Question

The monopoly’s cost is a function of its output, which is C(Q)=Q²+12, and the monopoly faces the linear inverse demand function: P=24—Q

(1) Calculate the following items: marginal cost, average fixed cost, average variable cost, average total cost, and marginal revenue

(2) Calculate profit-maximizing output and profit-maximizing price, determine its economic profit

Answer 1

C(Q)=Q^2+12

Inverse Demand Function is P=24-Q

Ans 1)

Marginal Cost=dC/dQ=2Q

Average Fixed Cost=Fixed Cost/Q=12/Q

Average Variable Cost=Variable Cost/Q=Q^2/Q=Q

Average Total Cost= AFC+AVC=(12/Q)+Q

Marginal Revenue=d(Revenue)/dQ

Revenue=Price *Quantity=(24-Q)Q=24Q-Q^2

MR=24-2Q

Ans 2)

Profit Maximizing output for monopoly is achieved when MR=MC

24-2Q=2Q

Q=6

Maximizing Output=6 units

Maximizing Price=24-6=$18

Economic Profit at max Price and Quantity is Revenue-Cost=18*6-(6^2)-12=$60