3.12 CES utility with weights a. Show that the CES function x8 a + 8 ото 8 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 8 = 1 (perfect substitutes) and 80 (Cobb-Douglas). 1 c. Show that the MRS is strictly diminishing for all values of 8 < 1.

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3.12 CES utility with weights
a. Show that the CES function
46
+
ото
8
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 8 = 1 (perfect substitutes) and
80 (Cobb-Douglas).
=
c. Show that the MRS is strictly diminishing for all values of
8 < 1.
d. Show that if x = y, the MRS for this function depends
only on the relative sizes of a and B.
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 x y? How would you
interpret this geometrically?
=
Transcribed Image Text:typed please 3.12 CES utility with weights a. Show that the CES function 46 + ото 8 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 8 = 1 (perfect substitutes) and 80 (Cobb-Douglas). = c. Show that the MRS is strictly diminishing for all values of 8 < 1. d. Show that if x = y, the MRS for this function depends only on the relative sizes of a and B. 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 x y? How would you interpret this geometrically? =
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