2) Suppose that the price of good X is $2 and the price of good Y is $3. You have $90 to spend and your preferences over X and Y are defined as:    

U(x,y) = x^2/3y^1/3                                                                                                 

Keep in mind that we review this concept because consumer choice is based on their preferences. People demand items that fulfill their Utility (perhaps happiness). As a result, we need to visualize how an individual’s budget is allocated to create the highest level of Utility.

1. 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. If you use calculus, show your work; if you use a spreadsheet, please submit the spreadsheet.

2. Calculate the Marginal Utility of Y

3. What is the optimal Choice of X and Y given the P_X = $2, P_Y = $3 and I = $100

£(X,Y) = x^2/3y^1/3 + ?(90 – 2X – 3Y)

           

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

Note that we would not change the utility function (only the income constraint changed)

5. 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.