Two firms compete in a Bertrand marketto produce a good.

Inverse demand is given by:P=100Q

Marginal cost of each firm is given by:MC=20

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(a) (4 points) How much of the good is produced by *each* of the firms in equilibrium?

(b) (6 points) The production of the good generates an externality that depends on the amount produced.The marginal external costs (MEC) (i.e., the externality) is given by MEC = Q.Thus, the marginal social costs for the industry are:MSC=MC+MEC=20+Q

.

Given this, what is the socially optimal price and quantity?

(c) (6 points) What is the optimal Pigouvian tax to charge the two Bertrand competitors?

(d) (10 points) Would your answer to part (c) change if the two firms were instead a monopoly?If not, briefly explain why not.If so, what is the optimal tax?