Question

The inverse demand for the monopolist's output is P = 240 − 20q and its marginal cost is MC = 40. Find the prot maximizing price (Pm) and the quantity for the monopolist (qm).

Answer 1

The inverse demand function is given as:

P = 240 - 20Q

The total revenue can be calculated by multiplying the price and quantity demanded. So,

TR = PQ = (240 - 20Q)(Q) = 240Q - 20Q²

The marginal revenue function is calculated by differentiating the total revenue function with respect to quantity. So,

MR = d(TR)/dQ = 240 - 40Q

The marginal cost (MC) is given as 40.

The monopolist maximizes the profit when the marginal cost is equal to the marginal revenue.

Equating MR and MC:

240 - 40Q = 40

40Q = 200

Q = 5

Putting Q = 5 in the inverse demand function:

P = 240 - 20(5) = 240 - 100 = 140

So, the profit-maximizing price is $140 and the profit-maximizing level of output is 5 units.