The following data are available for output (Q) and Long Run Total Cost (LTC) for a firm. Using appropriate calculations determine the range of outputs over which the firm's technology exhibits Increasing, Decreasing or Constant Returns to Scale.

Q LTC
1 33
2 54
3 75
4 100
5 150
6 228
7 350

1. (i) A competitive firm's total cost function is given by

TC = .25Q2 + 25
(with MC = .5Q).
The firm faces a market price of $15. Algebraically calculate the profit maximizing output and the level of optimal profit for the firm.

(ii) Suppose that fixed costs increase by $50 but the prevailing market price remains unchanged. Using algebra determine the effects of this change in cost on the profit maximizing output and the optimal profit. Do you see any change from your answer to (i) above? Explain why or why not.

2. A monopolist's demand function is given by

P = 80 - 3Q
(with MR = 80 - 6Q).

Its total cost function is

TC = 20Q + 200
(with MC = 20).

(i) Using algebra determine the profit maximizing output, price and optimal profit for the firm.

(ii) Suppose that instead of maximizing profit, the firm wants to maximize total revenue. Using algebra determine the optimal output, price, profit and revenue for the firm.