Problem:1 The United States currently imports all of its coffee. The annual demand for coffee by U.S. consumers is given by the demand curve Q = 250 - 10P, where Q is quantity (in millions of pounds) and P is the market price per pound of coffee. World producers can harvest and ship coffee to U.S. distributors at a constant marginal (= average) cost of $8 per pound. U.S. distributors can in turn distribute coffee for a constant $2 per pound. The U.S. coffee market is competitive. Congress is considering a tariff on coffee imports of $2 per pound. (PRM, Ch.9)

a. If there is no tariff, how much do consumers pay for a pound of coffee? What is the quantity demanded?

b. If the tariff is imposed, how much will consumers pay for a pound of coffee? What is the quantity demanded?

c. Calculate the lost consumer surplus.

d. Calculate the tax revenue collected by the government.

e. Does the tariff result in a net gain or a net loss to society as a whole?

Problem:2 What are the characteristics of a monopolistically competitive market? What happens to the equilibrium price and quantity in such a market if one firm introduces a new, improved product? (PRM, Ch. 12)

Problem:3. Some experts have argued that too many brands of breakfast cereal are on the market. Give an argument to support this view. Give an argument against it. (PRM, Ch. 12)

Problem:4. Consider two firms facing the demand curve P = 50 5Q, where Q = Q1 + Q2. The firms' cost functions are C1(Q1) = 20 + 10Q1 and C2(Q2) = 10 + 12Q2. (PRM, Ch. 12)

a. Suppose both firms have entered the industry. What is the joint profit-maximizing level of output? How much will each firm produce? How would your answer change if the firms have not yet entered the industry?

b. What is each firm's equilibrium output and profit if they behave non-cooperatively? Use the Cournot model. Draw the firms' reaction curves and show the equilibrium.

c. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but a takeover is not?

Problem:5. A monopolist can produce at a constant average (and marginal) cost of AC = MC = $5. It faces a market demand curve given by Q = 53 P. (PRM, Ch. 12)

a. Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits.

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. Market demand is now given by

Q1 + Q2 = 53 P.

Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of Q1 and Q2.

c. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of output on the assumption that its competitor's output is fixed. Find each firm's "reaction curve" (i.e., the rule that gives its desired output in terms of its competitor's output).

d. Calculate the Cournot equilibrium (i.e., the values of Q1 and Q2 for which each firm is doing as well as it can given its competitor's output). What are the resulting market price and profits of each firm?

e. Suppose there are N firms in the industry, all with the same constant marginal cost, MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as N becomes large, the market price approaches the price that would prevail under perfect competition.

Problem:6. This question is a continuation of question 9.We return to two firms with the same constant average and marginal cost, AC = MC = 5, facing the market demand curve

Q1 + Q2 = 53 P

Now we will use the Stackelberg model to analyze what will happen if one of the firms makes its output decision before the other. (PRM, Ch. 12)

a. Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2). Find the reaction curves that tell each firm how much to produce in terms of the output of its competitor.

b. How much will each firm produce, and what will its profit be?