1. Suppose a firm has the total cost function T C = 3/8Q^2 + 400(a) Is this firm in the short run or long run?
(b) Suppose this firm is facing a perfectly competitive marketwhere the price is P = 24. What is the firm’s marginal revenue?
(c) Write the firm’s profit function and solve for theprofit-maximizing quantity of production Q∗ . (3 points) (d) Howmuch profit does the firm make at the profit-maximizing level ofoutput? (1 point) (e) Write an equation for the firm’s short runaverage variable costs (AV C). (1 point) (f) Write the conditionfor whether a firm should continue to operate or shut down. Shouldthis firm shut down? If not, when should it shut down? (2points)
2. Suppose a firm faces an inverse demand curve P = 6 − 1/2Q andhas a total cost function T C = 1/4Q^2 − Q. (a) Is this firm aprice-taker or does it have market power? Explain. (2 points) (b)Write an equation for the firm’s profit function. (1 point) (c)Solve for the firm’s profit-maximizing level of output, Q∗ . (2points) (d) What price does the firm sell its product at? (1point)
