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What kind of preferences are represented by a utility function of the form u(71,72) = VE + z2? What about the function v(z1, z2) = 13z1 + 13z2? (d) Consider the function u(z1, 2) = VI. What kind of preferences does it represent? Is the function v(z1,zn) = rjn a monotonic transformation of

What kind of preferences are represented by a utility function of the form u(71,72) = VE + z2? What about the function v(z1, z2) = 13z1 + 13z2? (d) Consider the function u(z1, 2) = VI. What kind of preferences does it represent? Is the function v(z1,zn) = rjn a monotonic transformation of

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.5P
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Part C  and D

4. Let u(z) be a utility function that represents the preferences of a household. We say that the function v(r) is a monotonic transformation of u if f(-) is a strictly increasing function and v(z) = f(u(z)). (a) Show that if v(z) is a monotonic transformation of u, it represents the same preforences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are reprosented by a utility function of the form u(a1, 12) = VEi +#2? What about the function v(z1, r2) = 13z + 13r2? (d) Consider the function u(r1, 2) = VE1#2. What kind of preferences does it represent? Is the function (11, r2) jz a monotonic transformation of 1 u(r1, 12)? Is the function w(r1, 12) u(r1, 12)? = zfr a monotonic transformation of
Transcribed Image Text:4. Let u(z) be a utility function that represents the preferences of a household. We say that the function v(r) is a monotonic transformation of u if f(-) is a strictly increasing function and v(z) = f(u(z)). (a) Show that if v(z) is a monotonic transformation of u, it represents the same preforences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are reprosented by a utility function of the form u(a1, 12) = VEi +#2? What about the function v(z1, r2) = 13z + 13r2? (d) Consider the function u(r1, 2) = VE1#2. What kind of preferences does it represent? Is the function (11, r2) jz a monotonic transformation of 1 u(r1, 12)? Is the function w(r1, 12) u(r1, 12)? = zfr a monotonic transformation of
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