Suppose that market demand is given by P = 260 - 2Q and that foirms again have a

Question

Suppose that market demand is given by P = 260 - 2Q and that foirms again have a constant
marginal cost of 20, while incurring no fixed cost, but now assume that the firms are Bertrand
competitors and have unlimited capacity.
a. What is the one-period Nash equilibrium market price? Assuming that firms share the market
evenly any time they charge the same price, what is the output and profit of each firm in this
equilibrium?
b. What is the output and profit of each firm if each agrees to charge the monopoly price?
5. Return to Problem 4. Assume that the cartel is established at the monopoly price. Suppose one rm
now deviates from the agreement assuming that its rival continues to charge monopoly price.
a. Given the deviating firm's assumption, what price will maximize its profits?
b. If the deviating firm's assumption is correct, how much will the profit of the cheating rm be?
How much will be the profit of its non-cheating rival?
6. Return again to the cartel in Problems 4 and 5. Now suppose that the market game repeated
indefinitely. What is the discount factor (sigma) is necessary now in order to maintain the collusive
agreement in an indenitely repeated setting?

Explanation / Answer

Bertrand competition refers to the competion in the prices among the firms rather than the quantities. The firms under Bertrand competition will charge a price that is equal to its marginal cost and divide the market equally between them. This is due to the fact , that given the nature of the competition between them, if any one of them charged a higher price , he other firm will be tempted to reduce the price to capture the entire market. Even by reducing the price a little bit, will lead to other firm capturing the entire market. Therefore this temptation to reduce the market price to gain the entire market , will keep on reducing the market price until it reaches the level of Marginal cost of the product. No firm will be willing to set price lower than marginal cost, as it will lead to losses. The only Equilibrium point in this paradox is when the price is equal to the Marginal cost, as this is the point where no firm will be willing to deviate.

a) Given MC – 20,therefore this is the equilibrium price

Given the demand function , P = 260-2Q

20 = 260-2Q

Q = 120

Therefore each firm will sell 120/2 = 60 units at price 20, and earn zero profits. (as MC = P)

b) When they collude to form a monopoly:

MR = 260-4Q

MR = MC

260-4Q = 20

Q = 60 , 30 units for each firm

Price

260-2Q

P = 260-2*60 = 140

Therefore the price, if they follow the monopoly is $140.

The profit for firm 1 will be = TR-C

= 140*30-20*30 = $600

Similarly, firm 2

Profit = TR-C

= 140*30-20*30 = $600.

Therefore by forming a monopoly they will earn $600 each.

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