Question 1There are four utility functions defined as follows:U(r, y) 5 ln r +6 ln yU2(x, y) = r+yU3(x, y) r'yU(a, y) = r/y +91. Show that the utility functions U1(), Us() and Us() represent the same preference ordering.2. Show that utility functions U2() and Ua(-) do not represent the same preference ordering.3. Draw the indifference curve of each utility function at threshold 10 and shade in the uppercontour set. Based on your plots, state whether each utility function is quasi-concave or not.

Solution1: We have U1x,y=5lnx+6lny .... (1) U3(x,y)=x5y6 .... (2) and…

Question 1 There are four utility functions defined as follows: U(x,y) 5 ln r +6 ln y U2(x, y) = r+y U3(x, y) = r'y U(r, y) = r/"y +9 %3D %3D 1. Show that the utility functions U:(), Us() and Us() represent the same preference ordering.

Question 1 There are four utility functions defined as follows: U(x,y) 5 ln r +6 ln y U2(x, y) = r+y U3(x, y) = r'y U(r, y) = r/"y +9 %3D %3D 1. Show that the utility functions U:(), Us() and Us() represent the same preference ordering.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.11P

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