2) Suppose that the price of good X is $1 00 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 3 y 1 3 (18 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 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 workI recommend an excel spreadsheet If you use calculus, show your work if you use a spreadsheet, please submit the spreadsheet (3 Points) 1b Calculate the Marginal Utility of Y (3 Points) 1c What is the optimal Choice of X and Y given the P X $1 50, P Y $3 and I $90 This answer requires a numerical answer If you use a spreadsheet, please submit the spreadsheet if you derive the answer, please show your work (4 Points) (X,Y) x 2 3 y 1 3 (90 1 50X 3Y)this is a hint 1d If Income is decreased to $81 (I 1 $81) would your optimal choice of X and Y change and why This does not require math (2 Points) 1e You don't need math to answer this question In 2c, your income is $90 and in 2d, your income is $81 Which will have a higher level of Utility ( 2c or 2d) (2 Points)

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2) Suppose that the price of good X is $1.00 and the price of good Y is $3. You have $90 to spend and your

2) Suppose that the price of good X is $1.00 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(18 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.

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 workI recommend an excel spreadsheet. If you use calculus, show your work; if you use a spreadsheet, please submit the spreadsheet. (3 Points)

1b. Calculate the Marginal Utility of Y (3 Points)

1c. What is the optimal Choice of X and Y given the P_X = $1.50, P_Y= $3 and I = $90. This answer requires a numerical answer. If you use a spreadsheet, please submit the spreadsheet; if you derive the answer, please show your work. (4 Points)

(X,Y) = x^2/3y^1/3+ (90 - 1.50X - 3Y)this is a hint.

1d. If Income is decreased to $81 (I₁ = $81) would your optimal choice of X and Y change and why. This does not require math. (2 Points)

1e. You don't need math to answer this question.In #2c, your income is $90 and in #2d, your income is $81. Which will have a higher level of Utility (#2c or #2d) (2 Points)