Question

Suppose XER Inc. is a monopoly and produces a drug that cures the common cold. The weekly (inverse) market demand for its product takes the form P = 660 – 4Q, where Q is measured as number of tablets. The marginal costs (MC) and average total costs (ATC) are equal at $100 per tablet (that is, a horizontal marginal cost curve).

A. What is the price, output combination of the perfectly competitive market?

B. What is the price, output combination for the monopoly market?

C. What is the loss in consumer surplus from the market power of the monopolist compared to consumer surplus in the PCM? Provide a dollar value.

Answer 1

(A)

Perfectly Competitive Market -

Market demand function is as follows -

P = 660 - 4Q

MC = $100

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

P = MC

660 - 4Q = 100

4Q = 560

Q = 560/4 = 140

P = 660 - 4Q

P = 660 - (4*140)

P = 660 - 560 = 100

Thus,

The price in perfectly competitive market is $100 per unit.

The output in perfectly competitive market is 140 units.

(B)

Monopoly Market

Market demand is as follows -

P = 660 - 4Q

Total revenue function is as follows -

TR = P * Q

TR = (660 - 4Q) * Q

TR = 660Q - 4Q²

Marginal revenue function is as follows -

MR = dTR/dQ

MR = d(660Q - 4Q²)/dQ

MR = 660 - 8Q

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

MR = MC

660 - 8Q = 100

8Q = 560

Q = 70

P = 660 - 4Q

P = 660 - (4 * 70)

P = 660 - 280

P = 380

Thus,

The price in the monopoly market is $380 per unit.

The output in the monopoly market is 70 units.

(C)

Calculate the loss in consumer surplus -

Loss in consumer surplus = 1/2 * [price in monopoly market - price in competitive market] * [output in competitive market - output in monopoly market]

Loss in consumer surplus = 1/2 * [$380 - $100] * [140 - 70]

Loss in consumer surplus = 1/2 * $280 * 70 = $9,800

The loss in consumer surplus is $9,800.