Question

Example 1:

Suppose a monopolist faces an inverse demand function as p = 94 – 2q. The firm’s total cost function is 1.5q² + 45q + 100. The firm’s marginal revenue and cost functions are MR(q) = 90 – 4q and MC(q) = 3q + 45.

1. How many widgets must the firm sell so as to maximize its profits?
2. At what price should the firm sell so as to maximize its profits?
3. What will be the firm’s total profits?

Answer 1

p = 94 - 2q  

TR = pq  

TR = (94 - 2q)q  

TR = 94q - 2q²

dTR/dq = MR = 94 - 4q  

MR = 94 - 4q  

TC =  1.5q² + 45q + 100

dTC/dq = MC = 3q + 45

MC = 3q + 45

a) Profit maximising condition

MR = MC

94 - 4q = 3q + 45

94 - 45 = 3q + 4q  

49 = 7q  

q = 7

Therefore firm will sell 7 widgets to maximise its profit.

b)

p = 94 - 2q

p = 94 - 2(7)  

p = 94 - 14

p = 80

Firm should charge $ 7 to maximise its profit.

c)

Total Profit

= TR - TC  

= pq - 1.5q² + 45q + 100

= 80(7) - 1.5(7)² - 45(7) - 100

= 560 - 73.5 - 315 - 100

= 71.5