Question

Exercise 1. Your firm produces basketballs. The inverse demand function for your basketballs is given by: P = 100 – 3q. The cost function is C = 8 + 2q². a. Write down a function that states the firm's profit as a function of the amount of output (basketballs produced). b. What is the profit-maximizing amount of output? How much profit does it make when it maximizes profits? Total Revenue? Costs? c. At what minimum price will the firm produce a positive output in the short run (choose to operate rather than shutdown)?

Answer 1

(a)

Revenue (R) = P x q = 100q - 3q²

Cost (C) = 8 + 2q²

Profit (Z) = R - C

Z = 100q - 3q² - 8 - 2q²

Z = 100q - 5q² - 8

(b)

Profit is maximized when dZ/dq = 0

dZ/dq = 100 - 10q = 0

10q = 100

q = 10

R = (100 x 10) - (3 x 10 x 10) = 1000 - 300 = 700

C = 8 + (2 x 10 x 10) = 8 + 200 = 208

Z = 700 - 208 = 492

(c)

The minimum price is the minimum point of AVC, where MC intersects AVC.

AVC = TVC/q = 2q²/q = 2q

MC = dC/dq = 4q

Equating,

2q = 4q

This holds true when q = 0.

Minimum price = AVC = 2 x 0 = 0