Suppose the market for car batteries is a perfectly competitive market, but that
ID: 1142127 • Letter: S
Question
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.
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 equilibrium.
Explanation / Answer
a)
SMB = 220 – 0.2Q.
PMC = 40 + 0.1Q.
Equilibrium ; 220 - 0.2Q = 40 +0.1Q
180 = 0.3Q
Q = 180 /0.3
= 600
P =220 - 0.2(600)
= 220 - 120
= $ 100
Equilibrium Q = 600
Equilibrium P = $ 100
b)
Efficient Rate of production;
SMB = SMC
220 - 0.2Q = 40 + 0.16Q
180 = 0.36Q
Q =180/0.36
= 500
P = 220 - 0.2(500)
= 220 - 100
= $ 120
Efficient level of Q = 500
Efficient Level of P = $ 100
c)
Size of Pigouvian tax per car battery; EMC = 0.06(Q)
Tax per unit = 0.06(500)
= $ 30
d)
Size of DeadWeightloss = 0 .5 ( 120 - 100) (600 - 500)
= 0.5 (20)(100)
= 0.5 (2000)
= 1,000
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