Problem 1. In this problem we will get clear on the difference between the Slutsky and Hicks decompositions
of price effects. Let's explore the gasoline consumption of a consumer named Aliyah, who, after paying for
rent and food and all other essentials, has $400 per month to spend on gasoline, G, and dollars-worth of all
other discretionary spending, Y. Assume Aliyah has CES preferences represented by $U(G, Y) = (G^\gamma + Y^\gamma)^{\frac{1}{\gamma}}$
where $\gamma = 0.5$, and assume that initially the price of gasoline is $4.00. Note throughout this problem set
that if Y represents all other goods, then $P_y = 1$.
(b) Let's see what happens if the government imposes a tax on gasoline that raises the price per gallon by
$1.00.
(i) Compute Aliyah's consumption of gasoline under the new tax.
(ii) Add her new budget constraint and optimal bundle to your graph.
(iii) What is the total change in Aliyah's demand for gasoline as a result of the tax?
(iv) What is Aliyah's new utility level? Label her new indifference curve with this utility level.
