7. Firm Z is a monopolist and faces demand given by: P = 3,000 - Q, where P denotes price in dollars and Q is quantity of units sold per month.In its East coast factory, the firm's fixed costs are $250,000 per month, and its constant marginal cost of manufacturing the equipment is $1,000 per unit.

a)Find the firm's profit-maximizing output and price.What is its profit? (10 pts)

b)Suppose market condition changes and firm Z now faces demand given by P=2500-Q.Firm Z's marketing department judges that it now would have to cut price by $500 per unit in order to sell the same quantity as in part a.Is such a price cut part of a profit-maximizing strategy? If no, what is the new optimal price for firm Z? (5 pts)

c) Continue with part a. Suppose that a new market for the firm's product emerges in South America.Firm Z has begun selling the equipment in several test markets there and has found the elasticity of demand to be E_P = -3 for a wide range of prices (between $1,500 and $2,500).The cost of shipping to South America is $200 per unit.One manager argues that the foreign price should be set at $200 above the domestic price (in part a) to cover the transportation cost.Do you agree that this is the optimal foreign price? Use the markup rule to justify your answer. (10 pts)