Question

The inverse demand curve a monopoly faces is

p = 100 - 2Q

The​ firm's cost curve is

C (Q) = 20 + 6Q

What is the​ profit-maximizing solution?

The profit-maximizing quantity is _______. (Round your answer to two decimal places.)

The profit-maximizing price is $________. (Round your answer to two decimal places.)

What is the firm's economic profit?

The firm earns a profit of $________. (Round your answer to two decimal places.)

How does your answer change if C(Q) = 150 + 6Q? The increase in fixed cost

A. has no effect on the equilibrium​ quantity, but the equilibrium price increases and profit increases.

B. has no effect on the equilibrium price and​ quantity, but profit will decrease.

C. causes the firm to increase both the price and​ quantity, and profit increases.

D. has no effect on the equilibrium​ quantity, but the equilibrium price increases and profit decreases.

Answer 1

Answer : 1) Given,

P = 100 - 2Q

TR (Total Revenue) = P * Q = (100 - 2Q) * Q = 100Q - 2Q^2

MR (Marginal Revenue) = TR / Q = 100 - 4Q

C(Q) = 20 + 6Q

MC (Marginal Cost) = C(Q) / Q = 6

For monopoly the profit maximizing condition is, MR = MC. So

100 - 4Q = 6

=> 100 - 6 = 4Q

=> 94 = 4Q

=> Q = 94 / 4

=> Q = 23.50

From demand function we get,

P = 100 - (2 * 23.50)

=> P = 53

Therefore, here monopolist's profit maximizing quantity is, Q = 23.50 units.

The profit maximizing price is, P = $53.

TR = P*Q = 53 * 23.50 = 1,245.50

TC (Total Cost) = C(Q) = 20 + (6 * 23.50) = 161

Profit = TR - TC = 1,245.50 - 161 = $1,084.50

Therefore, here the profit is $1,084.50 .

2) The answer is option B.

Here only fixed cost increases. The MC depends only on variable cost. Hence if fixed cost change then the MC will not change. As a result, the equilibrium price and quantity will not change because the equilibrium condition is MR = MC. But as fixed cost increases hence the profit will decrease. For this reason except option B other options are not correct. Therefore, option B is the correct answer.