# Intermediate microeconomic theory. For this exercise replace A with the last digit and B with the second-to-last digit of your ASU ID#. Assume preferences can be represented by the following utility function: u(x1; x2) = (A + 1) ln (x1) + ln (x2); a. Is the utility function monotonic? Justify. b. Determine the set of bundles that are ranked higher than the bundle (x1; x2) = (10; 10) c. Set up the utility maximization problem for the consumer, when facing prices p1 = 6; p2 = B + 1 and income m = 2520(A + 2): d. Solve the problem by Önding (x 1 ; x 2 ): e. Graph the budget set, a couple of indi§erence curves and the optimal choice. Exercise 8: Assume preferences can be represented by the following utility function: u(x1; x2) = x1 2 + 150×1 2×2 2 + 100×2 + x1 x2 a. Is the utility function monotonic? Justify. b. Obtain a bundle that is ranked higher than the bundle (x1; x2) = (100; 100) c. Set up the utility maximization problem for the consumer, when facing: prices p1 = 2; p2 = 1 and income m = 30: d. Solve the problem by Önding (x 1 ; x 2 ): Exercise 9: Assume preferences can be represented by the following utility function: u(x1; x2) = 4 ln (x1) + x2 a. Is the utility function monotonic? Justify. b. Set up the consumerís utility maximization problem for prices p1; p2 and income m (the general case) c. Solve the problem. You will obtain solutions x 1 (p1; p2; m); x 2 (p1; p2; m) in terms of the parameters of the model (p1; p2; m): 1
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