Problem 1 A firm with market power faces a demand curve qd = 40 - 2P. The firm's Total Cost is TC = 0.25q2 +2q + 50. a) In a graph draw the firm's demand curve. Assume that the firm behaves like a one price monopolist and charges the same price on all units sold. b) Write the expressions of the firm's revenue and marginal revenue as functions of the quantity q. c) In your graph, add a curve to illustrate the firm's marginal revenue curve. d) Write the expression of the firm's profit as a function of q. Then take the first order conditions for profit maximization and find the firm's profit maximizing quantity. e) Find the price the firm would charge at the profit maximizing quantity. () In your diagram, illustrate the firm's profit maximizing quantity and price. g) Compute the firm's price elasticity of demand at the profit maximizing quantity and label is 6p. h) Verify that at the profit maximizing quantity price and marginal cost satisfy the condition P(1+1/6p) = MC. Keep in mind that En is a negative number. i) Now, write the expression of the firm's inverse demand function (or price line). i) Now, write the expression of the firm's profit as a function of the price P (instead of a function of the quantity q). Keep in mind that you have to express total cost as a function of price as well. k) Now take the firm's first order conditions with respect to Price to find the firm's profit maximizing price and verify that you find the same value you found in part e). I) Give an example of a firm with market power that you think might use price as its strategic variable and a firm that you think might use quantity as its strategic variable