Suppose that the inverse demand curve for energy drinks can be expressed as . The price elasticity of demand at a quantity of 25 is:

Question

Suppose that the inverse demand curve for energy drinks can be expressed as  . The price elasticity of demand at a quantity of 25 is:

Quizplus · Accepted Answer

To calculate the price elasticity of demand at a quantity of 25, we need to take the derivative of the inverse demand function with respect to price and then multiply it by the ratio of price to quantity.

Taking the derivative of the inverse demand function, we get:

dP/dQ = -11e^(-0.1P)

At a quantity of 25, the price can be found by plugging 25 into the inverse demand function:

P = 110 - 0.1Q = 110 - 0.1(25) = 107.5

Using the formula for price elasticity of demand, we get:

E = (dQ/Q)/(dP/P) = [(dQ/dP)(P/Q)]/[(P/Q)/(dP/dQ)] = [(1/(-11e^(-0.1P)))(107.5/25)]/[(107.5/25)/(-1/11e^(-0.1P))]

Simplifying this expression, we get:

E = -2.04

Therefore, the answer is C.

Suppose That the Inverse Demand Curve for Energy Drinks Can