Suppose there are N firms who produce an identical product and face the demand curve P...

Suppose there are N firms who produce an identical product and face the demand curve P = 170 – 3Q, where P is the price of the good (in dollars) and Q is the total quantity supplied by the firms. The marginal cost of production per firm is $20; there are no fixed costs.

If there is only one firm in the market (a monopolist), what is this firm's optimal output?

If there are four firms in the market (N=4), what is the symmetric Nash equilibrium output per firm?

What is the price in this market as N tends towards infinity?

Solutions

Expert Solution

If the product is identical, with demand curve P = 170 - 3Q

the total revenue will be

Thus marginal revenue will be

and MC is given as 20

Profit maximizing condition is MR = MC

Thus, 170 - 6Q = 20

150 = 6Q

Q = 25 units

Thus, if there is only one firm, the optimal output is 25 units.

If there are 4 firms, the symmetric Nash equilibrium output per firm will be as under:

25/4 = 6.25 units

If output is symmetric, each firm will produce about 6 units. This is assuming the firms are equal in size, and are profit maximizers.

Now, as N tends towards infinity, the market becomes more and more competitive. The number of firms becomes very large. With this, the price in this market will tend towards the marginal cost of production, which is $20.

When P = MC, the market represents perfect competition, and profits are driven down to zero.

Rahul Sunny answered 2 years ago

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