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A steel plant produces S tons of steel, at a total cost of S2 + X2...

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Economics

A steel plant produces S tons of steel, at a total cost of S2+ X2 - 8X dollars, where X denotes the number of gallons ofpollution that the plant dumps into a lake. On the same lake, afish farm produces F tons of fish, at a total cost of F2 + X2dollars. The market prices per ton are fixed at $4 for steel and$10 for fish.

A. Assuming that the two producers do not negotiate anagreement on the amount of pollution, find the equilibrium level ofX.

B. Derive the socially optimal level of X.

C. Suppose that the government imposes a tax of t dollars pergallon of pollution dumped by the steel plant. Calculate the valueof t that leads to the socially optimal level of X.

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