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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.

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