Question

Q1.Two firms produce in a market with demand P=100-Q. The marginal cost for firm 1 is constant and equals 10. The marginal cost of firm 2 is also constant and it equals 25. Firm 1 sets output first. After observing firm 1's output, firm 2 sets its output. (Please pay attention. Read the brackets correctly.)

1a. For firm 2, the best response is R₂(q₁)=(A-q₁)/2. The value for A is?

1b. Solve for the Stackelberg equilibrium. The quantity sold by firm 1 is?

1c. Solve for the Stackelberg equilibrium. The quantity sold by firm 2 is?

1d. Consider the Stackelberg equilibrium you derived in 1b and 1c, (q_1S, q_2S). Consider the two firms' isoprofit curves passing through (q_1S, q_2S). The slope of firm 1's isoprofit curve, (dq₂/dq₁)|π₁ , at (q_1S, q_2S) is equal to?

[By definition, an isoprofit curve for firm 1 collects all pairs of (q₁,q₂) which give firm 1 the same profit level. c.f.: indifference curves for consumers. For example, π₁(10,10)=π₁(20,35)=700. The pairs (10,10) and (20,35) are on the same isoprofit curve. ]

1e. The slope of firm 1's isoprofit curve at the Cournot equilibrium (35,20) is equal to?

1f. Suppose now that entry requires fixed cost F=100. Find the limit output that firm 1 has to produce to deter entry. q_1L=?

1g. Given F=100, the profit maximising output for firm 1 is q_1*=?

2. Which of the following is not a characteristic of a long-run equilibrium for a firm in a monopolistically competitive industry?

Select one:

a. The firm maximises profits.

b. Price will be greater than marginal cost.

c. Average total cost will be minimised.

d. Price will equal to average total cost.

Answer 1