Utility Function: U = ln (x) + ln (z)

Budget Constraint: 120 = 2x + 3z

(a) Find the optimal values of x and z

(b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z

Problem 4

(a) Derive the demand functions for the utility function

(b) Let a = 2, b = 5, p_x = 1, p_z = 3, and Y = 75. Find the optimal values for x and z.

Problem 5

Utility Function:

Time Constraint: H=24-

Income Constraint: Y=wH

w=16

Solve for the optimal values of and Y using the Substitution Method