Farmers’ Supply Response, Price of Corn Residue, and Its Economic Viability as an Energy Feedstock

Abstract

Previous economic analyses of energy from corn stover assumed yield reductions from residue removal (without nutrient replacement) and limited or no supply response by farmers to changes in the price of stover. We exploit agronomic and cost information from a randomized block design experiment to model and quantify farmers’ supply response to changes in relative prices of corn stover, corn grain, and soybean. We then couple this supply response with a model of a cost-minimizing processing plant. Results suggest that stover-based energy may be closer to economic viability than previously found. In addition, in areas where reductions in corn yield due to corn monoculture are small, processing plants may find optimal to pay a higher price for stover to induce farmers to adopt continuous corn because it reduces transportation cost. This suggests that such areas may experience changes in their land cover configuration if stover-based energy does become commercially viable.

Appendices

Appendix 1

Proof of proposition

CRCR will dominate CRCN if and only if

$$ {\pi_{\mathrm{CR}\mathrm{CR}}}-{\pi_{\mathrm{CR}\mathrm{CN}}}=y_{\mathrm{CR}}^c\ {p_c}-c_{\mathrm{CR}}^c+\left( {2y_{\mathrm{CR}}^c-y_{\mathrm{CN}}^c} \right)\left( {0.8} \right)\left( {0.85} \right)p_s^{{\mathrm{CR}\mathrm{CR},\ \mathrm{CRCN}}}-2c_{\mathrm{CR}}^s+c_{\mathrm{CN}}^s-y_{\mathrm{CN}}^c\ {p_c}+c_{\mathrm{CN}}^c\geq 0 $$

Where $y_{\mathrm{CK}}^c$ is continuous corn after residue was removed (K = R or was not removed (K = N, $\left( {K=N} \right)c_{\mathrm{CK}}^c$ is the (per hectare) cost of producing corn after corn with residue removal or without residue removal $\left( {K=N} \right)c_{\mathrm{CK}}^c$ is the (per hectare) cost of harvesting stover producing corn after corn with residue removal (K = R or without residue removal (K = N

Rearranging this expression yields:

$$ p_s^{{\mathrm{CR}\mathrm{CR},\ \mathrm{CRCN}}}\geq \frac{{-\left( {y_{\mathrm{CR}}^c-y_{\mathrm{CN}}^c} \right){p_c}+\left( {c_{\mathrm{CR}}^c-c_{\mathrm{CN}}^c} \right)+2c_{\mathrm{CR}}^s-c_{\mathrm{CN}}^s}}{{\left( {2y_{\mathrm{CR}}^c-y_{\mathrm{CN}}^c} \right)\left( {0.8} \right)\left( {0.85} \right)}} $$

If residue removal increases yield ($y_{\mathrm{CR}}^c>y_{\mathrm{CN}}^c$), we can re-express yield under CRCR as $y_{\mathrm{CR}}^c=y_{\mathrm{CN}}^c+\varDelta$, where Δ is a positive number. Let us assume that the cost of harvesting stover is independent of past rotations ($c_{\mathrm{CR}}^s=c_{\mathrm{CN}}^s$). Therefore:

$$ p_s^{{\mathrm{CR}\mathrm{CR},\ \mathrm{CRCN}}}\geq \frac{{-\left( {y_{\mathrm{CR}}^c-y_{\mathrm{CN}}^c} \right){p_c}+\left( {c_{\mathrm{CR}}^c-c_{\mathrm{CN}}^c} \right)+c_{\mathrm{CN}}^s}}{{\left( {y_{\mathrm{CN}}^c+2\varDelta } \right)\left( {0.8} \right)\left( {0.85} \right)}} $$

CNCN will dominate CRCN if

$$ {\pi_{\mathrm{CN}\mathrm{CN}}}-{\pi_{\mathrm{CR}\mathrm{CN}}}=y_{\mathrm{CN}}^c\ {p_c}-c_{\mathrm{CN}}^c-y_{\mathrm{CN}}^c\left( {0.8} \right)\left( {0.85} \right)p_s^{{\mathrm{CN}\mathrm{CN},\ \mathrm{CRCN}}}+c_{\mathrm{CN}}^s-y_{\mathrm{CR}}^c\ {p_c}+c_{\mathrm{CR}}^c\geq 0 $$

Rearranging this expression yields:

$$ p_s^{{\mathrm{CN}\mathrm{CN},\ \mathrm{CRCN}}}\leq \frac{{-\left( {y_{\mathrm{CR}}^c-y_{\mathrm{CN}}^c} \right)\ {p_c}+\left( {c_{\mathrm{CR}}^c-c_{\mathrm{CN}}^c} \right)+c_{\mathrm{CN}}^s}}{{y_{\mathrm{CN}}^c\left( {0.8} \right)\left( {0.85} \right)}} $$

CRCN will be dominated by either CRCR or CNCN if $p_s^{{\mathrm{CNCN},\ \mathrm{CRCN}}} > p_s^{{\mathrm{CRCR},\ \mathrm{CRCN}}}$, and this inequality will hold if and only if Δ is positive.

Appendix 2

Table 3 Corn stover removal partial budget