Amy consumes x and y and her preferences can be represented by the following utility function U (x, y) = 4x + y. 1. Are Amy's preferences transitive? 2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. 3. Can you use (2) to answer whether Amy's preferences are strictly monotonic? 4. What is MRSª.y? Is MRS.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. 6. Are Amy's preferences convex? Are they strictly convex? Explain

Microeconomic Theory
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ISBN:9781337517942
Author:NICHOLSON
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Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.2P
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Amy consumes x and y and her preferences can be represented by the following
utility function U(x,y) = 4x + y.
1. Are Amy's preferences transitive?
2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys
more x? Explain.
6-
3. Can you use (2) to answer whether Amy's preferences are strictly monotonic?
4. What is MRS.y ? Is MRSx.y diminishing, constant, or increasing as the consumer substitutes
x for y along an indifference curve?
5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference
curve. Also indicate on your graph whether the indifference curve will intersect either or both
axes. Label the curve U1.
6. Are Amy's preferences convex? Are they strictly convex? Explain
Transcribed Image Text:Amy consumes x and y and her preferences can be represented by the following utility function U(x,y) = 4x + y. 1. Are Amy's preferences transitive? 2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. 6- 3. Can you use (2) to answer whether Amy's preferences are strictly monotonic? 4. What is MRS.y ? Is MRSx.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. 6. Are Amy's preferences convex? Are they strictly convex? Explain
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