Question

Given the following estimated demand equation Answer the following questions

“From the data for 50 States in the United States , the following Regression Equation was estimated:

Ln C =    5.75 – 1.29 LnP + 0.67 LnY - 0.022LnA - 0.03LnExcT
T- Stats:    (0.91) (1.45)       (2.45)   (1.02)             (2.04)          
R2 = 0.87;
T- table value at 95%; and 46 degrees of freedom is 1.96.

Where C = Cigarette consumption packs per year
   P = real price per pack
   Y = Real disposable income per capita
       A= Per capita Advertising expenditure
       Exc = Excise tax per packet
   T-values are all in the parentheses  

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) Some people claim that Advertising has No bearing on consumption of cigarettes. Do you agree/ Why or Why Not?
d) Using your calculator, or EXCEL can you predict the level of Consumption of Cigarettes when the Price per pack is $6.25, Income per capita is $69,600, and Advertising expenditure is 30 million dollars? What is that number?
e) Suppose the State of Wisconsin is proposing to increase 10% increase in its Excise tax on cigarette for collecting more “sin-tax” and to promote healthy life-style. Do you think that measure will change anything? Why? Or Why not?

Answer 1

Answer a) The price elasticity of demand is measured by the partial slope coefficient value for the variable LnP which is 1.29. This means that as the price of cigarettes increases 1 percent, cigarette consumption pack per year on an average decreases by 1.29 percent holding all other variables as constant.

B) Income elasticity of demand is defined as the percentage change in cigarette consumption due to a percentage change in income. Here income elasticity of demand is 1.67 which shows that as income increases by 1 percent cigarette consumption pack per year increases by 1.67 percent holding all other variables as constant. It is statistically significant too beacuse the calculated t value which is 2.45 is greater than 1.96 and when this happens we reject the null hypothesis (Null hypothesis here is that the income variable is insignificant).

C) Here looking at the t value for advertising we find that the calculated t value is 1.02 which is less than 1.96 so we can't reject the null hypothesis. So the coefficient is statistically insignificant and we can say that advertising does not affect cigarette consumption.

D) ln C= 5.75 - 1.29 ln (6.25) + 0.67 ln (69600) - 0.022 ln (30,000,000)

Ln C = 5.75 - 2.364 +7.47 -0.379

Ln C = 10.477

C = 35489.77

E) Yes, with an increase in sin tax by 10 percent the cigarette consumption is expected to fall. Here from the regression results we can see that as sin tax increases by 10 percent the consumption of cigarettes on an average decreases by 0.3 percent holding all other variables as constant. Also the variable is statistically significant since the calculated t value is less than the critical t value.