This problem is meant to help you understand the relationship between utility maximization and expenditure minimization. Suppose you have the following utility function: U(x, y) = x1/3 y2/3 Let prices be px, py, and income be I.

a) Solve for the Marshallian demand for x and y, which we call gx(px, py, I) and gy(px, py, I).

b) Solve for the indirect utility function, which we call v(px, py, I).

c) Suppose now that you wants to achieve a utility level U. Solve for the Hicksian demand for x and y, which we will call hx(px, py, U) and hy(px, py, U). In other words, find the levels of x and y that minimize expenditure while achieving utility U.