SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS
DECEMBER, 1983
ENERGY-RELATED INPUT DEMAND BY CROP PRODUCERS
James B. Kliebenstein and Francis P. McCamley
Energy use in U.S. production of food and fiber is
extensive and has increased rapidly. A threefold in-
crease occurred from 1940 to 1970 (Carter and Yonde).
Food and fiber production accounted for about 13 per-
cent of the total energy consumed in the U.S. in 1980
(Duncan and Webb). Of the total energy use in food
and fiber production, farm level production directly
consumes about 21 percent (U.S. Senate Committee
on Agriculture and Forestry).
Since the early 1970s much attention has been de-
voted to energy demand by agriculture. Mensah and
Miranowski estimated the effects of prices, product
substitution, and technology on U.S. agriculture’s de-
mand for energy. Burton and Kline considered several
crop-production technologies and found that no-till is
the best option for relatively high energy prices. In
similar studies, Kliebenstein and Chavas, and Mira-
nowski projected shifts toward minimum tillage as en-
ergy prices increase. They found inelastic short-run
energy demand at the farm level. Capps and Havlicek
reported similar elasticity estimates. McCamley and
Kliebenstein concluded that the degree of producer risk
aversion has a larger impact on energy use levels than
do energy prices.1
Most previous energy-demand studies share two
limitations. One limitation is the narrow measure of
energy use adopted. Typically, only inputs, such as
diesel fuel, propane, and gasoline, which supply en-
ergy directly are considered. An exception is the study
by Eidman, Dobbins, and Schwartz. Energy required
to produce other agricultural inputs is often ignored.
This omission is serious because some of the com-
monly neglected inputs can be readily substituted for
energy-supplying inputs. For example, by modifying
tillage practices crop producers can substitute herbi-
cides for diesel fuel or vice versa. Thus, studies which
consider only energy-supplying inputs tend to over-
estimate the effects of changes in tillage practices on
energy demand. For this study, fertilizers, herbicides,
and pesticides, as well as the more obvious energy-
supplying inputs, are considered.
A second limitation of many studies is the assump-
tion of a risk-neutral attitude by crop producers. This
assumption is inconsistent with the findings by Lin,
Dean, and Moore, and others that farmers are not risk-
neutral. This study examines the effect of various de-
grees of risk aversion on energy consumption.
The approach used in this study is consistent with the
definition of simulation offered by Johnson and Raus-
ser. An expected income-variance (E-V) analysis model
of a typical farm is formulated. Since simple closed-
form expressions for the demand functions implied by
this model do not exist, optimal solutions are com-
puted for many different price and risk-aversion coef-
ficient combinations. An energy-demand function is
estimated from the solution data.
METHODOLOGY
The Model
An E-V analysis model of a typical Missouri crop
farm is developed. E-V efficient solutions are relevant
for many alternative-risk-programming objective
functions. These considerations, as well as the avail-
ability of a quadratic programming algorithm, prompt
the use of E-V analysis.2 Even though E-V analysis is
chosen primarily for intuitive and practical reasons, it
enjoys the added advantage of being consistent with the
maximization of expected utility if the utility function
is quadratic or profits (R) are normally distributed. For
the latter case, Freund has shown that maximizing an
expected utility function of the form
(1) U(R) = 1 - e~2“R
is equivalent to maximizing
(2) E(u) = μ — ασ2
where ∣x is expected profit, σ2 is the variance of profit,
and α is a risk-aversion coefficient. It has also been
shown that E-V analysis approximates other situations
James B. KIiebenstein and Francis P. McCamley are Associate Professors of Agricultural Economics, University of Missouri-Columbia.
The authors thank the anonymous reviewers for their constructive suggestions.
Approved for publication as Journal Paper No. 9197 of the Missouri Agricultural Experiment Station.
1 In this article we use several related phrases. We use ‘ ‘risk-aversion coefficient’ ’ or risk-aversion measure” when referring to a coefficient in a particular objective or utility function. We
use ‘ ‘degree(s) of risk aversion’ ’ and (more or less) ‘ ‘risk-averse’ ’ when discussing risk aversion in more general terms, i.e., without reference to a coefficient in a particular objective or utility
function.
2 MOTAD models and stochastic dominance techniques have increased in popularity in recent years. Buccola discussed the statistical advantages of using E-V analysis rather than MOTAD
analysis. Although stochastic dominance analysis is now widely used for comparing discrete risky alternatives, it is not widely used to analyze mixtures of risky alternatives.
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