Let u(r) be a utility function that represents and let f(.) be a continuous monotonic function. f(z) is monotonic when z > y = f(z) > f(y) (a) Show that any monotonic transformation of the utility function (f o u) can also represent the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function doesn't change the marginal rate of substitution? (Hint: MRS = ) (c) What kind of preferences are represented by a utility function of the form u(z1, 12) = Vn+n? What about the function e(1,72) = 13r, + 13r2? (d) Consider the function u(z1,72) = Van. What kind of preferences does it represent? Is the function v(I1,I2) = r¡12 a monotonie trans- formation of u(11,z2)? Is the function w(I1,72) = r7 monotonic transformation of u(1,12)?

Let u(r) be a utility function that represents and let f(.) be a continuous monotonic function. f(z) is monotonic when z > y = f(z) > f(y) (a) Show that any monotonic transformation of the utility function (f o u) can also represent the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function doesn't change the marginal rate of substitution? (Hint: MRS = ) (c) What kind of preferences are represented by a utility function of the form u(z1, 12) = Vn+n? What about the function e(1,72) = 13r, + 13r2? (d) Consider the function u(z1,72) = Van. What kind of preferences does it represent? Is the function v(I1,I2) = r¡12 a monotonie trans- formation of u(11,z2)? Is the function w(I1,72) = r7 monotonic transformation of u(1,12)?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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