1. Yvonne consumes only X and Y, which have prices PX = 3 and PY =1, and her income is 12.
a. Solve for Y on her budget line (as a function of X).
b. Differentiate Y with respect to X to find the slope of her budget line.
c. If Yvonne's utility is represented by U(X,Y) = X*Y^3, derive hers marginal utility of Y.
d. IF INSTEAD her utility is represented by U(X,Y) = X*Y (NOT X*Y^3), derive using calculus how much X she buys (hint: use your solution in a.).