Consider the following 6 utility functions: U1 = /x + 2y U2 = v2x + Jy U3 = 2x2 + y? + Jy U5 = min(x,y) +2 U6 = 2 In(x) + In(y) U4 %3D a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met.
Consider the following 6 utility functions: U1 = /x + 2y U2 = v2x + Jy U3 = 2x2 + y? + Jy U5 = min(x,y) +2 U6 = 2 In(x) + In(y) U4 %3D a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.11P
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![Consider the following 6 utility functions:
U1 = Vx + 2y
U2 = v2x + Vy
Uz = 2x2 + y?
+ Vy
U4
2
Ug = min(x,y)+;
2
Us = 2 In(x) + In(y)
%3D
a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and
determine whether monotonicity and convexity are met.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa1f2822-8ee5-4468-b761-4648e25887d9%2F34ad5253-8edb-46d5-911b-b36648018de1%2Friwy5ar_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following 6 utility functions:
U1 = Vx + 2y
U2 = v2x + Vy
Uz = 2x2 + y?
+ Vy
U4
2
Ug = min(x,y)+;
2
Us = 2 In(x) + In(y)
%3D
a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and
determine whether monotonicity and convexity are met.
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