Question #280140

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%?


1
Expert's answer
2021-12-17T11:53:20-0500

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

MR=P(1+1e)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(1+12)20=P2P=$4020=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$20=$25MC=1.25\cdot \$20=\$25

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

25=P2P=$5025=\dfrac{P}{2}\\[0.3cm] P=\$50

The percentage increase in price is equal to

ΔP=504040×100=25%\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%.


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