Question

Given the following estimated demand equation Answer the following questions

“From the data for 46 States in the United States for 1002, the following Regression Equation was estimated:

Ln C =             6.30 – 1.39 LnP + 0.67 LnY

T- Stats:          (0.91) (- 2.45)     ( 0.45)                      R² _=0.78

Where C = Cigarette consumption packs per year

            P = real price per pack

            Y = real disposable income per capita           

a). What is the elasticity of demand for cigarettes with respect to price? Is it statistically significant? Interpret this number in plain English

b) What is the Income Elasticity of Demand for Cigarettes? Is it statistically significant? Interpret this number

c) Using your calculator, or EXCEL can you predict the level of Consumption of Cigarettes when the Price per pack is $6.85, and Income per capita is $44,600? What is that number?

d) Suppose you are asked to identify the consumption pattern of women smokers, can you use this same estimated regression coefficients to comment on that? If not, Why not? What would you do differently?

Answer 1

a) when regression is in log-log form, coefficients represent elasticity with respect to the given variable.

1.39 is the elasticity of demand for cigarettes with respect to price.

t-stats for P is 2.45 ( see absolute value) which is greater than critical value of 1.96, so we reject the null hypothesis that the effect of price is 0. Therefore P is significant statistically. This price affects consumption of cigarettes.

b) 0.67 is the income elasticity. t stats is .45 which is less than critical value of 1.96. Thus we do not reject the null hypothesis and conclude that income is not statistically significant. income does not affect changes in consumption of cigarettes.

c) LnC= 6.30 -1.39(ln6.85) + 0.67(ln44600)

LnC = 6.30 -1.39(1.92) + 0.67(10.70)

LnC = 10.8002

C = antiln(10.8002)= 49030.6062

d) we cannot estimate pattern of women smokers with the same estimated regression coefficient. For that we need to add a dummy variable for gender, which will be 1 for females and 0 for males.