PRACTICE QUESTIONS

QUESTION 1:
Consider a government that is contemplating introducing a gasoline tax to reduce gasoline consumption together with a (lump-sum) rebate to consumers to alleviate the negative e ect of the gasoline tax on their well-being. Use an indi erence curve map for two goods
(gasoline and other goods) to show
(a) the equilibrium if the rebate is based on the nal (post-tax) consumption of gasoline,
(b) the equilibrium if the rebate is based on the original (pre-tax) consumption of gasoline,
(c) that the government pays out more than it receives in tax revenues if the rebate is based on the original consumption of gasoline, and
(d) that consumers are better o than before the tax if the rebate is based on the original consumption of gasoline.

QUESTION 2:
Consider an individual who consumes only two goods, x1 and x2 , and assume that the utility this individual receives from these goods (u) is given by: u = xa xb , where a > 0 and
1 2 b > 0. The individual's income is m = 100, and the prices of the two goods are p1 and p2 .
(a) Derive the ordinary demand functions for both x1 and x2 .
(b) Assume that a = b = 0:5 and p2 = 1 and consider an increase in p1 from 1 to 2.
(i) Compute the compensating variation.
(ii) Compute the equivalent variation.
(c) Assume that a = b = 0:25 and p2 = 1 and consider a decrease in p1 from 2 to 1.
(i) Compute the compensating variation.
(ii) Compute the equivalent variation.

QUESTION 3:
Consider an individual who consumes only two goods, x1 and x2 , and assume that the utility this individual receives from these goods (u) is given by: u = ax1 + ln xb , where
2
a > 0 and b > 0. The individual's income is m = 100, and the prices of the two goods are p1 and p2 .
(a) Derive the ordinary demand functions for both x1 and x2 .

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(b) De ne three ways of measuring the welfare change