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

3. Compare regimes from parts (1) and (2) with respect to consumer surplus. Comment on your results.