Question

A competitive firm sells its product at a price of $ 10 per unit. Its total is:

TC = 5 -0.5q + 0.001q2(q square) where TC is total cost ($) and q is output rate (units per time period)

a) Calculate the firm’s profit maximizing quantity. Is the firm earning a profit?

b) Is the firm in the long run in part (a). If not, what do you think will happen in the longrun?

c) What is the supply curve for this firm?. What is the shutdown price?

d) What is the price that the firm will charge in the long run?. What profit or loss will the firm make in the long run?

e) Given that there are 50 firms in the industry with identical cost structures, find the equation of the market supply curve.

Answer 1

Given that the firm is a competitive one and the price of a product is $10 per unit.

It's marginal revenue (MR) is the price

MR = $10

Now, TC = 0.001q² -0.5q + 5

MC =d(TC)/dq = 0.002q - 0.5

a) At equilibrium, MC = MR

0.002q - 0.5 = 10

0.002q =10.5

q* = 10.5/0.002 = 105x100/2 = 105x 50 = 5250

Total revenue = $ (5250x 10) = $ 52,500

Total cost = $( 0.001x5250² -0.5x5250+5) = $ 30,192.50

Now Profit = total revenue - total cost = $( 52500-30192.50) = $ 22,007 .50

Thus, yes the firm is making a profit.

b) the firm is not in the long run in part(a), because in a competitive market, no firm earns super Normal profit. They earn normal profits just enough to cover their economic costs. However, In part(a) the firm is earning supernormal profits.

c) the supply curve of a competitive firm is the portion of the Marginal cost curve above the shut down price.

Marginal cost (MC) = d(TC)/dq = 0.002q - 0.5

Shut down price = min{AVC} , where AVC is average variable cost.

Now, TC = Total variable cost (TVC) + Total fixed cost (TFC)

TC = 0.001q² - 0.5q + 5

Implies, 0.001q²- 0.5q is the TVC and 5 is the TFC.

Thus, TVC = 0.001q² - 0.5q

AVC = TVC/q = 0.001q - 0.5

min{AVC} = d(AVC)/dq = 0.001

e) the competitive market supply curve is given by the horizontal sum of each firm's supply curve

MC = 0.002q - 0.5 ,for a firm

For the market, MC_{​​​​​m} = 50(0.002q- 0.5) = 0.1q - 25

Therefore, the market supply curve function is given by 0.1q- 25