Mario and Luigi both have the utility function U(x,y) = (1/3)^4/3 x^2/3 y^4/3. They each spend their income I on goods x and y.

(a) Mario and Luigi only diﬀer in their incomes, which are $324 for Mario and $450 for Luigi. What is the aggregate demand function for good x in terms of its price px?

(b) Now forget about Luigi. Initially, prices are px = 4/3 and py = 3. Then the price of good x increases to px = 9/2. What is the total eﬀect of the price change on Mario’s consumption

(remember that Mario’s income is $324)?

(c) What is the utility Mario obtained under the old prices?

(d) What is the income Mario would need to be as well oﬀ after the price increase as before?

(e) What are the income and substitution eﬀects of that price change for Mario’s consumption of good x?