Consider a monopolist that produces for two periods. The demand curves in both periods are q^t = 1-p^t for t = 1; 2. The marginal costs are c in the first and c – λq¹ in the second period. Here, λ is a small and positive number. There is a discount factor of 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 q¹ and q² that the monopolist chooses in the two periods. 

3. Derive the restriction on λ that ensures that the profit function is strictly concave.