Question

Market price is $50. The firm's marginal cost curve is given by MC = 10 + 2Q.

a. Find the profit-maximizing output for the firm.

b. At this output, is the firm making a profit? Explain your answer.

Answer 1

a. Profit maximising output for the firm is where price equals marginal cost , that is :-

50 = 10 + 2Q

2Q = 40

Q = 20

b. At this level of output , to find whether the firm is making a profit or a loss , we need to have the total cost function. Without total cost function it is impossible to infer the level of profit or loss.

Profit = total revenue - total cost

Total revenue = price x quantity

Total revenue = 20 x 50 = $1000

Now , as we know marginal cost is the derivative of total cost function. So it means , total cost is the integration of marginal cost function.

Integrating marginal cost , we get ;

= 10Q + (2Q^2/2)

= 10Q + Q^2

So , total cost = 10Q + Q^2

Total cost at Quantity 20 = 10(20) + 20^2

Total cost = 200 + 400 = 600

To check , take derivate of total cost which is 10 + 2Q , which is the marginal cost.

So now , Profit = 1000 - 600

Profit = $400

So there is a profit of $400 to the firm at this level of output of 20.