The following table shows the relationship between Cigarette Excise Taxes per pa

Question

The following table shows the relationship between Cigarette Excise Taxes per pack and Cigarette Demand per Cigarette. Use the column b results. Interpret the coefficient on Excise Tax. Interpret the coefficient on income for a $I0.000 increase in income. Make sure to indicate whether the estimates are statistically different from zero. Use the column b results. Consider a person with income of $50,000. facing an excise tax on cigarettes of $1. This individual is a 30-year-old white. non-Hispanic male who completed high school (education level = 9 in these data). Calculate the elasticities of demand for cigarettes with respect to excise tax. income, and age. Now consider an individual with the exact same characteristics except where the person is female. What is the elasticity of demand for cigarettes with respect to excise tax in this case?

Explanation / Answer

(a) Coefficient of excise tax is - 2.28. It means that, ceteris paribus, if excise tax increases (decreases) by $1, demand for cigarette will decrease (increase) by $2.28

Coefficient of income is - 0.002. It means, as income increases (decreases) by $1,000, demand decreases (increases) by $0.002.

So, when income increases by $10,000 (a factor of 10), demand decreases by $0.02.

A regression coefficient is statistically significant if absolute value of its t-value is > 2. For Excise tax, absolute value of its t-statistic is 6.96 but for Income, it is 0.8. So Excise tax is statistically significant but Income is not.

(b) Regression equation is:

Demand, Q = 17.22 - 2.28 x Excise tax - 0.002 x Income + 2.23 x Male - 5.05 x AA + 0.13 x Age - 0.67 x Education - 6.5 x Hispanic

Note that, "Male", "AA" & "Hispanic" are dummy variables. For examples, if consumer is Male, then Male = 1, otherwise 0. If consumer is Hispanic, then Hispanic = 1, otherwise 0.

With given values,

Q = 17.22 - 2.28 x 1 - 0.002 x 50 + 2.23 x 1 - 5.05 x 1 (non-Hispanic = AA = 1 if true) + 0.13 x 30 - 0.67 x 9 - 6.5 x 0

Q = 17.22 - 2.28 - 0.1 + 2.23 - 5.05 + 3.9 - 6.03 = 9.89

(1) Elasticity for excise tax = (dQ / dExcise) x (Excise / Q) = - 2.28 x (1 / 9.89) = - 0.23

(2) Elasticity for Income = (dQ / dIncome) x (Income / Q) = - 0.002 x (50 / 9.89) = - 0.01

(3) Elasticity for Age = (dQ / dAge) x (Age / Q) = 0.13 x (30 / 9.89) = 0.39

(c) If the person is female, everything remains the same, only the part (2.23 x Male) becomes 0. So, new Q becomes

Q* = Q - 2.23 = 9.89 - 2.23 = 7.66

Elasticity for Excise tax = (dQ / dExcise) x (Excise / Q) = - 2.28 x (1 / 7.66) = - 0.30

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