Question

There are two firms. Firm 1 (or, a small firm) produces a single product, product A, at zero cost. Firm 2 (or, a big firm) is a multi-product firm that sells both products A and B. Firm 2 is less efficient in producing A. It incurs a constant marginal cost c > 0 for producing A. However, firm 2 is a monopolist of the market of product B and its cost of producing product B is zero.

A unit mass (i.e. a total measure of 1) of consumers all have the same preference which is known to producers, and view the two products as independent. To consumers, the value of product A is vA > c while the value of product B is vB > 0. If a consumer buys both products, the gross payoff is vA + vB . (Note that, unlike in the lecture slides where consumers are heterogenous and their values are distributed in [0, 1], here the setting is simpler and all consumers are homogenous and have the same vA and vB)

Firms compete in prices and set their prices simultaneously and inde- pendently. We assume whenever indifferent, consumers buy from the firm that can slightly reduce its price without making a negative profit.

Firstly, suppose firm B separately sets prices for the two products.

1. What price p2B does firm 2 set for product B?

2. The two firms basically engage in Bertrand competition in the market for product A. What are the equilibrium prices p1A and p2A

3. Based on [a.] and [b.], calculate both firms’ profits π1 and  π2？

4. What is the consumer surplus, CS?

Answer 1

Pa ho;- с solution - Sees From given, @ And here, Consumer the value of vB f Cost of making B is o for from 2, P2B = VB 1 is o 6 And since the cost of making A for from and from 2 is c Then here, If from sells at lower cost than from 2, from 1 takes away the whole market. In Bertrand Competition to avoid this, PLA = P2A = VA. Then © 711 - sold price - Cost poice T 1 VA -0 O 14 = VA. 119A en Cost poice. sold price VA -c. - Cost price TT2B = sold poice VB-O = VB. T = T 2A + T2B VA + VB-C

ognoj- And we get here, The consumer surplus = consumer surplus of A + Consumer suo plus of B =(A-c)+ (VB-0) :: The Consumer surplus, - VA VB-C,