For many years, the American sportswear market has been dominated by two firms: a local producer Mikey and a foreign firm Eddie Dance. The marginal cost of producing and delivering one unit for Mikey is $20. The cost structure of Eddie Dance is unknown; what is known, however, is that it has run a marketing campaign "Under 40? Buy for $40!" which has essentially committed Eddie Dance to sell at a price of $40 a unit.

The marketing department at Mikey has estimated the demand curve for Mikey and found it to be

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Where and are prices of Mikey and Eddie Dance, in dollars per unit, an is quantity demanded, in millions of units, per year

a. How much should Mikey charge for a unit? What is the quantity sold and what is the profit in this case?

Mikey has hired you as a consultant to get advice on potential scenarios that might arise in the future. Consider each of the following scenarios independently.

For the remainder of this question (parts (b)-(f)), explicit calculations are not required (or even possible). However, please clearly explain your reasoning.

b. Rumors tell you that the board of directors of Eddie Dance is mulling abandoning its marketing campaign, and to subsequently lower the price. If that rumor materializes, would Mikey want to raise its price, lower its price, or keep its price the same?

c. Mikey is considering relocating production overseas. This would reduce Mikey's marginal cost considerably. Would Mikey find it optimal to increase the price, decrease it, or keep the same? What would happen to Mikey's profits?

d. The marketing department at Mikey tells you that a substantial number of customers buy Mikey (as opposed to Eddie Dance) precisely because of local production. If Mikey moves production overseas, these customers are likely to stop buying from either company (but, of course, the marginal cost would still go down, as specified in part c). The exact number of such customers is unknown. In this scenario, should we advise Mikey to raise the price, lower it, keep the same, or there is not enough information? What can we say about profits?