Question

An economist is interested in examining how an individual’s cigarette consumption (C) may be influenced by the price for a pack of cigarettes (P) and the individual’s annual income (I). Using data from 50 individuals, she estimates a log-log model and obtains the following regression results.

In(C)ˆ  =  3.79−1.18     In  (P)+0.14    In(I)In(C)^⁢  =  3.79−1.18⁢     In⁢  (P)+0.14⁢    In(I)

p-values = (0.0000) (0.0054) (0.3926)

a.	Interpret the value of the elasticity of demand for cigarettes with respect to price. (Round your answer to 2 decimal places.)

As the price increases by 1%, consumption (Increases/decreases) by __ %.

b.	At the 5% significance level, is the price elasticity of demand statistically significant?
	Yes No

c.	Interpret the value of the income elasticity of demand for cigarettes. (Round your answer to 2 decimal places.)

As the annual income increases by 1%, consumption (increases/decreases) by ___ %.

d.	At the 5% significance level, is the income elasticity of demand statistically significant?

(Yes/No), since the p-value is (greater than/less than) 0.05, we (can/cannot) conclude that income elasticity of demand for cigarettes is statistically significant.

Answer 1

a) in a log -log model , the coefficient of variable give the value of elasticity i.e by how will the dependent variable change when the independent variable changes by 1%

In(C)^⁢  =  3.79−1.18⁢     In⁢  (P)+0.14⁢    In(I)

since coefficient of price is negative , when price increases by 1% , consumption decreases by 1.18%

b) yes , since the p value < 0.05 , we can say that   price elasticity of demand is statistically significant.

P value = 0.0054 < 0.05

c) As the annual income increases by 1%, consumption increase by _0.14__ % since coefficient of income elasticity is positive , so when. income increase , consumption will increase

d)NO  , since the p value > 0.05 , we can say that   income elasticity of demand is not statistically significant so we cannot conclude that income elasticity of demand for cigarettes is statistically significant.

P value = 0.3926> 0.05