1. Consider the utility function u(x1, x2)=xxx-a where a > 0. The consumer faces the prices p = (P1, P2) and wealth w. (a) Write the consumer's Utility Maximization Problem (UMP). (b) Write down the Lagrangian function and Kuhn-Tucker conditions of UMP. (c) Find the Walrasian demands. (d) Find the Slutsky matrix from Walrasian demands. (e) Are good 1 and good 2 compliments? Substitutes? (f) Find the indirect utility function. (g) Show that the partial derivative of the indirect utility function with respect to w equals the Lagrange multiplier of UMP. (h) Find the expenditure function without using EMP. (i) Find the Hicksian demands without using EMP.

1. Consider the utility function u(x1, x2)=xxx-a where a > 0. The consumer faces the prices p = (P1, P2) and wealth w. (a) Write the consumer's Utility Maximization Problem (UMP). (b) Write down the Lagrangian function and Kuhn-Tucker conditions of UMP. (c) Find the Walrasian demands. (d) Find the Slutsky matrix from Walrasian demands. (e) Are good 1 and good 2 compliments? Substitutes? (f) Find the indirect utility function. (g) Show that the partial derivative of the indirect utility function with respect to w equals the Lagrange multiplier of UMP. (h) Find the expenditure function without using EMP. (i) Find the Hicksian demands without using EMP.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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