Suppose that two competing firms, A and B, produce a homogeneous good. Both firms have a marginal cost of MC = \(50. Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium, and (iii) Bertrand equilibrium.

  1. Because Firm A must increase wages, its MC increases to \)80.

  2. The marginal cost of both firms increases.

  3. The demand curve shifts to the right.

Short Answer

Expert verified
  1. The market output will reduce, and the price will increase in Cournot equilibrium. In Collusive equilibrium, the market output and price will remain the same. In Bertrand equilibrium, the market output will fall, and the market price will increase.

  2. The market output will reduce, and the price will increase in Cournot equilibrium. In Collusive equilibrium, the market output will fall, and the price will increase. In Bertrand equilibrium, the market output will fall, and the market price will increase.

  3. The market output will increase, and the price will rise in Cournot equilibrium. In Collusive equilibrium, the market output will increase, and the price will increase. In Bertrand equilibrium, the market output will increase, and the market price will not change.

Step by step solution

01

Step 1. Explanation for part (a)

In Cournot equilibrium, the reaction curve of firm 1 will shift inward; thus, the output will fall, and firm B will produce more, taking some share of firm A. Thus, the total market output will fall, and the price in the market will increase.

In Collusive equilibrium, as the marginal cost of firm A increases, firm A will produce zero, and all the output will produce by firm B; hence, there will be no change in market output and price.

In Bertrand equilibrium, the price is equal to price; thus, firm A price will increase, and firm B will sell at a price lower than firm A; thus, taking all the output of firm A. Hence, with the price rise, market output falls.

02

Step 2. Explanation for part (b)

In Cournot equilibrium, after the increase in marginal cost, the firm's output will fall; thus, total output will fall, and the market price will increase.

In Collusive equilibrium, the market output will fall, and the price will increase as the marginal cost increases.

In Bertrand equilibrium, as the marginal cost increases, the price increases; thus, the output will fall.

03

Step 3. Explanation for part (c)

After the rightward shift in the demand curve, the output produced by both firms will increase; thus, the total output will increase, and the price increases in Cournot equilibrium.

In Collusive equilibrium, the marginal revenue increases with demand; thus, both output and price will also increase.

In Bertrand equilibrium, the rise in demand will increase total output, but the marginal cost does not change; thus, the market price will not change.

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Most popular questions from this chapter

A lemon-growing cartel consists of four orchards. Their total cost functions are

TC1 = 20 + 5Q12

TC2 = 25 + 3Q22

TC3 = 15 + 4Q32

TC4 = 20 + 6Q42

TC is in hundreds of dollars, and Q is in cartons per month picked and shipped.

  1. Tabulate total, average, and marginal costs for each firm for output levels between 1 and 5 cartons per month (i.e., for 1, 2, 3, 4, and 5 cartons).
  2. If the cartel decided to ship 10 cartons per month and set a price of $25 per carton, how should output be allocated among the firms?
  3. At this shipping level, which firm has the most incentive to cheat? Does any firm not have an incentive to cheat?

Two firms compete by choosing price. Their demand functions are

Q1 = 20 - P1 + P2

and

Q2 = 20 + P1 - P2

where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero.

  1. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.)
  2. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be?
  3. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.

Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.

Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 – Q where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2's marginal cost to $15. Firm 1's marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level.

Demand for light bulbs can be characterized by Q = 100 - P, where Q is in millions of boxes of lights sold and P is the price per box. There are two producers of lights, Everglow and Dimlit. They have identical cost functions: Ci = 10Qi +1/2Qi2(i = E, D) Q = QE + QD

  1. Unable to recognize the potential for collusion, the two firms act as short-run perfect competitors. What are the equilibrium values of QE, QD, and P? What are each firm’s profits?
  2. Top management in both firms is replaced. Each new manager independently recognizes the oligopolistic nature of the light bulb industry and plays Cournot. What are the equilibrium values of QE, QD, and P? What are each firm’s profits?
  3. Suppose the Everglow manager guesses correctly that Dimlit is playing Cournot, so Everglow plays Stackelberg. What are the equilibrium values of QE, QD, and P? What are each firm’s profits?
  4. If the managers of the two companies collude, what are the equilibrium values of QE, QD, and P? What are each firm’s profits?
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