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


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?
P x
x = y
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
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
CV= ( 36- 9 + 36) - (72)
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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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