Consider a monopolist that produces for two periods. The demand curves in both periods are qe = 1-pt for t = 1,2. The marginal costs are c in the first and and c-lg" in the second period. Here, I is a small and positive number. There is a discount factor of 8 between the periods.
1. Explain briefly how the monopolist's problem changes compared to a situation where the marginal cost is c in both periods.
2. Find the quantities q' and g? that the monopolist chooses in the two periods. Hint: Start by solving the monopolist's problem in the second period and then continue to the first period.
3. Derive the restriction on that ensures that the profit function is strictly concave