Antonio's utility function for the goods X and Y is U(X, Y) = 2(√X + √Y).
For this utility function,
MUX = 1√X
MUY = 1√X
a. What is his MRSXY? Do his preferences satisfy the declining MRS property?
b. Suppose his monthly income is $1,800 and X and Y both cost $1 per unit. What is his best choice?
c. Suppose the price of good X rises to $2 per unit. What is his new best choice? Decompose the change in his purchase into substitution and income effects. What is his compensating variation for the price change?
d. If you measured the change in consumer surplus from the price change in part (c) using Antonio's uncompensated (i.e., ordinary) demand curve for good X, would you overstate, understate, or get exactly correct the compensating variation?