1. (20) Suppose that you sell shamrock t-shirts for St. Patrick’s Day. The market for these t-shirts is

perfectly competitive. Your short-run cost function is given by:

C(q)=5.4+(W +t+0.25)q+0.10q^3
where W is the wholesale price of each t-shirt and t is the shipping price of each t-shirt. Assume

that W = 0.50 and t = 0.25.

(a) (5) What is your short-run marginal cost function (as a function of q)?
(b) (5) How high must the retail price be for you to sell a positive quantity of t-shirts in the short-run (if no costs are sunk)?
(c) (5) What is your short-run supply function?
(d) (5) Show your answer to (b) and (c) graphically. Include all relevant cost curves in your graph.

2. (30) Suppose now that you now sell Duke t-shirts for March Madness. Demand for these t-shirts is given by:

q(p) = 20, 000 − 20p
You are lucky enough to be the only seller of Duke t-shirts in the entire country. Your costs are

given by:

C(q) = 2, 000 + 5q

(a) (4) What is your revenue function? What is marginal revenue?
(b) (6) What is your revenue maximizing q∗ and p∗?
(c) (8) Show your answers to (a) and (b) graphically. Use two side-by-side graphs. The left graph should include demand and marginal revenue. The graph on the right should include total revenue.
(d) (8) What is your profit function? What is your profit maximizing q∗ and p∗?
(e) (4) Calculate profits under revenue-maximizing and profit-maximizing behavior.

(20) Suppose that you sell shamrock t-shirts for St. Patrick’s Day. The market for these t-shirts is