Throughout this problem, the following is true:

The representative firm has a cost function of c(q) = 200 + 2q2

Market Demand is given by P = 390 1Q

Use this information to answer the following 3 problems:

1)Perfect Competition in the short-run:

If there are 9 identical firms all profit maximizing, calculate equilibrium market price P* and Quantity Q*, individual firm optimal q*, and profits for the individual firm. [4 marks]

2)

Perfect Competition in the long-run:

Given the profits in (1), determine the long-run equilibrium number of firms N* and the new equilibrium market price P* and Quantity Q*. [3 marks]

3)Suppose a single representative firm is able to obtain the exclusive right/ability to produce this good and becomes a Monopoly (this means that q = Q for the cost function above). What Q will they choose to maximize profits? What price will they charge? Are their profits higher or lower than all profits of the firms combined in (1)? Show your work. [3 marks]