(Prices as signals of quality). Assume that a firm is a monopolist that produces a good of quality . The firm knows the quality, the consumers do not....

(Prices as signals of quality).

Assume that a firm is a monopolist that produces a good of quality θ.

The firm knows the quality, the consumers do not.

If quality were observable, the firm would face a demand curve Q = θ−P.

Quality can be either high (θ = 2) or low (θ = 1). The marginal cost to the

firm of producing a low quality good is zero. The marginal cost of producing

a high quality good is c > 0. There is no fixed cost. The firm chooses

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prices as a function of θ. Denote by µ(P) be the probability that consumers

assign to the good being high quality given a price P. The demand curve is:

Q = 2µ(P) + (1 − µ(P)) − P

(i) First find the full information optimal prices and compute profits.

(ii) Find a c∗ such that for c>c∗, the full information optimal prices

constitute a separating equilibrium.

(iii) Assume now that c<c∗. What is the price that will be chosen by a

low quality firm in a separating equilibrium? Find the lowest price charged

by the high quality firm in a separating equilibrium. Does a separating

equilibrium always exist?