# Suppose a firm's inverse demand curve is P = 100 - Q and its marginal cost is constant at $20....

## Question:

Suppose a firm's inverse demand curve is {eq}P = 100 - Q {/eq} and its marginal cost is constant at {eq}\$20 {/eq}. Show that the value of the Lerner index at the profit-maximizing quantity is {eq}0.67 {/eq}. Find the corresponding price elasticity of demand.

## Lerner Index

In business and economics, one of the measures of the market power for a firm is the Lerner index. It measures the market power by giving the percentage amount by which a firm is able to raise its price above the marginal cost.

## Answer and Explanation: 1

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The formula for calculating the Lerner index is:

{eq}L=\dfrac{P-MC}{P} {/eq}

Therefore, given the firm's demand curve as P=100-Q, its marginal...

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