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 productB 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 independently. We assume whenever indifferent, consumers buy from the firm that can slightly reduce its
Second, suppose that firm 2 uses pure bundling and set a bundle price p2AB. Firm 1 still sets price p1A for product A (which may differ from what was found in [b.]).
5. Calculate a consumers’ payoff of buying only product A from firm 1 (and therefore don’t buy B) when the prices are given by p1Aand p2AB.
6. Calculate a consumer’s payoff of buying the bundle from firm 2 when the prices are given by p1A and p2AB.
7. When will consumers prefer buying the bundle from firm 2 instead of buying only A from firm 1 (identify a suitable range for p2AB ).
8. What p2AB will firm 2 set? What p1A will firm 1 set?
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