Question

In: Economics

A monopolist meets the demand curve P = 200-8Q. The company has a fixed cost of...

A monopolist meets the demand curve P = 200-8Q. The company has a fixed cost of 200 and a marginal cost of MC = 40. This means that the total cost is TC = 200 + 40Q. How big is the monopoly gain?

I repeat if you dont know the answer dont even bother idiots.

Expert Solution

Demand curve is as follows -

P = 200 - 8Q

Calculate Total Revenue -

TR = P * Q = (200 - 8Q) * Q = 200Q - 8Q²

Calculate Marginal Revenue -

MR = dTR/dQ = d(200Q - 8Q²)/dQ = 200 - 16Q

MC = 40

A monopolist maximizes profit when it produce that level of output corresponding to which MR equals MC.

MR = MC

200 - 16Q = 40

16Q = 160

Q = 10

P = 200 - 8Q = 200 - (8*10) = 200 - 80 = 120

Thus,

The profit-maximzing Quantity in case of monopoly (Q_m) is 10 units

The profit-maximizing price in case of monopoly (P_m) is $120 per unit.

Calculate profit-maximizing price in case of perfect competition -

A perfectly competitive firm maximizes profit when it produce that level of output corresponding to which Price equals MC

P = MC

200 - 8Q = 40

8Q = 160

Q = 20

P = 200 - 8Q = 200 - (8*20) = 200 - 160 = 40

The profit-maximizing price in case of perfect competition (P_pc) is $40 per unit.

Calculate monopoly gain -

Monopoly gain = (P_m - P_p_c) * Q_m = (120 - 40) * 10 = 80 * 10 = 800

The monopoly gain is $800.

Rahul Sunny answered 2 years ago

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