Suppose That Firms Compete In Prices

Consider a duopoly in which homogeneous consumers of mass 1 have unit demand. Their valuation for good i = 1 2

Question

Consider a duopoly in which homogeneous consumers of mass 1 have unit demand. Their valuation for good i = 1; 2

is v(i) = vi with v1 v2. Marginal cost of production is assumed to be zero. Suppose that firms compete in prices.

1. Suppose that consumers make a discrete choice between the two products. Characterize the Nash equilibrium.

2. Suppose that consumers can now also decide to buy both products. If they do so they are assumed to have a valuation v(1, 2) = v12 with v1 + v2 v12 v1. Firms still compete in prices (each firm sets the price for its product- there is no additional price for the bundle) Characterize the Nash equilibrium.

Economics