Question

1. The market for laser printer has a demand curve given by P=1400-2Q, where P is industry price and Q is industry quantity. Currently HP and EPSON are the only two firms in this market. Each firm has a constant marginal cost of production equal to 200 and there are no fixed costs.

i). Assume that the two firms collude where each produces half of the total output. What is the equilibrium market price, each firm’s equilibrium quantity, and the combined profits of the two firms?

ii). Same question as in i), except now rather than colluding, assume that the two firms act as Cournot competitors.

iii). Now suppose a third firm, call it COMPAQ, enters the market. This firm also has a constant marginal cost of production equal to 200 and no fixed costs. Assuming again Cournot competition, derive the equilibrium market price, each firm’s equilibrium quantity, and the combined profits of the three firms.

Suppose that COMPAQ and EPSON are considering merging and forming a new firm called COMSON. The CEO’s of the two firms hire you as a consultant to make a recommendation concerning whether they should merge. In answering iv), assume a merged firm would have a constant marginal cost of production equal to 200 and no fixed costs.

iv). Assuming that after merging COMSON would engage in Cournot competition with HP, what is your recommendation?

Answer 1

Answer:

1) The given statement is true because tax will increase the cost to competitive fringe and price by reducing the supply. This will shift the consumers from competitive fringe to dominant firm and it will increase the profits of dominant firm.

2)

i) P = 800, Q = 300, and profit = 180,000

ii) P = 600 , Q = q1+q2 = 200+200 = 400, and combined profit = 320,000

iii) P = 500, Q = q1+q2+q3 = 150+150+150 = 450 , and combined profit = 225,900.

The firms should collude.

iv) I would recommend the collusion of COMPAQ and EPSON because this will result in more profits to both the firms.

.

Explanation:

1)

The given statement is true. A lumpsum tax on firms in competitive fringe will increase their cost of production, which will reduce supply. A fall in the supply will lead to an increase in the price and this will shift the consumers from competitive fringe to dominant firm. It implies that there would be an increase in the demand for dominant firms, which will increase its profitability.

.

2)

i) If the two firms collude to be a single firm, then it will behave like a monopoly and produce where marginal revenue (MR) is equal to the marginal cost (MC).

The demand function is given as:

P = 1400 - 2Q

TR = (1400 - 2Q)Q = 1400Q - 2Q²

MR = 1400 - 4Q

Equilibrium condition is:

MR = MC

1400 - 4Q = 200

Q = 300

Both firm will produce half of the total output (Q), which is 300/2 = 150.

By substituting the value of Q in demand function,

P = 1400 - 2(300) = 800

.

Combined profit = TR - TC

             = 1400(300) - 2(300)² - 200(300)

             = 180,000

ii)

P = 1400 - 2Q

P = 1400 - 2(q1 + q2)

TR1 = 1400q1 - 2q1² - 2q1q2

MR1 = 1400 - 4q1 - 2q2

TR2 = 1400q2 - 2q1q2 - 2q2²

MR2 = 1400 - 2q1 - 4q2

.

For firm 1:

MR1 = MC1

1400 - 4q1 - 2q2 = 200

q1 = (1400 - 200 - 2q2)/4                                                                     .....(1)

.

For firm 2:

MR2 = MC2

1400 - 2q1 - 4q2 = 200

q2 = (1400 - 200 - 2q1)/4                                                                     ......(2)

By substituting the value of q1 in this equation :

q2 = [1400 - 200 - 2{(1400 - 200 - 2q2)/4}]/4

q2= 150 + q2/4

3q2/4 = 150

q2= 200

By substituting this value of q2 in equation (1):

q1 = 200

.

By substituting the value of Q = q1+q2 in demand function,

P = 1400 - 2(200+200) = 600

Combined profit = TR - TC

             = P*Q - MC*Q

             = 600*(200+200) + 200(200+200)

             = 320,000

Profit of both individual firms = 320,000/2 = 160,000

.

iii)

If there are 3 firms, Q = q1+q2+q3

P = 1400 - 2(q1+q2+q3)

TR1 = 1400q1 - 2q1² - 2q1q2 - 2q1q3

MR1 = = 1400 - 4q1 - 2q2 - 2q3

TR2 = 1400q2 - 2q1q2 - 2q2² - 2q2q3

MR2 = 1400 - 2q1 - 4q2 - 2q3

TR3 = 1400q3 - 2q1q3 - 2q2q3 - 2q3²

MR3 = 1400 - 2q1 - 2q2 - 4q3 = 200

.

For firm 1:

MR1 = MC1

1400 - 4q1 - 2q2 - 2q3 = 200

q1 = (1400 - 200 - 2q2 - 2q3)/4                                                                        .....(1)

Similarly,

q2 = (1400 - 200 - 2q1 - 2q3)/4                                                          ......(2)

q3 = (1400 - 200 - 2q1 - 2q2)/4                                                         ......(3)

By substituting the value of q1 in equation (2):

q2 = [1400 - 200 - 2{(1400 - 200 - 2q2 - 2q3)/4 } - 2q3]/4                         

q2 = 300 - 600/4 + q2/4 + q3/4 - q3/2

3q2/4 = 150 - q3/4

q3 = 4(150) - 3q2                                                                                   ......(4)

Similarly, by substituting the value of q2 in equation (3):

3q3/4 = 150 - q2/4                                                                                ...... (5)

By substituting the value of q3 in this equation :

q2 = 150

q1 = q2 = q3 = 150

.

By substituting the value of Q = q1+q2+q3 in demand function,

P = 1400 - 2(150+150+150) = 500

Combined profit = TR - TC

             = P*Q - MC*Q

             = 500*(150+150+150) + 200*(150+150+150)

             = 225,900

Profit per firm = 225,900/3 = 75,300

.

If the two firms (COMPAQ and EPSON) collude and called as COMSON, then there are only two competitive firms, i.e. COMSON and HP. If these two of similar cost structure compete in the market then the output will be similar to as in part ii). It means that both firms will earn the profit of 160,000. The profit of 160,000 to COMSON will be equally divided between COMPAQ and EPSON. It implies that profit of both firms will 160,000/2 = 80,000, which is greater than 75,300.

Thus, firms should collude to increase their profits.

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iv) As shown in the above part, collusion of COMPAQ and EPSON will increase their individual profit share in the market by competing with HP. So, my recommendation is that COMPAQ and EPSON should collude and compete against HP.