Suppose that a monopolist produces two products, product 1 and product There is a mass 1 of consumers. A share λ of consumers are heterogeneous among each other and are described by their type θ. This type is distributed uniformly on the unit interval. The willingness-to-pay for product 1 is assumed to be r₁ = θ and r₂ = 1 – θ. A share (1 – λ) = 2 of consumers has willingness to pay r₁ = 2/3 and r₂ = 0. The remaining share (1 – λ)=2 of consumers has willingness to pay r₁ = 0 and r₂ = 2/3. The firm can sell products 1 and 2 independently at prices p₁ and p₂, respectively. Alternatively, it may only sell a bundle at price p. This is a situation referred to as pure bundling. A third possibility is that the firm sells the bundle and the independent products, a situation referred to as mixed bundling.

1. Suppose that λ = 1. Determine whether independent selling, pure or mixed bundling are profit maximizing. Calculate associated prices and profits.

2. Suppose that λ > 0 and characterize the solution under independent selling for all λ > 0.

3. Suppose that λ = 4/5. Characterize the profit-maximizing solution under independent selling, pure bundling, and mixed bundling. Show which of the selling strategies is profit-maximizing. Discuss your result.

4. Repeat the previous question with λ = 2/3.