Question

1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose U(X1, X2) = min{5X1, X2}. (6pts) a. Write out the Marshallian demands for x, and X, as functions of p1, p2, and m. b. Now, solve for these when P, = 3, P2 = 1, and m = 16. c. Is this an interior or corner solution? d. Is the budget exhausted here? Yes/no 3. Suppose U(X1, X2) = 2.5x, + 7.5x2 (8pts) a. Write out the Marshallian demands for x, and X, as functions of p1, p2, and m. (Hint: there will be more than one solution based on the MRT and MRS values!) b. Now, solve for these when P, = 6, P, = 4, and m = 36. c. Is this an interior or corner solution? d. Is the budget exhausted here? Yes/no 4. Suppose U(x, y) = x/2x2 (6pts) a. Solve for the marshallian demands for x, and x,, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers. Start by writing down the budget equation and finding MRS and MRT.)

Answer 1

,-.2ma, 3/M2, 3 RS 2 3 31 Leyek MRS, 3 2 31, 3P A,P = 서 시122+h. 13M SP2 M 오m 1 MS 2M

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