Consider a monopolist producing at dates t = 1,2. The good that it produces is perishable in that it will not last beyond one period. Therefore, the demand in each period is unaected by past and future periods. The inverse demand curve in period t as a function of the period t quantity qt is denoted pt(qt). If q1 is the number of units produced in period 1, the monopolist incurs a cost of C1(q1) that exhibits decreasing returns of scale. The cost of production in the second period depends on both the amount produced in period 2 as well as period 1. If q2 is the number of units produced in period 2 given q1 units produced in period 1, the cost incurred will be C2(q1,q2). This second period cost is increasing in q2 holding q1 xed. It exhibits decreasing returns to scale in q2, holding q1 xed. However, C2(q1,q2) is decreasing in q1 holding q2 xed. This captures the idea of 'learning by doing'.

1. Write down the monopolist's total prot as a function of q1 and q2.

2. Write down the rst order conditions for optimality.

3. Let p be the price that maximizes rst period prots only. Explain why this price will be higher than the optimal rst period price from part (2).