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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 + 0.2Q.
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.
Expert Answer
A)
In perfectly competitive market , Equilibrium is established where Demand =supply
SMB = Demand
PMC = Supply
Hence;
220 – 0.2Q = 40 + 0.2Q
220 -40 = 0.2Q +0.2Q
180 = 0.4Q
Q = 180/0.4
=450
Price = 220 – 0.2(450)
= 220 – 90
= $ 130
b)
Socially Optimal level of output ;
SBM = SMC
220 – 0.2Q = 40+0.26Q
180 = 0.46Q
Q = 180/0.46
= 391.30
P = 220 – 0.2(391.30)
= 220- 78.26
= $141.76
Note: SMC = MPC + EMC
it should be 40 +0.26Q
