Homework 8: Monopolistic Competition/Oligopoly (to be handed in on Thursday 15th April)

1.  What are the key characteristics of a monopolistically competitive market? Some experts have argued that too many brands of breakfast cereal are on the market. Give an argument to support this view, and an argument against this view. (1.5 points)

The key characteristics are that firms sell differentiated products and there is free entry and exit (ensures zero economic profit). In a monopolistically competitive market, too many brands of any single product signals excess capacity, implying an output level smaller than the one that would minimize average cost. On the other hand, consumers value variety.

2.  Explain the meaning of a Nash equilibrium when firms are competing with respect to price, and give an example. Why is the equilibrium stable? Why don’t the firms raise prices to the level that would maximize joint profits? (1.5 points)

A NE in prices occurs when each firm chooses its price, taking its rival’s price as fixed: each firm is making the best response to each other. The equilibrium is stable as firms are maximizing profit and have no incentive to deviate (they are making their best responses!). To maximize joint profits requires colluding which is very difficult to enforce as firms have an incentive to deviate from the collusive arrangement. I.e. by lowering its price, the cheating firm can increase market share and profits.

3.  “Because firms in any industry can always make greater profits by colluding, there is an inevitable tendency for competitive industries to become cartels over time”. Applying the Prisoner’s dilemma, briefly discuss the validity of this statement (1 point)

Applying the lessons learned from the Prisoner’s Dilemma, the dominant strategy (i.e. the best choice whatever your rival does) is to deviate from the collusive agreement. Thus, the incentive to cheat is high, which makes it highly unlikely that industries become cartelized over time.

4.  Suppose that two identical firms, Firm 1 and Firm 2, produce widgets and that they are the only firms in the market. Their total costs are given by Ci = 30Qi, which means MC1 = 30; MC2 = 30. The two firms choose their output levels simultaneously, and market demand is given by P = 150 – Q, where Q = Q1 + Q2. The marginal revenue schedules for each firm are as follows:

MR1 = 150 – 2Q1 – Q2

MR2 = 150 – 2Q2 – Q1

a)  Determine each firm’s reaction function and find the Cournot-Nash equilibrium. Determine the output, price and profit of producing widgets for each firm. (2 points)

Reaction function: each firm chooses its profit maximizing output level taking the other’s output as given.

Firm 1: MR1 = MC1. Thus, MR1 = 150 – 2Q1 – Q2 = 30. Q1 = 60 – ½Q2. By symmetry (identical firms), Q2 = 60 – ½Q1. In equilibrium, Q1 = 60 – ½[60 – ½Q1]. Thus, Q1 = 30 + 1/4Q1 so Q1 = 40. By symmetry, Q2 = 40. Market price = $150 – (Q1+Q2) = 150 – 80 = $70.

Profit for each firm = TR – TC = (70*40) – (30*40) = $1600

b)  Suppose that the two firms collude and form a cartel. What will be the resulting output, price and profit for each firm? [Hint: market marginal revenue is 150 – 2Q, because total revenue = P*Q = (150-Q)*Q] (1 point)

To act as a monopolist, the two firms will jointly set MR = MC. This implies that 150 – 2Q = 30. Thus, Q = 60, and P = $90. Each firm will product 30 widgets, charging a price of $90.

Profit for each firm = TR – TC = (90*30) – (30*30) = $1800.

c)  Suppose Firm 1 were the only firm in the market. How would the market output and Firm 1’s profit differ from that found in your answer to 4b) above? (1 point)

If Firm 1 were the only firm in the market, it would produce 60 widgets, and earn the monopoly profit of $3600.

5.  Suppose that the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(Q) = 40Q; MC = 40. Assume the demand curve for the industry is given by P = 100 – Q and that each firm expects the other to behave as a Cournot competitor. The marginal revenue schedules for each firm are as follows:

MRA = 100 – 2QA – QT

MRT = 100 – 2QT – QA

a)  Calculate the Cournot-Nash equilibrium for each firm, assuming that the each firm choose the output level that maximizes profits taking its rival’s output as given. What are the profits for each firm? (1 point)

MRA = 100 – 2QA – QT = 40. Thus, QA = 30 – ½QT. By symmetry, QT = 30 – ½QA.

Thus, QA = 30 – ½[30 – ½QA]. QA = 15 + ¼ QA so QA = 20, which implies QT = 20.

Market price = 100 – 20 – 20 = $60. The profit for each firm = TR – TC = (60*20) – (40*20) = $400.

b)  Suppose that Texas Air’s costs dropped to AC = MC = 25, and American costs remained at AC = MC = 40. Work out the equilibrium quantity, price and profit for each firm. (1 point)

MRT = 100 – 2QT – QA = 25. Thus, QT = 37.5 – ½QA.

Since American has the same cost structure, their reaction function is the same as before. Thus, QA = 30 – ½QT.

To work out the equilibrium output levels, we substitute into the reaction functions. Thus, QT = 37.5 – ½[30 – ½QT] so QT = 30. Similarly, QA = 30 – ½[37.5 – ½QA] so QA = 15.

Market price = 100 – 30 – 15 = $55.

The profit for Texas Air Corp = TR – TC = (55*30) – (40*30) = $1650 - $1200 = $450

The profit for American = TR – TC = (55*15) – (40*15) = $825 - $600 $225