Answer to Question #280140 in Microeconomics for Rita

Question

A monopolist firm faces a demand with constant elasticity of -2. It has a constant marginal cosy of 20$ per unit and sets price to maximize profit. If marginal cost should increase 25%, would the price charged also rise by 25%?

Answer 1

A monopolist produces where MR=MC. But the marginal revenue can be expressed as

$MR=P\left(1+\dfrac{1}{e}\right)$

Where "e" is the elasticity of demand.

Therefore, if a monopolist's marginal cost is $20 and elasticity is -2, then its optimal price is equal to

$20=P\left(1+\dfrac{1}{-2}\right)\\[0.3cm] 20=\dfrac{P}{2}\\[0.3cm] P=\$40$

If the marginal cost increases by 25%, it will become

$MC=1.25\cdot \$20=\$25$

Therefore, the new price charged by the firm will be equal to

$25=\dfrac{P}{2}\\[0.3cm] P=\$50$

The percentage increase in price is equal to

$\Delta P=\dfrac{50-40}{40}\times 100=25\%$

Therefore, the firm must also increase the price by 25% when the marginal cost increases by 25%.