Suppose a profit maximizing monopolist has total costs C(Y)= 10Y. The monopolist is charging a profit maximizing price or p = 15. If market demand has a constant price elasticity, then the price elasticity of demand must be equal to:
A)1.
B)3.
C)3/2.
D)2/3.

Question

Quizplus · Accepted Answer

The price elasticity of demand (PED) in a monopoly setting where the monopolist is maximizing profit can be determined using the formula for the Lerner Index, which is $P - MC = \frac{-P}{E_d}$, where $P$ is the price, $MC$ is marginal cost, and $E_d$ is the price elasticity of demand. Rearranging this formula to solve for $E_d$, we get $E_d = -\frac{P}{P - MC}$. Given $P = 15$ and $MC = C'(Y) = 10$, substituting these values gives $E_d = -\frac{15}{15 - 10} = -3$. The negative sign indicates the direction of the relationship between price and quantity demanded, so the magnitude of the price elasticity of demand is 3.

Suppose a Profit Maximizing Monopolist Has Total Costs C(Y)= 10Y