Question

6. (16 points) Suppose we realize that the market described in question 1 (Market demand is still Q = 18 – P) has a negative externality. The cost function C(Q) = Q2 is private cost. We now know the cost of the externality is Ca(Q)=Q?. a. What is the marginal cost of the externality, MCE? b. What is the marginal cost to society of production MCS? c. What is the Socially Optimal quantity and price? d. How does the socially optimal quantity compare to the competitive market equilibrium quantity you found in question 1.b? e. How does the socially optimal quantity compare to the monopoly quantity you found in question 1.c? f. In this case, does market power increase or decrease total social welfare? 8. Suppose the government wanted to tax a monopoly in this market with a negative externality. How much should a unit tax t be to arrive at the socially optimal quantity you calculated in partc?

Answer 1

MCp = dCp/dQ = Q

Q = 18 - Q

(a)

MCE = dCE/dQ = 2Q

(b)

MCS = MCp + MCE = Q + 2Q = 3Q

(c)

In social optimum, P = MCS

18 - Q = 3Q

4Q = 18

Q = 4.5

P = 18 - 4.5 = 3.5

(d)

In competitive equilibrium, P = MCp

18 - Q = Q

2Q = 18

Q = 9

P = 9

So, socially optimal price is lower and output is lower.

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