Question

Suppose that there are 1,000 firms in a perfectly competitive industry, each with a short-run total cost curve given by TC = 800 + 8Q + 0.1Q2. A) What is the profit-maximizing output level for each firm at a market price of $20? B) How much profit does each firm make at a market price of $20? C) Explain whether the industry will expand or contract in the long run.

Answer 1

(a)

The short-run total cost curve is as follows -

TC = 800 + 8Q + 0.1Q²

Derive the marginal cost function -

MC = dTC/dQ

MC = d(800 + 8Q + 0.1Q²)/dQ

MC = 8 + 0.2Q

The marginal cost function is 8 + 0.2Q

The market price is $20.

A perfectly competitive firm maximizes profit when it produce that level of output correspondinig to which price equals the marginal cost.

P = MC

20 = 8 + 0.2Q

0.2Q = 12

Q = 12/0.2

Q = 60

Thus,

The profit-maximizing output level for each firm is 60 units.

(b)

Calculate profit -

Profit = Total revenue - Total cost

Profit = [Price * Quantity] - [800 + 8Q + 0.1Q²]

Profit = [$20 * 60] - [800 + (8 * 60) + [0.1 * (60)²]

Profit = $1,200 - $1,640

Profit = -$440

Thus,

The profit is -$440

The negative profit implies economic loss.

So,

Each firm would incur an economic loss of $440.

(c)

In a perfectly competitive market, if firm incur loss in short-run then there is exit of firms from the market in the long-run.

In the given case, each firm is making loss in the short-run.

So,

There will be exit of firms from the industry in the long run.

Thus,

The industry will contract in the long run.