Question

Market demand is given as QD = 300 – 6P. Market supply is given as QS = 4P. Each identical firm has MC = 6Q and ATC = 3Q. What is a firm’s profit? Show your work

Answer 1

All firms are identical. This implies that given market is a perfectly competitive market.

In perfectly competitive market, each firm is a price taker.

The market price is determined by the industry taking into account the market demand and market supply.

Market demand is as follows -

QD = 300 - 6P

Market supply is as follows -

QS = 4P

At equilibrium,

QD = QS

300 - 6P = 4P

10P = 300

P = 300/10 = 30

Thus,

The market price is 30.

In order to maximize profit, firm in a perfectly competitive market produce that level of output corresponding to which price equals MC.

Equating price and MC

P = MC

30 = 6Q

Q = 30/6 = 5 units

So, each firm will produce 5 units.

Calculate total revenue -

Total revenue = Price * Output = 30 * 5 = 150

ATC = 3Q = 3 * 5 = 15

Calculate Total cost -

Total cost = ATC * Output = 15 * 5 = 75

Calculate profit -

Profit = Total revenue - Total cost = 150 - 75 = 75

Thus,

A firm's profit is 75.