Question

Assume the following inverted demand function of a firm in the short run: P = 100 - 5Q which yields the MR function as 100 - 10 Q. Now assume the total cost function of this firm is : TC = 100 + 160Q - 20Q^₂

The above cost function yields the MC function as 160 - 40Q

Is this firm earning a profit or incurring a loss? What is the amount of short-run profit or loss? Explain fully. Show your work in this space? DO NOT COPY/PASTE

Answer 1

Answer : For firm the profit maximizing condition is MR = MC. So,

100 - 10Q = 160 - 40Q

=> - 10Q + 40Q = 160 - 100

=> 30Q = 60

=> Q = 60 / 30

=> Q = 2 units

From demand function we get,

P = 100 - (5 * 2)

=> P = $90

TR (Total Revenue) = P*Q = 90 * 2 = $180

TC = 100 + (160 * 2) - {20 * (2)^2}

=> TC = 100 + 320 - 80

=> TC = 340

Profit = TR - TC = 180 - 340 = - $160

Therefore, here the firm facing a loss situation.

Here the firm's short run loss is $160.