EC: 434/534 Environmental Economics Homework 1

EC: 434/534 Environmental Economics Homework 1

Consider the market for footballs. Suppose the demand for footballs is given by F = 50 P − 1. (1)

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Suppose further that the marginal private cost of producing footballs is $10 per football.

Also assume that pollution from the leather tanning process is generated in proportion to the number of footballs made. The external marginal damage from the pollution is $15 per football produced. a) Suppose the football market is competitive. What price will the market generate, and how many footballs will be produced/consumed? b) In the outcome in a), calculate i) consumer surplus, ii) producer surplus, and iii) total surplus. Now consider the possibility that each football produced generates a different external marginal cost. We can represent the new MEC as MEC(F) = 2F (2) c) Given this external cost, calculate total surplus. d) Suppose the firm producing footballs acted as if the external cost was their own (internalizing the externality). Calculate i. The new market equilibrium ii. Consumer surplus iii. Producer surplus iv. Total surplus 1 2). Consider a valley where only two consumers live: Walt and Jesse. Suppose Walt’s demand for clean air is given by qW (p) = 1 − p where p is Walt’s marginal willingness to pay for clean air. Jesse’s demand is given by qJ (p) = 2 − 2p. Clean air can be supplied according to the supply function q(p) = p, where p is the marginal cost of production. a) Suppose, hypothetically, a competitive market for clean air existed and a firm supplied clean air according to the function above. How much clean air would be produced by the market? (What is the private market equilibrium?) b) Graph the aggregate inverse demand for air quality along with the individual inverse demand functions. c) What is the efficient amount of air quality? 3). 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 water 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. 2

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