typed please3.12 CES utility with weightsa. Show that the CES function46+ото8is homothetic. How does the MRS depend on the ratioy/x?b. Show that your results from part (a) agree with ourdiscussion of the cases 8 = 1 (perfect substitutes) and8 = 0 (Cobb-Douglas).=c. Show that the MRS is strictly diminishing for all values of8 < 1.d. Show that if x = y, the MRS for this function dependsonly on the relative sizes of a and B.e. Calculate the MRS for this function when y/x = 0.9and y/x1.1 for the two cases 8 = 0.5 and 8 = -1.What do you conclude about the extent to which theMRS changes in the vicinity of x y? How would youinterpret this geometrically?=

Marginal Rate Substitution is the ratio of marginal utility obtained from one good, say x and…

a. Show that the CES function 46 a + 8 28 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 8= 0 (Cobb-Douglas). c. Show that the MRS is strictly diminishing for all values of 8 < 1.

a. Show that the CES function 46 a + 8 28 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 8= 0 (Cobb-Douglas). c. Show that the MRS is strictly diminishing for all values of 8 < 1.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

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
8 = 0 (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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