Problem 3: Collusion Consider a market with (inverse) demand p- 260-2Q. There ar

Question

Problem 3: Collusion Consider a market with (inverse) demand p- 260-2Q. There are two firms in the mar- ket with constant marginal costs of $20, which incur no fixed costs. Now, assume that the firms compete in prices (a la Bertrand). As usual, assume that the firms share the market evenly any time they charge the same price. a) Determine the Bertrand equilibrium quantities and price. What is the profit of each firm in this market equilibrium? b) What would be the collusive (joint-profit maximizing) price and quantity?

Explanation / Answer

1) P=260-2Q and MC=20

In bertrand competition price=MC=20 because if any firm charge price higher than 20 then other firm has an incentive to charge a little smaller price than the other firm.

Profit=0 for both firm amd total demand will be 120 and each firm will share 60-60 output each.

2) Profit is maximised when they act as monopoly

P=260-2Q and MR=260-4Q and Mc=20

Profit is maximised when MR=MC

Thus 260-4Q=20 which implies Q=240/4=60

And price=140

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