solution

Ethanol, which is distilled from corn, is blended into gasoline, (allegedly) to burn cleaner and to increase the supply of fuel. Given that ethanol is a close substitute for gasoline, its price in a competitive market would be closely tied to the price of gasoline. However, ethanol usually costs more to make than gasoline, so its usage depends on federal incentives and clean-air legislation mandates for oil companies to use cleaner fuels.

a. Suppose that without federal clean-air legislation mandates, ethanol and gasoline are perfect substitutes. Derive the wholesale-market demand function for ethanol. How does this market demand function depend on the price of gasoline?

 b. Suppose that federal clean-air legislation mandates that at least 5% of automobile fuel must contain ethanol. Derive the wholesale-market demand function for ethanol.

c. Compare the wholesale-market demand functions of parts a and b.

d. Suppose that for any refining plant output, q gallons per day, the marginal cost of ethanol refining, MC_e(q), is greater than the marginal cost of gasoline refining, MCg(q). Compare the wholesale market supply functions of ethanol and gasoline. Show that if the wholesale price of gasoline is sufficiently low, federal mandates are needed to ensure that ethanol is produced, but that if the price of gasoline is sufficiently high, federal mandates are not needed.