changed.

Four price levels are selected for each commodity
(com, sorghum, soybeans, and wheat) produced (Ta-
ble 2). Only the most unlikely crop price combinations
are not considered.³ Sorghum and com are both feed
grains and are highly substitutable. Therefore, it is not
reasonable to consider price combinations involving a
high sorghum price and a low com price or vice versa.
Omitting combinations of this sort is consistent with
Eidman’s suggestion that disequilibrium price combi-
nations not be considered.

In contrast to the assumptions stated above for en-
ergy-related inputs, it is assumed that the farmer faces
both price and yield risk for the crops produced. The

Table 1. Input Prices Used in the Study

Table 2. Output Prices Used in the Study

price levels in Table 2 are regarded as average prices
rather than as known prices. It is assumed that chang-
ing average commodity prices changes the expected net
returns and the dispersion of net returns without
changing the shape of the returns distributions. This
allows obtaining the VarianceZcovariance matrix for any
trial by (pre and post) multiplying the base variance/
covariance matrix by an appropriate diagonal matrix.
Each diagonal element is the ratio of the average price
level selected for the commodity to its average price
level in the base period.⁴

The sixth factor varied is the risk-aversion coeffi-
cient. Levels for this experimental variable are not
specified in advance. Instead, for each combination of
energy and output prices, this coefficient is varied from
0.05 (representing a high degree of risk aversion) to
zero (risk neutrality). An observation is recorded at each
basis change. It is well known that this procedure gen-
erates the most relevant portion of the E-V frontier.

Demand Function Estimation

As noted elsewhere in the paper, the energy-de-
mand functions implied by the E-V analysis model do
not have a simple form. Therefore, linear, quadratic,
and cubic approximations of the energy-demand func-
tion are estimated. These can be regarded as Taylor-
series approximations of the energy-demand function.
The dependent variable is the energy associated with
diesel fuel, propane, chemicals, and fertilizer used in
crop production. Energy use is measured in millions of
BTU ’ s and was computed using the factors shown in
Table 3.⁵ The amounts of energy used per acre for the
crop activities are shown in Table 4. The independent
variables are diesel fuel price (used as a proxy for the
prices of all inputs derived from fossil fuels), com-
modity prices, and a measure of risk aversion.

Three alternative measures of risk aversion are used.
The set of E-V efficient solutions is consistent with
many different objective functions and thus with dif-
ferent attitudes toward risk. The coefficients of any of
these functions are candidates for risk-aversion meas-
ures. For this paper, one family of functions of the fol-
lowing form are considered:

(3) f(μ,σ) = μ - βσ^δ; β ⅛ 0, δ ⅛ 1

³ Candler and Cartwright suggested that the appropriate experimental design depends upon the objective of research. Rotatable designs are useful if the objective is the maximization of
some function, but relatively complete “factorial” designs, such as that used in this study, allow approximation of a Iargerportion of the response (energy demand) function.

⁴ The gross-returns vector for each set of crop prices is obtained by multiplying the base exρected-gross-retums vector by the diagonal price-ratios matrix. The net-returns vector is obtained
by subtracting a vector of constant (not affected by energy price) variable costs and a vector of energy input costs from the gross-returns vector.

⁵ For most economic analyses, it is appropriate to measure energy use in value terms since that approach comes closer to measuring the value of all of the resources used to manufacture
the energy-related inputs. However, this study is more concerned about the impact of crop production on fossil fuel resources.

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