Question

Roland Incorporated manufactures and sells portable hair dryers. If the price of a hair dryer is $ 127.00, then the company sells 116 hair dryers per week, and the elasticity of demand is −0.463. Assume that the demand function is differentiable and that the only time the company sells exactly 116 hair dryers per week is when the price of a hair dryer is $ 127.00. Given this situation, which of the following do you know MUST be true?
a. The marginal revenue is negative when Roland sells 144 driers per week.
b. The marginal profit is negative when Roland sells 144 driers per week.
c. The marginal profit is positive when Roland sells 144 driers per week.
d. The marginal revenue is positive when Roland sells 144 driers per week.

Answer 1

Answer:

The marginal revenue is positive when Roland sells 144 driers per week ( D

Explanation:

Elasticity of demand = -0.463

P = $127

116 hair dryers sold per week ( q )

demand function is differentiable

prove  the true statement below

Revenue = price per unit * quantity

determine the Marginal revenue = dr / dq

∴ MR = P + q dp/dq

price elasticity of demand E(p) = - dq / dp * p/q

where : E ( p ) = - 0.463  , q = 116 , p = $127

q * dp/dq = P / 0.463

∴ MR = P * 1.463 / 0.463

         = 127 * 3.16 = $401.32

since the Marginal revenue > 0 HENCE The marginal revenue will be  positive when Roland sells 144 driers per week.