The U.S. demand for sweat-trapping headbands is summarized by the function qd = 1200- p, where p is the market price of a headband. There are currently 49 identical, prot- maximizing domestic headband producers in the U.S., each with the cost function TC(q)= 72 + 0.5q2. U.S. consumers consider domestically produced headbands to be identical to foreign-produced headbands, and currently have access to a huge supply of foreign-made handbands at a constant price of $10 per band (that is, we can think of the worldwide supply of sweat-trapping headbands as a horizontal curve at p = 10).

(a) Write down an expression for the supply curve for an individual domestic headband producer. If there is perfectly free international trade in sweat-trapping headbands, what will be the market price of a headband in the U.S.? How many headbands will be purchased in the U.S.? How many of those will be imported from abroad? 

(b) What will be the profits of each domestic headband producer? What will be the total profits earned by firms in the U.S. domestic headband industry? Assume, for now, that the number of domestic producers remains fixed at 49. Illustrate your answer with two diagrams: one showing the profit-maximization decision of an individual domestic firm, the other showing the entire U.S. headband industry.

(c) What do you predict would happen to the U.S. domestic headband industry in the long run?

(d) Suppose the U.S. government passes a dramatic new trade bill, the Sweat- Trapping Headbands Industry Protection Act of 2009, outlawing all imports of foreign- made head-bands. If the number of domestic headband producers remains fixed at 49, what will be the new market price of a headband? How many headbands will be purchased in the U.S.?

(e) What will be the profits of each domestic producer after the new law is passed? What is the total increase in profits in the domestic headband industry as a result of this new trade law? Depict  graphically the change in consumer surplus for headband buyers in the United States as a result of this policy as compared to your answers in (a). Under which scenario will consumer surplus be larger?

(f) Assuming that the law described in (d) remains in force, but that there is free entry and exit in the domestic headband industry over time, what do you predict will be the long-run market equilibrium price? How many sweat-trapping headbands will be sold in the U.S.? How many headband-producing firms will there be in the U.S. in the long run?

(g) Suppose that instead of the bill described in (d), the U.S. government decides to pass a less extreme law, assessing a t% tax on all imports of foreign headbands. How large must t be (5%? 10%? etc.) in order to ensure that the 49 existing domestic producers can remain in business in the long run?