# At the profit-maximizing quantity, the firm's marginal cost is $40 and it charges a price of $60....

## Question:

At the profit-maximizing quantity, the firm's marginal cost is $40 and it charges a price of $60. What is the price elasticity of demand at the profit-maximizing quantity?

-0.5

-3

-0.67

-1.5

## Profit Maximization and Elasticity of Demand:

Price elasticity of demand measures the responsiveness of quantity demanded due to change in its own price, holding all other factors constant.

Price Elasticity theory maintains that profit maximization depend upon ideal pricing, or producing a good to the point where the marginal cost (MC) equals marginal revenue (MR).

## Answer and Explanation: 1

Monopolists maximize their profits at the point where marginal revenue equals to marginal cost. {eq}MR=MC {/eq}

But {eq}MC=P(1+\frac{1}{\epsilon}) {/eq} where {eq}\epsilon=\text{Price elasticity of demand} {/eq}

Substituting for {eq}P=$60{/eq} and

{eq}MC=$40{/eq}.

{eq}40=60(1+\frac{1}{\epsilon}){/eq}

Solving for {eq}\epsilon{/eq}

{eq}1+\frac{1}{\epsilon}=\frac{40}{60}{/eq}

}]

{eq}\frac{1}{\epsilon}=\frac{2}{3}-1{/eq}

{eq}\frac{1}{\epsilon}=\frac{-1}{3} {/eq}

{eq}\epsilon=-3{/eq}

The price elasticity of demand at the profit-maximizing quantity is {eq}\epsilon=-3{/eq}.

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Chapter 3 / Lesson 54Learn what price elasticity is. Discover how to find price elasticity of demand, study examples of price elasticity, and examine a price elasticity graph.

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