Question

Assume that a monopolist sells a product with the cost function C(x) F + 20x, where C(x) is total cost, F is a fixed cost, and x is the level of output. The market inverse demand function is p(x) 60 − x, where p is the price in the market. The firm will earn zero economic profit when it charges a price of $30 (this is not the price that maximizes profit). How much profit does the firm earn when it charges the price that maximizes profit?

Answer 1

$100

Step-by-step explanation:

C(x) = F + 20x,

where,

C(x) is total cost,

F is a fixed cost,

and x is the level of output

At p = 30,

x = 60 - 30

= 30

Total revenue = px

= 30 × 30

= 900

Total cost = F + 20x

= F + 20 × 30

= F + 600

At zero economic profit,

TR = TC

F + 600 = 900

F = 300

Total cost = 300 + 20x

Marginal cost = 20

Demand, p = 60 - x

Total revenue = px

= (60 - x) x

= 60x - x^2

Marginal revenue = 60 - 2x

Equilibrium: MR = MC

60 - 2x = 20

x = 20

p = 40

Profit = TR - TC

= 40 × 20 - 300 - 20(20)

= 800 - 300 - 400

= $100