Question

Each firm in a competitive market has a cost function​ of:

Upper C equals 36 plus q squaredC=36+q2​,

so its marginal cost function is

MC equals 2 qMC=2q.

The market demand function is

Upper Q equals 48 minus pQ=48−p.

Determine the​ long-run equilibrium​ price, quantity per​ firm, market​ quantity, and number of firms.

The output per firm is

nothing.

​(round your answer to the nearest​ integer)

Answer 1

Each firm in a competitive market has a cost function​ of C = 36 + q2​ with a marginal cost function MC=2q and average cost function AC = C/q = 36/q + q.

In the long run we have P = MC = AC

This gives 2q = 36/q + q

q^2 = 36

q = 6 units

P = 2*6 = $12

Market quantity Q = 48 - 12 = 36 units

Number of firms = Market quantity / per firm quantity = 36 / 6 = 6 firms

Hence,

• long-run equilibrium​ price is $12
• quantity per​ firm is 6 units
• market​ quantity is 36 units
• number of firms is 6.