5. P5: Lagrange Multiplier Method a. Consider the following utility function: U=X¹Y¹, x,y> 0. Let Pa = 2 and Py = 3 and M 100. Find the utility-maximizing consumption bundle. b. Find the marginal utilities of the goods, x and y. Are they always positive? c. Sketch their graphs. d. By implicit differentiation, find the slope of any difference curve and show that it is given by the ratio of marginal utilities of the two goods. Are the indifference curves always negatively sloped? Sketch their graphs.

5. P5: Lagrange Multiplier Method a. Consider the following utility function: U=X¹Y¹, x,y> 0. Let Pa = 2 and Py = 3 and M 100. Find the utility-maximizing consumption bundle. b. Find the marginal utilities of the goods, x and y. Are they always positive? c. Sketch their graphs. d. By implicit differentiation, find the slope of any difference curve and show that it is given by the ratio of marginal utilities of the two goods. Are the indifference curves always negatively sloped? Sketch their graphs.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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