Question

A perfectly competitive market is characterized by every firm having the following cost structure: C = 100 + q². In long-run equilibrium, what is the market price?

	P = $12
	P = $20
	P = $60
	P = $35

Answer 1

In perfectly competitive market at long run equilibrium the price is equal to the marginal cost and average total cost of production.

So the average costs of production is here is given as

Average total cost = C/q

Average total cost = (100 + q^2)/q

Average total cost = 100/q + q --------(1)

And the marginal cost is calculated as,

Marginal cost = d(C)/dq

Marginal cost = d(100 + q^2)/dq

Marginal cost = 2q ---------(2)

Putting equation ATC = MC, (1) = (2) we get

100/q + q = 2q

100/q = 2q - q

100/q = q

q×q = 100

q^2 = 100

Taking underoot both the sides we get,

q = (100)^1/2

q = 10.

So the equilibrium quantity will be equal to 10.

Now we can put q = 10 in wither (1) or (2) To calculate the equilibrium price since the long run equilibrium price in competitive market is equal to marginal cost and average total cost.

Putting q = 10 in equation (1) we get,

= 100/q + q

= 100/10 + 10

= 10 + 10

= $20

So the long run equilibrium price of the competitive market is equal to $20.

Hence the correct option is option 2, P = $20.

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