3.14 CES utility

a. Show that the CES function + B 8 is homothetic. How does the MRS depend on the ratio y/x? aw/ax

b. Show that your results from part

(a) agree with our discussion of the cases = 1 (perfect substitutes) and 80 (Cobb-Douglas). plug in

c. Show that the MRS is strictly diminishing for all values of 8 <1. +2/n - 2/1tatn+fitzz 722

d. Show that if xy, the MRS for this function depends only on the relative sizes of a and B. plug

e. Calculate the MRS for this function when y/x = 0.9 and y/x=1.1 for the two cases 8 = 0.5 and 8 -1. What do you conclude about the extent to which the MRS changes in the vicinity of xy? How would you interpret this geometrically?