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?

$100

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

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