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)

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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).