Question 4 - Income & Substitution Effects - Subsidy II (8 points)

Xavier's preferences over cookies (x) and vodka (y) can be represented by the following utility function:

U(x; y) = xy³ where cookies are measured by boxes and vodka is measured by bottles.

1. If the price of a box of cookies is Px, the price of vodka is Py per bottle and Xavier has I (capital i) dollars to

spend, find Xavier's demand functions for cookies and vodka. (2 points)

2. Suppose that Px = 2; Py = 3 and I = 120. Using your answer in 1) find Xavier's demands for cookies

and vodka. (0.5 points)

3. Follow 2). Suppose due to climate change, average temperature dropped by 20^oF and the government

decides to give out 40/3 bottles of vodka for free to everyone to make them stay warm. Find the new

best bundle for Xavier. (1.5 points)

4. Still Follow 2). Now ignore the assumptions made in 3). Suppose instead of giving out vodka for free,

government decides to give price subsidy per unit of vodka such that Xavier achieves the same utility

level as the case with 40/3 bottles of vodka for free in 3). How much should be the subsidy per unit

and the total subsidy paid by the government? (Use calculator if needed.) (2 points)

5. Compare the expenditures by the government in 3) and 4). Explain the difference. (2 points)