4. Let u(z) be a utility function that represents the preferences of a household. Wesay that the function v(r) is a monotonic transformation of u if f(-) is a strictlyincreasing function and v(z) = f(u(z)).(a) Show that if v(z) is a monotonic transformation of u, it represents the samepreforences.(b) Can you explain why taking a monotonic transformation of a utility functiondoes not change the marginal rate of substitution?(c) What kind of preferences are reprosented by a utility function of the formu(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 itrepresent? Is the function (11, r2)jz a monotonic transformation of1u(r1, 12)? Is the function w(r1, 12)u(r1, 12)?= zfr a monotonic transformation of

The utility is the want satisfying power of the commodity. The utility would result in the demand of…

(c) What kind of preferences are represented by a utility function of the form u(21,72) = VE1+ 12? What about the function v(z1,2) = 13z + 13z2? (d) Consider the function u(z1, r2) represent? Is the function v(z1, 2) = a a monotonic transformation of = Vın. What kind of preferences does it

(c) What kind of preferences are represented by a utility function of the form u(21,72) = VE1+ 12? What about the function v(z1,2) = 13z + 13z2? (d) Consider the function u(z1, r2) represent? Is the function v(z1, 2) = a a monotonic transformation of = Vın. What kind of preferences does it

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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Question

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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