# Question & Answer: Suppose the market for car batteries is a perfectly competitive market, but that the production of car batteries creates externa…..

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.

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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