Ann consumes 2 goods, x and y. Her utility function is U(x; y) = x^(1/3)*y(2/3) Let Px and Py denote the prices of goods x and y, respectively, and let m denote Ann's income.

(1) Find Ann's Marshallian demand functions for x and y.

(2) Ann would like to know the least expensive bundle for each utility level. Find this optimal bundle as a function of px; py, and utility level (i.e., the Hicksian demand functions).

(3) Assume that Px = 4; Py = 1, and m = 12. Using your answers to part (1) and part (2),and the Hicksian substitution and income effects if the price of x changes to 1.

(4) Repeat (3) using only Marshallian demand functions (not Hicksian demand functions).