Consider a monopolist selling computer software. Software is of high or low quality and is chosen by Nature: quality is high with probability ρ and low with probability 1 – ρ. Consumers can buy the software in period 1 and consume it in periods 1 and 2, where the discount factor is δ < 1. Software is produced at fixed cost F_i and marginal costs c_i, i = H, L. The software producer learns quality before period 1 whereas consumers only learn the quality after purchase. Each consumer has the same willingness-to-pay r_H for high quality and 0 for low quality. There is mass M of consumers.

1. Suppose ρr_H ≥ c_H and (1 + δ) (r_H - c_H)^M- F_H < 0 but (1 + δ) (ρr_H - c_H)^M- F_H < 0. What is the equilibrium in this market? Interpret your result. Compare your result to the solution under full information.

2. Suppose now that consumers can copy the software at an opportunity cost p^c and value the copy at r^c_i with r_H > r^c_H > r^c_L= 0, i.e., copies of high- quality software are an imperfect substitute for the original. Suppose that (1 +δ)rc_H > p^c and r_H - r^c_H > max{c_L, c_H} for a share λ of consumers who are considering to copy the product (“pirates”). The remaining share 1 – λ will never copy the software. Copiers learn the product quality after period 1 and have the option to buy the product in period 2 given the price set in period 2. Is it possible that the firm is better off under the presence of copying compared to the situation where λ = 0? Prove your answer formally. What is the intuition?

3. Discuss what would happen if the firm could choose the degree of copyright enforcement λ (without any cost). What is the optimal level of copyright protection? Provide some intuition and discussion without necessarily doing the calculations.