1. A monopolist faces amarket demand curve given by Q = 53-P. Its cost function is given by C = 5Q + 50, i.e.its MC =$5.
(a) Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its optimal profit.
(b) Suppose a second firm enters the market. Let q1 be the output of the first firm and q2 be the output of the second. There is no change in market demand, which is given by Q = 53- P, but note that Q = q1 + q2. The second firm has the same MC as the first (incumbent) firm, but its fixed cost is $80. Assuming that both firms behave as Cournotduopolists who want to maximize individual profits, determine the best response function for each firm. Calculate the optimal outputs of each firm at the Nash Cournot equilibrium. Calculate the market price and individual and industry profits.
(c) Suppose firm 1 can invest in a new technology that can lower its MC to $3.50. Assuming that firm 2’s cost structure remains unchanged, calculate optimal output of firm 1 if it can successfully lower its MC to $3.50. Also calculate firm 2’s output and the market price at the new Nash Cournot equilibrium. What is the maximum amount that firm 1 will be willing to invest in this cost saving technology?
(d) Suppose that both firms have the same cost structure described in part (a) or (b), i.e. the MC of each firm is $5. The two firms now form a cartel to maximize joint profits. Determine the total output produced by the Cartel, if the Cartelwants to maximize joint profit. Determine the individual outputs, the market price and the individual as well as the Cartel’s profit.
2. The market demand for a special type of wood that is essential for producing acoustic guitars is given by Q = 70,000-2000P, where Q is measured in thousands of pounds per year and P is the price of a pound of wood. Suppose that there are 1000 small producers of such wood, each with marginal cost given by MC = q +5, where q is the output of the typical firm.
(a) Assuming that each small firm acts as a price taker and that collectively they act as a “competitive fringe “(CF). Determine the (aggregate) supply curve for the CF. Calculate equilibrium output market price of wood.
(b) Now suppose a very large source of this special type of wood is discovered in California such that a firm in California that controls that resource becomes the dominant firm in the world that acts as a price leader. It sets the price in the market and produces accordingly to maximize its own profit. The “CF” continues to act as a competitive group and accepts the price set by the leader in California. Calculate the profit maximizing output and price of the dominant firm in California. Calculate the total output produced by the CF. Calculate the market demand, the profit of the “CF” as well as the profit of the dominant firm.
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