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

Suppose a consumer's utility function is given by U ( X , Y ) = X 1 2 Y 1 2. The price of X is P_X=8 and the price of Y is P_Y=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 P_X decreases to $4. What is the new bundle of X and Y that the consumer will demand?
d) (4 points) Calculate the compensating variation.
e) (4 points) How much extra money would the consumer need in order to have the same utility level after the price change as before the price change?
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?

Expert Solution

Rahul Sunny answered 1 year ago

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