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10476130I think I've got A-D correct but need help on E!

attachment_09232019.png

CD
M : 72
Px = 1
Py = 1
1. (24 total points) Suppose a consumer's utility function is given by U(X, Y) = X12*Y12. Also, the
consumer has $72 to spend, and the price of Good X, Px = $1. Let Good Y be a composite good whose
price is Py = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available
to spend on all other goods for any given value of X.
a) (2 points) How much X and Y should the consumer purchase in order to maximize her utility?
mux
P x
x = y
my
Py will
x* = 36
* = 36
b) (2 points) How much total utility does the consumer receive?
U = X//2 - 4/2 80 36120 36'2-36
c) (2 points) Now suppose Px increases to $9. What is the new bundle of X and Y that the consumer will
demand?
X = 4
9= 36
d) (2 points) How much additional money would the consumer need in order to have the same utility
level after the price change as before the price change? (Note: this amount of additional money is called
the Compensating Variation.)
01= 412 - 36/2 = 12
TOWOMIO
CV= ( 36- 9 + 36) - (72)
JOY augATe geAaJa
e) (2 points) Of the total change in the quantity demanded of Good X, how much is due to the substitution
effect and how much is due to the income effect? (Note: since there is an increase in the price of Good X,
these values will be negative).

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