Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (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 represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?
Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (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 represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.11P
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Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)).
(a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences.
(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 represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?
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