Suppose the demand for (blended) fuel F, can be given by the following demand function:

P=200-4F

Fuel retailers are indifferent between using corn derived ethanol E, and crude oil derived gasoline G, in the fuel they sell to consumers. To produce blended fuel, assume ethanol is splash blended in tanker trucks at no additional cost and there are no limits to how much ethanol can be blended into fuel. This fuel retailers are willing to supply fuel according to:

F=E+G

Assume that fuel retailers are the only demanders for ethanol and gasoline.

Ethanol supply is given by:

S=1.45+6E

Gasoline supply is given by:

GS=1.25+2G.

For simplicity suppose fuel, ethanol, and gasoline are all denominated in the above in energy equivalent gallons of gasoline (hereafter, supply 'gallons'). Suppose all of the gasoline that is supplied is from crude oil imported from abroad.

Suppose corn growers in Iowa convince the government to subsidize ethanol by $4.50/gallon.

Relative to the nosubsidy, competitive market equilibrium:

a. What is the change in producer surplus to ethanol producers due to the subsidy?

b. What is the change in producer surplus to gasoline producers due to the subsidy?

c. What is the change in fuel demander's consumer surplus due to the subsidy?

d. What is the final bill to taxpayers for the subsidy?

e. What is the change in total welfare due to the subsidy?

f. Iowa corn growers argued that the subsidy would help 'reduce our dependence on foreign oil.' This is the same thing as saying that they believe there is an additional societal benefit for each gallon of gasoline displaced by the subsidy relative to the competitive market equilibrium, given our prior assumptions. Suppose this is the case. Is the ethanol subsidy a good way to achieve this goal? Why or why not? 

g. How large would the benefits from reducing oil dependency (per gallon of gasoline displaced) need to be to justify the welfare loss due to the subsidy?