Question

Suppose we have a perfectly competitive market where at the equilibrium price the total market demand is 300 units. Each individual firm in the market has a cost function C(Q) = 50 -2Q + 0.9Q^2. The number of firms this market can support in the long run is _____?

Answer #1

We assume that the market is in long run equilibrium and at this stage the total market demand is 300 units which is a supplied by all the firms existing in the market

Marginal cost is given by MC = 1.8Q - 2 and average cost is given by AC = 50/Q - 2 + 0.9Q. in the long run the price should be equal to the marginal cost as well as to the average cost. This implies

1.8Q - 2 = 50/Q - 2 + 0.9Q

0.9Q = 50/Q

This gives Q = 7.45 units

In the long run there will be 300/7.45 = 40 firms.

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