about game theory,

1. There is a monopoly company operating over two periods. For each period, the market demand curve is p(q)=abq , and the production cost of one period is c1>0 . The marginal cost of production of the second unit decreases with the output of the first unit, so that c2=c1mq1 . (This is called "learning by doing" and means that more efficient production becomes possible by the experience of first production.) a>c and b>m . In addition, the monopolist maximizes the sum of profits for each period (no discount over time).

(a) How much output does the monopoly take for each period to maximize the sum of its profits?

(b) If a policy maker who wants to maximize social welfare decides both the first and second periods of the monopoly company, what will happen to each output?

(c) If the monopoly company decides the output for the second period and the policy maker decides only the output for the first period, what quantity will be selected?