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

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}.