Question

Consider two identical firms competing in a market described by:

• (Inverse) Demand: P = 50 − Q , where Q = q1 + q2

• Cost Firm 1: C1 = 20q1 +q1^2

• Cost Firm 2: C2 = 20q2 + q2^2

a. (1 point) What is firm 1’s marginal cost? Firm 2’s marginal cost? What can you observe about these two firms?

b.(2 points) What are the equilibrium price (P∗), production quantities (q∗1,q∗2), and profits(π∗1,π∗2), if these firms are rivals – what is the outcome in the perfectly competitive model?

c. (2 points) What are the equilibrium price (P∗), production quantities (q∗1,q∗2), and profits(π∗1,π∗2), if these firms collude – what is the outcome in the monopoly model?

Answer 1

Answer for a

MC for Firm 1

MC1=20+2q1

MC for Firm 2

MC1=20+2q2

Both firms are identical and change in cost for each additional output depends on quantity and MC is non zero even if no production happens at all.

Answer for 2

When both the firms are rivals of each other they observe other firm's output level and gives the best response to maximise the profit.