Question: Suppose a consumer's utility function is given byU(X,Y)=X12Y12 .The price of X is PX=8 and the price of Y is PY=5.The consumer has M=80 to

Suppose a consumer's utility function is given byU(X,Y)=X12Y12

.The price of X is PX=8 and the price of Y is PY=5.The consumer has M=80 to spend.

You may find that it helps to draw a graph to organize the information in this question. You may draw in the blank area on the front page of the assignment, but this graph will not be graded.

a) (2 points) How much X and Y should the consumer purchase in order to maximize their utility?

b) (2 points) How much utility does the consumer receive?

c) (4 points) Now suppose PXdecreases to $4. What is the new bundle of X and Y that the consumer will demand?

d) (4 points) Calculate the equivalent variation.

e) (4 points) How much money would the consumer be willing to pay to avoid the price increase?

f) ( 4 points) 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?

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