3. Suppose that the utility functions u(r, y) and v(x, y) are related by v(r, y) = f(u(x,y)). In each case below, check if f is a positive monotonic transformation' of u. %3D (a) f(u) = 3.141592u (b) f(u) = 5000 – 23u (c) f(u) = = (d) f(u) = -u-1

3. Suppose that the utility functions u(r, y) and v(x, y) are related by v(r, y) = f(u(x,y)). In each case below, check if f is a positive monotonic transformation' of u. %3D (a) f(u) = 3.141592u (b) f(u) = 5000 – 23u (c) f(u) = = (d) f(u) = -u-1

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.3P

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Question

3. Suppose that the utility functions u(x, y) and v(x, y) are related by v(x, y) = f(u(x, y)).
In each case below, check if f is a positive monotonic transformation' of u.
(a) f(u)
= 3.141592u
(b) f(u) = 5000 – 23u
(c) f(u) = !
%3D
(d) f(u) = -u-1

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4.An individual consumes products X and Y and spends $30 per time period. The prices of the two goods are $3 per unit for X and $3 per unit for Y. The consumer in this case has a utility function expressed as: U(X.Y) = 0.5XY How much X should this individual consume, given that he is maximizing the utility? ( A) 4.17 ( B) 5 (C)6 D) 6.25
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4