Question

1.Consider an industry with only two firms that produce identical products. Each of the firms only incurs a fixed cost of $1000 to produce and marginal cost is 20. The market demand function is as follows:

Q=q1+q2=400-P

a. Assuming that the firms form a cartel, calculate the profit-maximizing quantity of output, price and profits

b. If the firms choose to behave as in the Cournot model, what would be the profit- maximizing quantities of output, price and profits?

c. if the firms interact with each other as in the Stackelberg model and assuming that firm 1 is the leader, what would be the outcomes on output, price and profits?

d. “Firms in an oligopolistic industry may attain a long-run zero profit equilibrium as in perfect competition due to entry of new firms. But oligopolistic firms do not produce at the minimum point of the average cost curve.” Explain this phenomenon.

e. Explain the concepts of moral hazard and adverse selection in economics of information.

Answer 1

a)

Q = 400 - P

P = 400 -Q

Cartel means, firms are operating in monopoly market:

P = 400 -Q

TR = 400Q - Q^2

MR = 400 - 2Q

MC= 20

MR = MC

400 - 2Q = 20

380 = 2Q

Q = 380/2

= 190

P = 400 -190

= 210

Profit = 210*190 - 190*20 - 2000

=34,100

Each firm profit = 17050

b)

Cournot:

Firm 1:

P = 400 -Q

TR = 400Q - Q1^2 - Q1Q2

MR1 = 400 - 2Q1 - Q2

MC= 20

MR=MC

400 - 2Q1 - Q2 = 20

380 -Q2 = 2Q1

Q1 = 190 -0.5Q2 ---(1)

Since this symmetric problem

Q2 = 190 - 0.5Q1 ---(2)

Substitute Q2 in Q1

Q1 = 190 - 0.5(190 - 0.5Q1)

= 95 + 0.25Q1

0.75Q1 = 95

Q1 = 95/0.75

=126

Q2 = 126

P = 400 - 253

=147

Profit = 147*253 - 2000-253*20

= 30,131

Each firm profit= 30,131

c)

Stackelberg model:

Q2 = 190 -0.5Q1

Substitute it in firm 1 function:

P = 400 -Q

TR = 400Q - Q1^2 - Q1(190 -0.5Q1)

= 400Q - Q1^2 - 190Q1 +0.5Q^2

MR1 = 400 -2Q1 -190 +Q

= 210 -Q1

MC= 20

MR=MC

210 -Q1 = 20

Q1 = 190

Q2 = 190 - 0.5(190)

= 95

Price = 400 - 285

=115

Leader profit = 115*190 - 1000 -190*20

= 17050

Profit of follower:

=95*115 - 1000 - 20*95

= 8,025

d)

Oligopoly market is not efficient ones, it does not produce where ATC is minimum, it produces where MR = MC and MC cuts the MR before cutting AC. Hence, oligopoly is not productively efficient.