Sandra's preferences over consumption bundles (x, y) are summarized by the following utility function: u (x1,...

 

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Sandra's preferences over consumption bundles (x, y) are summarized by the following utility function: u (x1, x2) = 16x-2x² + 4y, where x is the amount of good x that Sandra consumes and y is the amount of good y that Sandra consumes. Let p. and py be the prices of goods x and y, respectively. Let me be Sandra's income. Sandra's goal is to maximize her utility subject to her budget constraint. [40 marks] a. Find an algebraic expression for Sandra's marginal rate of substitution between goods x and y. Show your work. In addition, give a concise explanation of the meaning of the marginal rate of substitution. 2 AV2022/23 Semester 1 b. Suppose that p. - py-2 and m= 24. Use your answer from part (a) to determine Sandra's optimal consumption bundle. Show your work. c. Suppose now that p. increases to 6, while p, and m remain the same. What are Sandra's optimal choices for x and y in this case? Is Sandra better or worse off than she was in part (b)? Explain. d. How much extra income must Sandra be given in order to compensate her for the increase in the price of good x in part (c)? Explain. Sandra's preferences over consumption bundles (x, y) are summarized by the following utility function: u (x1, x2) = 16x-2x² + 4y, where x is the amount of good x that Sandra consumes and y is the amount of good y that Sandra consumes. Let p. and py be the prices of goods x and y, respectively. Let me be Sandra's income. Sandra's goal is to maximize her utility subject to her budget constraint. [40 marks] a. Find an algebraic expression for Sandra's marginal rate of substitution between goods x and y. Show your work. In addition, give a concise explanation of the meaning of the marginal rate of substitution. 2 AV2022/23 Semester 1 b. Suppose that p. - py-2 and m= 24. Use your answer from part (a) to determine Sandra's optimal consumption bundle. Show your work. c. Suppose now that p. increases to 6, while p, and m remain the same. What are Sandra's optimal choices for x and y in this case? Is Sandra better or worse off than she was in part (b)? Explain. d. How much extra income must Sandra be given in order to compensate her for the increase in the price of good x in part (c)? Explain.

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Step 12 1 MRS MUx MUy 16 4 x 4 4x MRS is the rate at which an individual is willing to gi... View the full answer