1. (10 points) Suppose the market for car batteries is a perfectly competitive m
ID: 1139179 • Letter: 1
Question
1. (10 points) Suppose the market for car batteries is a perfectly competitive market, but that the production of car batteries creates external costs from water pollution. Recall that in a perfectly competitive market, the supply curve is part of the industry's marginal private cost curve, and that the demand curve is the marginal (social) benefit curve. The equation for the marginal social benefit is SMB 220-0.20 The equation for the industry's marginal private cost is PMC-40+0.20. The equation for the industry's marginal external costs is EMC 0.060 So that the equation for the industry's marginal social cost is SMC 40+0.160 a. Calculate the price and quantity at the industry's free-market equilibrium. b. Calculate the quantity and the price that consumers would pay at the efficient rate of production when SMB- SMC c. Calculate the efficient size of a corrective (Pigouvian) tax per car battery d. Calculate the size of the deadweight loss at the free-market equilibriunm SMC 220 PMC SMB 40Explanation / Answer
a) For the free market, equate PMC = EMC. That is, 40+0.2Q = 0.16Q => 40 = 0.14Q => Q = 285.71 and price will be equals to EMC, that is 45.71.
b) SMB = SMC, => 220-0.2Q = 40+0.16Q => 180 = 0.18Q => Q = 1000. And price will be equals to SMC, that is 200.
c) Let the effective tax rate is t per unit, tQ so 40+0.2Q = 0.16Q+tQ. And put the Q equals 285.71. t will come out to = 18% (Approx.)
d)
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