Problem 2: Suppose for now that X R (for example, imagine that there are two goo

Question

Problem 2: Suppose for now that X R (for example, imagine that there are two goods in this economy, and any vector x = (21,22) E X represents how much a person consumes of each). Jack and Jill work for a super secretive organization that tracks the purchases of students in campus supermarkets, and check whether those choices satisly and B. Their friend, John, being the rational person he is, makes choices that indeed satisfy and A, so Jack and Jill both come up with a utility function that can be used to model John's choices. Jack comes up with U(x1,x2)-xi and Jill comes up with V(zi,T2) 1n(n) + ln(T2). Their boss tells them to get their act together and decide which one is "the true" utility function that represents John's choices: is it U or is it V? They proceed to explain that both U and V can be used to model the choices John makes. Explain why.

Explanation / Answer

Yes. Both of them can be used to used the ultilty function of John.

This is beaucse of the the assumption of monotonocity. Here U2 is a monotonic transformation of U1.

taking log on both side of U1 will give us 1/2 U2.

Also, since they are incresing functions in MU x1 and MU x2. We can use the monotonic transformation.

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