Question

# 2) Suppose that the price of good X is \$2 and the price of good Y...

2) Suppose that the price of good X is \$2 and the price of good Y is \$3. You have \$140 to spend and your preferences over X and Y are defined as U(x,y) = x2/3y1/3

a. Calculate the marginal utility of X (remember, this is the change in utility resulting from a slight increase in consumption of X). You can either do this using calculus or an excel spreadsheet—both work. £(X,Y) = x2/3y1/3 + λ(140 – 2X – 3Y)

b. Calculate the Marginal Utility of Y

c. What is the optimal Choice of X and Y given the PX = \$2, PY = \$3 and I = \$140 £(X,Y) = x2/3y1/3 + λ(140 – 2X – 3Y)

d. At an income of \$140 and the price of good X is \$2 and the price of good Y is \$3, what is the total utility achieved given the Utility Function.

e. If Income is decreased to \$84 (I1 = \$84) calculate and show your work on how the optimal choice of X and Y change.

f. At an income of \$84 and the price of good X is \$2 and the price of good Y is \$3, what is the total utility achieved given the Utility Function.