Suppose there are n identical firms in a market in long run. Each firms cost fun

Question

Suppose there are n identical firms in a market in long run. Each firms cost function is given by C=32+.5q^2, where q is the amount that an individual firm produces. This means that an individual firms marginal cost is given by MC=q. Also, the market demand is given by P=96-2Q, where Q is the total amount of the good produced by all of the firms combined. Therefore, Q=n*q.

A.) How much output will each of them produce?

B.)What will be the market price?

C.) How many firms operate in the long run? (find n)

D.) What is the consumer surplus?

E.) What's the market supply curve

Thanks!!!

Explanation / Answer

Suppose there are n identical firms in a market in long run. Each firms cost function is given by C=32+.5q^2, where q is the amount that an individual firm produces. This means that an individual firms marginal cost is given by MC=q.

Also, the market demand is given by P=96-2Q, where Q is the total amount of the good produced by all of the firms combined. Therefore, Q=n*q.

A.) How much output will each of them produce?

MC = MR

MR = P = 96 - 2Q = 96 - 2nq

MC = q = Q/n

So we set MR = MC and solve for q:

P = 96 - 2Q = 96 - 2nq = q = Q/n

96 - 2nq = q

96 = (2n + 1)q

q = (2n + 1)/96 will be produced by each firm (note that q depends on the number, n, of firms in the market!)

B.)What will be the market price?

Likewise, P = 96 - 2nq = 96 - 2n(2n + 1)/96 = 96 - (4n^2 + 2n)/96 = price

C.) How many firms operate in the long run? (find n)

q = (2n + 1)/96 and price = 96 - (4n^2 + 2n)/96

Q = nq and

P = 96 - 2Q = 96 - (2n^2 + 2n)/96,

solving the equations give us n = 4, aka 4 firms

D.) What is the consumer surplus?

Consumer surplus is the difference between the total amount that consumers are willing and able to pay for a good or service (indicated by the demand curve) and the total amount that they actually do pay (i.e. the market price for the product).

Here, each firm is maximizing profits, so consumer surplus is 0.

E.) What's the market supply curve

the same as the MC curves of all of the firms added up; in other words, the curve

Q = qn = (2n^2 + n)/96

I hope that you found this answer useful towards your studies. It took a considerable amount of thought, time, and effort to compose, and and I'd sincerely appreciate a lifesaver rating! It would really make my day! :)

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