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Price of good X is $1.50 and the price of good Y is $3. You have $45 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).  

MY TRY: MUx= 2/3 (x-1/3y1/3)

b. Calculate the Marginal Utility of Y

MY TRY: MUy= 1/3(x2/3y-2/3)

c. What is the optimal choice of X and Y given the PX = $1.50, PY = $3 and I = $45. This answer requires a numerical answer. £(X,Y) = x2/3y1/3 + λ(45 – 1.50X – 3Y)—this is a hint.

d. If Income is decreased to $81 (I1 = $81) calculate and show your work on how the optimal choice of X and Y change.  

e. At an income of $81 and the price of good X is $1.50 and the price of good Y is $3, what is the total utility achieved given the Utility Function.