3.12 Ces utility

a. Show that the CES function

is homothetic. How does the MRS depend on the ratio y/x?

b. Show that your results from part

(a) agree with our discussion of the cases δ = 1 (perfect substitutes) and δ = 0 (Cobb–Douglas).

c. Show that the MRS is strictly diminishing for all values of δ

d. Show that if x = y, the MRS for this function depends only on the relative sizes of α and β.

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

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