Suppose that the 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) = x^1/3y^2/3(23 Points)

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.

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 spreadsheetboth work.If you use calculus, show your work; if you use a spreadsheet, please submit the spreadsheet.(4 Points)

b.Calculate the Marginal Utility of Y(4 Points)

c.What is the optimal Choice of X and Y given the P_X = $1.50, P_Y = $3 and I = $45.This answer requires a numerical answer.If you use a spreadsheet, please submit the spreadsheet; if you derive the answer, please show your work.(6 Points)

(X,Y) = x^1/3y^\2/3 + (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. (4 Points)

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