Question

US corn production is used primarily to feed cattle and hogs to produce meat for human consumption and to produce biofuels. Suppose the demand for corn as livestock feed is given by: Qfeed=24.5-4P ,where quantities are in billions of bushels and the price, P, is in dollars. The US government mandates that a fixed percentage of US gasoline be blended with ethanol-based biofuel.

Assume this mandate fixes the total quantity of corn used for domestic fuel production at 10.5 m. bushels per year. Assume the U.S. supply of corn is given as Qs=3P

Suppose the government decides to eliminate the biofuels mandate. The demand for corn by ethanol producers is given as, Qfuel=12-10P (in the absence of any mandate).
(c) Derive the producer surplus in the US corn market with and without the mandate. Are producers better or worse off under the biofuels mandate?
(d) In your opinion, is the biofuels mandate a regressive or progressive policy? Explain your answer.

Answer 1

c) Q s = 3P.

Under mandate Q d = 10.5 + 24.5 - 4P = 35 - 4P

Qs= Qd => P* = 5, Q* = 15.

Producer surplus = P* . Q* - 1/2 P*. Q* = 37.5

Without mandate,

the demand of corn as livestock feed is much higher than the demand of corn for biofuels. Hence only that market will be served as they are willing to pay a higher price. ( As a proof, you can try adding up the demands and solve for P, if you then put the equilibirum P in the demand equation for corn by ethanol producers you'd get negative demand, hence that market will collapse, and only the demand of corn for feed remains.)

Hence, Q d = 24.5 - 4 P.

3P = 24.5- 4P => P*=3.5

Q* = 10.5

Producer surplus = P* . Q* - 1/2 P*. Q* = 18.375.

Essentially under the mandate there is a shift of the Q feed curve to the right by the amount 10.5 m.

Hence producers are better off under the mandate.

d) It is a progressive policy since it is better for the environment and if the mandate is not imposed the biofuels would not be produced at all. The consumers, are in a way worse off as they are having to pay a higher price but it is the price they are having to pay for the production of a clean good.