Suppose that an individual gains utility from two goods: X and Y. For the purposes of...

 

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Suppose that an individual gains utility from two goods: X and Y. For the purposes of this question, keep Good X on the x-axis and Good Y on the y-axis (for drawing figures). This individual also has a Utility Function given by: U(X,Y) = XY 1. Plot an Indifference Curve for a Utility Level of U = 16. Label (at least) three points on this Indifference Curve. [2 points] Note that this utility function has the following Marginal Utilities (the following is not a typo): MUX = Y MUY = X 2. Suppose that an individual decides to purchase 8 units of Good X and 24 units of Good Y. What utility do they gain from this bundle of goods? What is their Marginal Rate of Substitution (MRS) at this bundle? [2 points] Suppose also that the price of Good X (px) is $15 per unit and the price of Good Y (py) is $45 per unit. 3. What ratio must this individual consume X to Y if they are utility maximizing? [2 points] Finally, suppose that this individual has a total income (m) of $450 to spend on X and Y. 4. What must their utility-maximizing choice of X and Y be, given their income? What utility do they gain from this bundle [2 points] 5. Draw a figure with the following: [2 points] a. The Budget Constraint, including the x-intercept and y-intercept. b. The utility-maximizing bundle. c. The Indifference curve that the utility maximizing bundle is on. Include at least one other bundle of X and Y that is on this same Indifference Curve. Suppose that an individual gains utility from two goods: X and Y. For the purposes of this question, keep Good X on the x-axis and Good Y on the y-axis (for drawing figures). This individual also has a Utility Function given by: U(X,Y) = XY 1. Plot an Indifference Curve for a Utility Level of U = 16. Label (at least) three points on this Indifference Curve. [2 points] Note that this utility function has the following Marginal Utilities (the following is not a typo): MUX = Y MUY = X 2. Suppose that an individual decides to purchase 8 units of Good X and 24 units of Good Y. What utility do they gain from this bundle of goods? What is their Marginal Rate of Substitution (MRS) at this bundle? [2 points] Suppose also that the price of Good X (px) is $15 per unit and the price of Good Y (py) is $45 per unit. 3. What ratio must this individual consume X to Y if they are utility maximizing? [2 points] Finally, suppose that this individual has a total income (m) of $450 to spend on X and Y. 4. What must their utility-maximizing choice of X and Y be, given their income? What utility do they gain from this bundle [2 points] 5. Draw a figure with the following: [2 points] a. The Budget Constraint, including the x-intercept and y-intercept. b. The utility-maximizing bundle. c. The Indifference curve that the utility maximizing bundle is on. Include at least one other bundle of X and Y that is on this same Indifference Curve.