Given the demand function in log-linear form: Q = 120

Question

Given the demand function in log-linear form: Q = 120 - 1.5P + 12ADV where Q = quantity,P = price,and ADV = advertising expenditures,what is the price elasticity?
A)1.5, inelastic
B)-1.5, elastic
C)120, elastic
D)12, elastic

Quizplus · Accepted Answer

To calculate the price elasticity, we need to take the derivative of the demand function with respect to price (P) and multiply it by P/Q. Taking the derivative of the demand function, we get:

dQ/dP = -1.5

Multiplying by P/Q, we get:

(P/Q)dQ/dP = (-1.5)(P/Q)

Using the midpoint formula, we can rewrite this as:

(P2 - P1) / [(P1 + P2)/2] / (Q2 - Q1) / [(Q1 + Q2)/2] = (-1.5)(P/Q)

Since we do not have specific values for P and Q, we cannot solve for the price elasticity exactly. However, we can determine that the price elasticity is negative (since the derivative is negative) and greater than 1 (since the absolute value of the derivative is greater than 1. This means that demand is elastic with respect to price. The correct answer is therefore B.