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Suppose that Helena's utility over goods x and y is given by U (x, y) = 2/¤ + VG Solve Helena's utility maximization problem to find her ordinary demand functions for x and y. Show carefully each step you take. A. Next, solve Helena's expenditure minimization problem to find compensated demand for x and y. C. Consider a particular set of parameters: Px=5, Py=10, and l=60. Draw the budget constraint and the optimal consumption bundle in an (x,y) graph, being careful to label the axes and any relevant coordinates. Next, suppose that the price of good y decreases, so that Py'=5. (The price of x and income remain the same.) Add the new budget line and optimal basket to the graph. B.

Suppose that Helena's utility over goods x and y is given by U (x, y) = 2/¤ + VG Solve Helena's utility maximization problem to find her ordinary demand functions for x and y. Show carefully each step you take. A. Next, solve Helena's expenditure minimization problem to find compensated demand for x and y. C. Consider a particular set of parameters: Px=5, Py=10, and l=60. Draw the budget constraint and the optimal consumption bundle in an (x,y) graph, being careful to label the axes and any relevant coordinates. Next, suppose that the price of good y decreases, so that Py'=5. (The price of x and income remain the same.) Add the new budget line and optimal basket to the graph. B.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.13P
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Suppose that Helena's utility over goods x and y is given by U (x, y) = 2/a + G А. Solve Helena's utility maximization problem to find her ordinary demand functions for x and y. Show carefully each step you take. В. Next, solve Helena's expenditure minimization problem to find compensated demand for x and y. С. Consider a particular set of parameters: Px=5, Py=10, and I=60. Draw the budget constraint and the optimal consumption bundle in an (x,y) graph, being careful to label the axes and any relevant coordinates. Next, suppose that the price of good y decreases, so that Py'=5. (The price of x and income remain the same.) Add the new budget line and optimal basket to the graph.
Transcribed Image Text:Suppose that Helena's utility over goods x and y is given by U (x, y) = 2/a + G А. Solve Helena's utility maximization problem to find her ordinary demand functions for x and y. Show carefully each step you take. В. Next, solve Helena's expenditure minimization problem to find compensated demand for x and y. С. Consider a particular set of parameters: Px=5, Py=10, and I=60. Draw the budget constraint and the optimal consumption bundle in an (x,y) graph, being careful to label the axes and any relevant coordinates. Next, suppose that the price of good y decreases, so that Py'=5. (The price of x and income remain the same.) Add the new budget line and optimal basket to the graph.
Expert Solution
Step 1

A.

U(x, y) = 2x +y

MRS = MUxMUy = 22x12y = 2yx

equating MRS to price ratio:

2yx  = pxpy

y = x px2 pyy* = x px24 py2

substituting in budget constraint:

px*x +py*y = Mpx*x + py * (x px24 py2) = M

Demand function for x:

x* = Mpx + px24 py

Demand function for y:

y* = Mpy + 4py2px

 

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