Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y.

a. (4 pts) Show the demand function for X is X* = (Py /Px)^2. Then derive the demand function for Y.

b. (6 pts) Ceteris paribus, how does X* change when the price of X increases? When the price of Y increases? When income Increases? Show your work.

c. (6 pts) Now, let Py = $1, I = 24, and Px increases from $0.5 to $2. Decompose the effect of this price increase into the substitution effect and the income effect, and calculate their magnitude.

d. (8 pts) For the same price change (i.e., Px increases from $0.5 to $2), find the Compensating Variation (CV) and the Equivalence Variation (EV). How does your answer to this part relate to parts (b) and (c)?