Suppose U.S. Steel has a steel factory on the Monongahela River in Southwestern

Question

Suppose U.S. Steel has a steel factory on the Monongahela River in Southwestern PA. Suppose further that steel is sold in a competitive market at a price of $5 per unit. The private marginal cost of steel production is MC(s) = 2 + 0.5s. The factory produces wa-ter pollution that causes economic damages to the Monongahela River Kayak Association (MRKA). These damages can be represented by the function MEC(s) = 2.

a) What is the producer surplus in market equilibrium? What is the external surplus? Calculate the deadweight loss.

b) Suppose the MRKA successfully petitioned for the right for clean water on the river and U.S. Steel is liable for damages in court. What would be steel output given the property rights regime if U.S. Steel wants to maximize their own surplus? Will there be transfers between U.S. Steel and MRKA? Calculate producer surplus, external surplus, and deadweight loss under this level of output.

Explanation / Answer

P = $5

MC(s) = 2 + 0.5s

MEC(s) = 2.

a. The producer will Produce till, P =MC

$5 = 2 + 0.5s

s = 6

Producer Surplus = 1/2(Price - Vertical intercept of MC)*Quantity

= 1/2(5 - 2)*6

= 9

External surplus = 1*6 = 6

b.

For social optimal

P = MC + MEC

5 = 2 + 0.5s + 2

s = 2

Producer Surplus = 1/2(5 - 4)*2

= 1

External Surplus = 1*2 = 2

Dead Weight Loss = 1/2 change in price*change in Quantity = 1/2 (5 - 3)(6 -2) = 4

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