Question

The demand function for good X is ln Qd = a + b ln P +c ln M +e, where Px x x is the price of good X and M is income. Least squares regression reveals thatâ = 7.42, bˆ = -2.18, and cˆ = 0.34.a. If M = 55,000 and Px = 4.39, compute the own price elasticity of demand based on these estimates. Determine whether demand is elastic or inelastic.b. If M = 55,000 and Px = 4.39, compute the income elasticity of demand based on these estimates. Determine whether X is a normal or inferior good.

Answer 1

Answer:

(a) -2.18; Elastic

(b) 0.34; Normal good

Explanation:

Given that,

Demand function for good X: Qd = a + b ln P +c ln M + e

Px - Price of good X

M - Income of the consumer

Least squares regression reveals:

â = 7.42

bˆ = -2.18

cˆ = 0.34

(a) Own price elasticity of demand measures the responsiveness of quantity demanded to any change occur in the price level.

Taking log,

lnQd = a + b ln P +c ln M + e

Now, differentiating the above demand function with respect to price,

$\frac{dlnQ_{d} }{dPx}=b$

Therefore, the own price elasticity of demand based on these estimates is (-2.18).

Since, the absolute value is greater than 1, the own price elasticity of demand is elastic in nature.

(b) Income elastic of demand measures the responsiveness of quantity demanded to any change in the income level of the consumer.

lnQd = a + b ln P +c ln M + e

Now, differentiating the above equation with respect to income,

$\frac{dlnQ_{d} }{dPx}=c$

Therefore, the income elasticity of demand based on these estimates is 0.34.

Since, the positive income elasticity of demand indicates that there is a positive relationship between the quantity demanded and the income of the consumer. Therefore, good X is a normal good.