Question

The following 5 questions relate to the information provided here. A competitive industry consists of 100 firms. The short-run marginal cost curve for each firm is given by MC = 200 + 0.3Q. The demand curve faced by the industry is given as P = 400 - .1Q.

How much profit is each firm making if fixed costs are $375 per firm?

I do not understand why some people have TC=200Q+15Q^2+375 not TC= 200Q+0.15Q^2+375

Answer 1

A competitive industry consists of 100 firms. The short-run marginal cost curve for each firm is given by MC = 200 + 0.3Q. The demand curve faced by the industry is given as P = 400 - .1Q.

How much profit is each firm making if fixed costs are $375 per firm?

Answer - A competitive industry consists of 100 firms.

In a perfectly competitive industry, all the firms sell identical product and they are price takers. There is free entry and exit in the industry and hence all firms make zero economic profit in the long run.

The short-run marginal cost curve for each firm is given by MC = 200 + 0.3Q.

If fixed cost of each firm is $375, then from the short-run marginal cost curve of each firm we can say that the total cost (TC) is: TC = 200Q + 0.15Q^2 + 375.

By dividing the TC function by Q, we get that AVC = 200 + 0.15Q.

Now let us derive the market supply function from the individual firm’s marginal cost curve.

We know that in perfect competition, P = MC.

Therefore, substituting P = MC in each firm’s short run marginal cost curve, we get P = 200 + 0.3Q

or, 0.3Q = P – 200

or, Q = 3.33P – 666.67, which is basically individual firm’s supply equation.

Since the market consists of 100 firms, the market supply equation is S = 100 * Q = 333P – 66667, where S = industry supply.

Rearranging we can write that P = 0.003S + 200.2

Now, let us find the equilibrium price and quantity produced by the industry as a whole.

To find equilibrium, we need to equate Market Demand = Market Supply

The demand curve faced by the industry is given as P = 400 - .1Q and the supply curve faced by the industry is given as P = 0.003S + 200.2.

Solving the above two equations we get that equilibrium price (P*) = $206 and equilibrium industry quantity (S*) = 1942.

Therefore, each firm will produce: Q = S*/100=1942/100=19.42.

Thus, profit(π) each firm is making is:

Π = P∗Q−AVC∗Q−FC

or, π = 206∗19.42−(200+0.15∗19.42) ∗ 19.42−375=-$315.05