- 6 Note That The Slopes Of The Indifference Curves For Each Of The Utility Functions Of Question 5 Are The Same This Is 1 (80.83 KiB) Viewed 35 times
I interpret the previous question as:
Want to show:
given F'(u) > 0 & u > 0
that (du/dx1)/(du/dx2) = (dF(u)/dx1)/(dF(u)/dx2)
Since dF(u)/dx1 = (dF(u)/du)(du/dx1)
and dF(u)/dx2 = (dF(u)/du)(du/dx2),
(dF(u)/dx1)/(dF(u)/dx2)
= (dF(u)/du)(du/dx1)/(dF(u)/du)(du/dx2) [chain rule]
= (du/dx1)/(du/dx2) [dF(u)/du != 0]
Can someone please tell me what I missed?
6. Note that the slopes of the indifference curves for each of the utility functions of question 5 are the same. This is because of the functional relationship between the utility functions. That is, û F(u) = u? and ū= F(u) = Buk. = = FOR FUNCTIONS OF N-VARIABLES In both cases the derivative of the F function, F'(-), is positive on u > 0. We call such an F function a positive monotonic transformation of u. Show that for any such F used to generate a function of some original function u(x1,4?). the resulting function has indifference curves (or more generally level curves) with the same shape.