Suppose a consumer\'s utility function is given by U(X,Y) = X*Y. Therefore; MUx=

ID: 1216490 • Letter: S

Question

Suppose a consumer's utility function is given by U(X,Y) = X*Y.

Therefore;

MUx=Y

MUy=X

Also, the consumer has $36 to spend, and the price of X, PX = 9, and the price of Y, PY = 2.

A) How much X and Y should the consumer purchase in order to maximize her utility?

B) How much total utility does the consumer receive?

C) Now suppose PX decreases to 1. What is the new bundle of X and Y that the consumer will demand?

D) How much money would the consumer need in order to have the same utility level after the price change as before the price change?

E) Of the total change in the quantity demanded of X, how much is due to the substitution effect and how much is due to the income effect?

U = X.Y

Budget line: 36 = 9X + 2Y

(a) Consumption is optimal when (MUX / MUY) = PX / PY

Y / X = 9 / 2

9X = 2Y

Substituting in budget line,

36 = 9X + 2Y = 9X + 9X = 18X

X = 36/18 = 2

Y = 9X / 2 = (9 x 2) / 2 = 9

(b) When X = 2 & Y = 9,

U = X.Y = 2 x 9 = 18

Consumption is optimal when (MUX / MUY) = 1 / 2

Y / X = 1 / 2

X = 2Y

Substituting in budget line,

36 = X + 2Y = X + X = 2X

X = 36 / 2 = 18

Y = X / 2 = 18 / 2 = 9

(D) Utility before price change = 18

Putting X = 2Y in utility function,

18 = X.Y = 2Y x Y = 2Y2

Y2 = 18 / 2 = 9

Y = 3

X = 2Y = 2 x 3 = 6

Income required to buy 6X & 3Y using old prices = 6 x 9 + 3 x 2 = 54 + 6 = 60

Note: First 4 sub-parts are answered.

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