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?

Short Answer

Expert verified

a. The tabulate total, average, and marginal cost for each firm is given below:

b. Firms 1 and 4 will produce 2 units each, and firms 2 and 3 will produce 3 units each.

c. Firm 2 has the incentive to cheat. Firm 3 and 4 have no incentive to cheat, and firm 1 is indifferent.

Step by step solution

01

Explanation for part (a)

The total cost, average and marginal cost for firm1 is calculated below:

TC1= 20 + 5Q12TCQ = 0= 20 + 502= 20ACQ=0=TCQ=200= -MCQ=0= TCn- TCn - 1= -TCQ = 1= 20 + 512= 20 + 5= 25AC =TCQ=251= 25MC = TCn- TCn - 1= 25 - 20= 5

Similarly, the total, average, and marginal costs are calculated from 0 to 5 units.

The table below shows the total cost, average cost, and marginal cost of all 4 firms.

02

Explanation for part (b)

The cartel will assign the production in such a manner that the lowest marginal cost is achieved:

Cartel Unit Assigned

Firm Assigned

MC

1

2

3

2

3

4

3

1

5

4

4

6

5

2

9

6

3

12

7

1

15

8

2

15

9

4

18

10

3

20

Thus, firms 1 and 4 will produce 2 units each, and firms 2 and 3 will produce 3 units each.

03

Explanation for part (c)

The firm whose marginal cost is lowest beyond its allocation has an incentive to cheat. Thus, firm 2 has the lowest marginal cost for producing the 4thunit than the other; also, marginal cost is lower than the price; hence, firm 2 has an incentive to cheat. The other firm has marginal cost either greater than or equal to price. Firms 3 and 4 have marginal costs greater than the price; thus, there is no incentive to cheat. Firm 1 is indifferent as its marginal cost is less than the price.

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Most popular questions from this chapter

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 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 that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by C1 = 60Q1 and C2 = 60Q2, where Q1 is the output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve P = 300 – Q where Q = Q1 + Q2.

  1. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.
  2. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit.
  3. Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1’s profit differ from that found in part (b) above?
  4. Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement, but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm’s profits?

Suppose the market for tennis shoes has one dominant firm and five fringe firms. The market demand is Q = 400 - 2 P. The dominant firm has a constant marginal cost of 20. The fringe firms each have a marginal cost of MC = 20 + 5q.

a. Verify that the total supply curve for the five fringe firms is Qf = P - 20.

b. Find the dominant firm’s demand curve.

c. Find the profit-maximizing quantity produced and the price charged by the dominant firm, and the quantity produced and the price charged by each of the fringe firms.

d. Suppose there are 10 fringe firms instead of five. How does this change your results?

e. Suppose there continue to be five fringe firms but that each manages to reduce its marginal cost to MC = 20 + 2q. How does this change your results?

Consider two firms facing the demand curve P = 50 - 5Q, where Q = Q1 + Q2. The firms’ cost functions are C1(Q1) = 20 + 10 Q1 and C2(Q2) = 10 + 12 Q2.

  1. 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?
  2. What is each firm’s equilibrium output and profit if they behave noncooperatively? Use the Cournot model. Draw the firms’ reaction curves and show the equilibrium.
  3. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but a takeover is not?
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