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2. Jacob's preferences for goods X and Y can be described by U(X,Y) = X+2Y+XY. Jacob has an income of $20 and faces prices Px = PY = $5. a. Derive Jacob's utility maximizing bundle given his budget constraint. Use the Lagrange method or simply the optimality condition. b. Now suppose Jacob's income falls to $5. Redo part a. c. Calculate Jacob's MRS of X for Y at this new utility maximizing bundle. How does it compare to the market trade-off of X for Y? d. On one graph, depict Jacob's utility maximizing bundles using indifference curves and budget lines, both before and after his income decreases.

2. Jacob's preferences for goods X and Y can be described by U(X,Y) = X+2Y+XY. Jacob has an income of $20 and faces prices Px = PY = $5. a. Derive Jacob's utility maximizing bundle given his budget constraint. Use the Lagrange method or simply the optimality condition. b. Now suppose Jacob's income falls to $5. Redo part a. c. Calculate Jacob's MRS of X for Y at this new utility maximizing bundle. How does it compare to the market trade-off of X for Y? d. On one graph, depict Jacob's utility maximizing bundles using indifference curves and budget lines, both before and after his income decreases.

Micro Economics For Today
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 9SQP
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2. Jacob's preferences for goods X and Y can be described by U(X,Y) = X+2Y+XY. Jacob has an income of $20 and faces prices Px = PY = $5. a. Derive Jacob's utility maximizing bundle given his budget constraint. Use the Lagrange method or simply the optimality condition. b. Now suppose Jacob's income falls to $5. Redo part a. c. Calculate Jacob's MRS of X for Y at this new utility maximizing bundle. How does it compare to the market trade-off of X for Y? d. On one graph, depict Jacob's utility maximizing bundles using indifference curves and budget lines, both before and after his income decreases.
Transcribed Image Text:2. Jacob's preferences for goods X and Y can be described by U(X,Y) = X+2Y+XY. Jacob has an income of $20 and faces prices Px = PY = $5. a. Derive Jacob's utility maximizing bundle given his budget constraint. Use the Lagrange method or simply the optimality condition. b. Now suppose Jacob's income falls to $5. Redo part a. c. Calculate Jacob's MRS of X for Y at this new utility maximizing bundle. How does it compare to the market trade-off of X for Y? d. On one graph, depict Jacob's utility maximizing bundles using indifference curves and budget lines, both before and after his income decreases.
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