1. Consider the utility function U(x; y) = min(2x; 3y) Let Px, Py and I denote the price of x, the price of y and the income level, respectively.
a) Find the Hicksian demand functions for x and y.
b) Find the expenditure function.
c) Without solving the utility maximization problem, recover the indirect utility function and the Marshallian demand functions.
d) Now suppose that Px = 4, Py = 3 and I = 50. Compute the value of the Marshallian demands for x and y and the corresponding optimal utility level, u
e) Use the utility level computed in part (d) to verify that the Hicksian demands are equal to the Marshallian demands for x and y.
2. Jane's utility function has the following form: U(x; y) = x2 + xy The prices of x and y are Px and Py respectively. Jane's income is I.
a) Find the Marshallian demands for x and y and the indirect utility function.
b) Without solving the cost minimization problem, recover the Hicksian demands for x and y and the expenditure function from the Marshallian demands and the indirect utility function.
c) Write down the Slutsky equation determining the eect of a change in Px on the demand of x. Indicate which component represents the total price eect, which component represents the substitution eect, and which component represents the income eect.
d) Now assume that Px = 6, Py = 2, and I = 200. Using the Slutsky equation from part (c) compute the total, substitution, and income effect of a change in Px on the demand of x