|Question||Sam’s utility function for his monthly consumption of goods X and Y is U(X, Y) = 100 X – X2 + Y.
Assume this function applies only for bundles that contain no more than 100 units of X; bundles with greater amounts of X are not relevant for the question. Sam’s monthly income is $3,000, and the price of Y is $1.
a. What is Sam’s uncompensated demand function for X, as a function of PX?
b. Suppose the price of X is initially $20, and that it rises to a price PX greater than $20. What is Sam’s compensating variation for this price change (expressed as a function of PX)?
c. What is Sam’s compensated demand function for good X, fixing the utility level he achieved at the original price of good X(PX = $20)? How does it compare to your answer in part (a)? Why?
d. Compute the change in consumer surplus for this change to a price PX greater than $20. How does it compare to your answer in part (b)?