Question

1. Consider a monopolist selling a product in two markets, 1 and 2. For each i ∈ {1, 2}, let yi be the demand in market i and pi the price in market i. The inverse demand for market 1 is p1(y1) = 10 − 2y1 and the inverse demand for market 2 is p2(y2) = 6 − y2. To produce, the monopolist should pay a fixed cost of 1 and a constant marginal cost of 2.

(a) Let y be the total quantity produced by the monopolist. Find the cost of producing y units.

(b) The monopolist is wondering if he can use third-degree price discrimina- tion. Under what assumptions is this possible? (It is enough to write down one key assumption.)

(c) When the monopolist uses third-degree price discrimination, how much does he sell in each market and what is his profit?

(d) When the monopolist cannot price discriminate (that is, when he charges a single price to both markets), how much does he sell in the two markets and what is his profit? How does the maximum profit in this case compare to the maximum profit in part (c)?

(e) A correct solution to parts (c) and (d) would say that the total quantity sold by the monopolist does not change, regardless of whether he price discriminates or not. But the maximum profits in (c) and (d) are different. Is this puzzling? Explain.

2. Consider the following two-player game

Answer 1