Rising Fuel Prices and the Potential of Input Substitution in US Corn Production Henry Thompson, 1 Osei-Agyeman Yeboah, 2 & Victor Ofori-Boadu. 2 1 Auburn.

Rising Fuel Prices and the Potential of Input Substitution in US Corn Production

Henry Thompson,1 Osei-Agyeman Yeboah,2

& Victor Ofori-Boadu.2

1Auburn University2North Carolina A&T State University

Motivation Energy prices are projected to continue a slow increase

over the coming decades as reserves of oil are depleted

There is no doubt that rising diesel prices will play a role in agricultural production decisions over the coming years

Outcomes of energy policies often hinge on energy substitution but there is little consensus on energy substitute

Berndt and Wood (1975) find energy a substitute for labor but complement with capital while Griffin and Gregory (1976) find energy a substitute for both labor and capital

Background

This study estimates energy substitution in US corn production from 1975 to 2004 in a translog cost function

Cross price elasticities describe the adjustment in capital, labor, energy and fertilizer inputs to the price of energy as well as the adjustment in energy input to the other factor prices

The findings of this study is to give some idea of the potential to substitute other inputs for energy as energy prices rise over the coming decades

Input substitution in agricultural production

There are numerous input-output relationships in Agriculture since the rates at which inputs are transformed into output vary among soil types, animals, technologies, rain fall amounts etc.

The Leontief production function for example, has the property that, a decrease in the utilization of any input implies that output will fall, no matter what happens to the utilization of other inputs.

However, it has been long observed that decreased utilization of one input may be compensated for increase utilization of another input.

The ability of one input to compensate for another has been found to be significant in most farming operations.

It is therefore possible to produce a constant output level with variety of input combinations

The importance of input substitutability has led to the definition of various elasticities of substitution providing unit-free measures of the substitutability between inputs

Input substitution in agricultural production

The theory of energy substitution

Energy input involves work that transforms matter and includes fuels based on natural resources

Energy substitution starts with the production function x = x (K, L, F, E)

The firm or industry is assumed to produce the profit maximizing output x* hiring the optimal inputs of capital K, labor L, fertilizer F, and energy E that minimize cost of production

The theory of energy substitution

The model assumes competitive price taking in the input and output markets and comparative static substitution between energy and the other inputs given cost minimization

Shephard’s lemma states that input levels are derivatives of the cost function c(r, w, e; x) with respect to input prices. Thus E* = δc/δe

The theory of energy substitution

Estimation of cross price elasticities can begin with the translog cost function (TCF) Fuss and McFadden (1978) and Saicheua (1987)

where wi is the price of input i, r is the price of capital, w the wage, f the price of fertilizer, e the price of energy, and t represents technology

lnc =c0 + Σicilnwi + .5ΣiΣkciklnwilnwk + Σiailnwit = c0 + cKlnr + cLlnw + cElne + .5[cKK(lnr)2 + cLL(lnw)2 + cEE(lne)2 + 2cKLlnrlnw + 2cKElnrlne + 2cLElnwlne] + aKtlnr + aLtlnr + aFtlnf + aEtlne (1)

The theory of energy substitution

The elasticity of cost with respect to the price of energy is the partial derivative of the TCF with respect to the price of energy

δlnc/δlne = cE + cKElnr+ cLElnw + cEElne + aEt (2)

By Shephard’s lemma, E = δc/δe and δlnc/δlne = (δc/δe) (e/c) = E (e/c) = eE/c

For a competitive firm, cost c equals revenue c = px = x. It follows that δlnc/δlne = eE/x = θE, making (2) the energy factor share equation

The theory of energy substitution

Factor share equations for the other inputs are similar, leading to the cost share system (See equations below)

(3)

Estimates from the above equations provide the coefficients to derive substitution and cross price elasticities

θK = cK + cKKlnr + cKLlnw + cKFlnf + cKElne + aKt θL = cL + cLKlnr + cLLlnw + cLFlnf + cLElne + aLt

θF = cF + cFKlnr + cFLlnw + cFFlnf + cFElne + aFt θE = cE + cEKlnr + cELlnw + cEFlnf + cEElne + aEt

The theory of energy substitution

The second cross partial derivative of the TCF for energy price e and labor prices w is used to solve for their cross price elasticities

εEL= (cEL + θEθL)/θE (4)

Own price elasticities are derived as:

εii= (cii – θi + θi2)/θi (5)

Data Historical data from 1975 to 2004 on per unit price, quantity

of corn produced, labor, fertilizer, and energy used in corn production were obtained from USDA/ Economic Research Service online database.

The shares of the four inputs are plotted in Figure 1.

Capital share is declining as the others increase.

Especially energy and fertilizer shares increase during the period.

Fertilizer is an energy-intensive product and its price and factor share may move along with those of energy.

Figure 2 shows the history of factor prices. Fertilizer prices have indeed risen during the period, while energy prices have been stationary or slightly declining

Figure 1. Factor Shares

0.00.10.20.30.40.50.60.70.80.91.0

1975 1980 1985 1990 1995 2000 2005

SE SF SL SK

Figure 2. Factor Prices

0

20

40

60

80

100

120

140

1975 1980 1985 1990 1995 2000 2005

e f w r

Results Below are the estimated factor share equations:

θK = 24.4* - .035*lnr + .225lnw + .229*lnf - .007lne -.013*t (3.89) (.019) (.215) (.108) (.069) (.002) F = 31.4* adjR2 = .840 autocorr = .203 θL = -3.90* + .008lnr - .109*lnw - .101*lnf + .007lne + .002*t (1.10) (.005) (.061) (.031) (.020) (.0006) F = 7.87* adjR2 = .543 autocorr = .246 θF = -13.8* + .018lnr - .184lnw - .117lnf - .009lne + .007*t (2.56) (.012) (.141) (.071) (.046) (.001) F = 28.5* adjR2 = .826 autocorr = .104 θE = -5.74* + .009lnr + .064lnw - .011lnf + .010lne + .003*t (1.21) (.006) (0.67) (.034) (.022) (.001)

F = 22.4* adjR2 = .786 autocorr = .327

Results

The null hypothesis of continuously improving technology cannot be rejected in any of the factor share estimates

The overall explanatory power of the factor share regressions is fairly high and autocorrelation of the residuals is not a problem

Only 2 of the 16 factor price coefficients in (6) are significant but the present goal is estimation of substitution elasticities and the coefficients are used in the calculations

Results Constant returns CRS implies the sum of the

constant terms is one and but the sum of the estimated coefficients is 0.96

CRS also implies the sums of the factor price coefficients in the four factor share equations should equal one but these sums are K = .412, L = -.195, F = -.292, and E = .072

This suggest a decrease return to scale in corn production. Corn farmers could lower all inputs and total cost would fall by a lower percentage than output

Results The derived matrix of substitution elasticities

following (4) and (5) is

KK KL KF KE -0.33 0.36 0.51 0.04 LK LL LF LE = 0.90 -3.38 -2.06 0.21 FK FL FF FE 0.81 1.03 -1.44 .002 EK EL EF EE 0.92 1.32 -0.18 -0.75

There is limited substitution potential when energy prices rise in fuel production

The own energy substitution elasticity of -0.75 implies that a 10% increase in the price of diesel will reduce diesel input only 7.5% and expenditure will rise 2.5%

Results The results show a weak substitution toward labor input with

labor input rising 2.1%

There is virtually no substitution of capital or fertilizer for energy

Corn producers respond more to rising wages. If slower labor immigration raises wages on the farm by 10% there would be a 33.8% reduction in labor input and a 23.8% reduction in the labor bill

There would be strong substitution toward energy input with a 13.2% increase. Corn farmers can substitute energy for labor to a high degree

Fertilizer substitution has near unit value and fertilizer input would match the wage increase in percentage terms

Results There is much less substitution of capital for labor

Combining a 10% increase in the wage due to tougher immigration policy with a 10% increase in the price of energy, labor input falls 31.7% and energy input rises 4.7%. The labor bill would fall 21.7% but the energy bill would rise 14.7%

Higher fertilizer prices have an elastic own effect with enough substitution that fertilizer spending falls with a higher price. Labor and energy inputs also falls with higher fertilizer prices

Energy input substitutes for capital and labor but is a complement with fertilizer

Conclusion The present estimates predict corn producers will spend

more on energy as energy prices rise

An increasing price of diesel only inelastically lowers diesel input while raising labor input

Corn farmers are sensitive to wages, however, they will substitute energy for labor as wages rise

The combination of tougher immigration laws with rising diesel prices leaves little room for substitution

The estimated decreasing returns to scale suggests overproduction of corn

If subsidies are cut as fuel prices rise over the coming decades, the present model of substitution predicts a substantial decrease in US corn production