1.(10 points) Suppose the market for car batteries is a perfectly competitive ma

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 – 0.2Q. The equation for the industry’s marginal private cost is PMC = 40 + 0.1Q. The equation for the industry's marginal external costs is EMC = 0.06Q. So that the equation for the industry's marginal social cost is SMC = 40 + 0.16Q. 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 equilibrium.

Explanation / Answer

In market equilibrium, SMB = PMC

220 - 0.2Q = 40 + 0.1Q

0.3Q = 180

Q = 600

P = 220 - (0.2 x 600) = 220 - 120 = 100

In efficient outcome, SMB = SMC

220 - 0.2Q = 40 + 0.16Q

0.36Q = 180

Q = 500

P = 220 - (0.2 x 500) = 220 - 100 = 120

(c) When Q = 500:

SMC = 40 + (0.16 x 500) = 40 + 80 = 120

PMC = 40 + (0.1 x 500) = 40 + 50 = 90

Corrective Pigouvian tax = SMC - PMC = 120 - 90 = 30

(d) When Q = 800, PMC = 100 & SMC = 40 + (0.16 x 800) = 40 + 128 = 168

Deadweight loss = (1/2) x (168 - 100) x (800 - 500) = (1/2) x 68 x 300 = 10,200

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