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Each person tries to balance his or her time between leisure and work. The tradeoff is that as you work less your income falls. Therefore each person has indifference curves which connect the number of hours of leisure, I, and income, s. If, for example, you are indifferent between 0 hours of leisure and an income of $1125 a week on the one hand, and 10 hours of leisure and an income of $750 a week on the other hand, then the points 1 = 0, s = 1125, and I = 10, s = 750 both lie on the same indifference curve. The table below gives information on three indifference curves, I, II, and III. Weekly Income Weekly Leisure Hours III I II III I 1125 1250 1375 0 750 875 1000 10 II 20 40 30 50 500 625 750 20 40 60 375 500 625 30 50 70 250 375 500 50 70 90 (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference curves. (You will need these to answer part (d) of this problem.) (b) You have 95 hours a week available for work and leisure combined, and you earn $21.45/hour. Write an equation in terms of 1 and s which represents this constraint. constraint: (c) Graph this constraint with your graph of the indifference curves. (d) Estimate from the graph what combination of leisure hours and income you would choose under these circumstances. leisure hours = weekly income = What is the corresponding number of hours per week you would work? work hours =

Each person tries to balance his or her time between leisure and work. The tradeoff is that as you work less your income falls. Therefore each person has indifference curves which connect the number of hours of leisure, I, and income, s. If, for example, you are indifferent between 0 hours of leisure and an income of $1125 a week on the one hand, and 10 hours of leisure and an income of $750 a week on the other hand, then the points 1 = 0, s = 1125, and I = 10, s = 750 both lie on the same indifference curve. The table below gives information on three indifference curves, I, II, and III. Weekly Income Weekly Leisure Hours III I II III I 1125 1250 1375 0 750 875 1000 10 II 20 40 30 50 500 625 750 20 40 60 375 500 625 30 50 70 250 375 500 50 70 90 (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference curves. (You will need these to answer part (d) of this problem.) (b) You have 95 hours a week available for work and leisure combined, and you earn $21.45/hour. Write an equation in terms of 1 and s which represents this constraint. constraint: (c) Graph this constraint with your graph of the indifference curves. (d) Estimate from the graph what combination of leisure hours and income you would choose under these circumstances. leisure hours = weekly income = What is the corresponding number of hours per week you would work? work hours =

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 87CR
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Each person tries to balance his or her time between leisure and work. The tradeoff is that as you work less your income falls. Therefore each person has indifference curves which connect the number of hours of leisure, I, and income, s. If, for example, you are indifferent between 0 hours of leisure and an income of $1125 a week on the one hand, and 10 hours of leisure and an income of $750 a week on the other hand, then the points 1 = 0, s = 1125, and 1 = 10, s = 750 both lie on the same indifference curve. The table below gives information on three indifference curves, I, II, and III. Weekly Income Weekly Leisure Hours II I II III I 1125 1250 1375 0 20 40 750 875 1000 10 30 50 500 625 750 20 40 60 375 500 625 30 50 70 250 375 500 50 70 90 (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference curves. (You will need these to answer part (d) of this problem.) III (b) You have 95 hours a week available for work and leisure combined, and you earn $21.45/hour. Write an equation in terms of I and s which represents this constraint. constraint: (c) Graph this constraint with your graph of the indifference curves. (d) Estimate from the graph what combination of leisure hours and income you would choose under these circumstances. leisure hours = weekly income = What is the corresponding number of hours per week you would work? work hours =
Transcribed Image Text:Each person tries to balance his or her time between leisure and work. The tradeoff is that as you work less your income falls. Therefore each person has indifference curves which connect the number of hours of leisure, I, and income, s. If, for example, you are indifferent between 0 hours of leisure and an income of $1125 a week on the one hand, and 10 hours of leisure and an income of $750 a week on the other hand, then the points 1 = 0, s = 1125, and 1 = 10, s = 750 both lie on the same indifference curve. The table below gives information on three indifference curves, I, II, and III. Weekly Income Weekly Leisure Hours II I II III I 1125 1250 1375 0 20 40 750 875 1000 10 30 50 500 625 750 20 40 60 375 500 625 30 50 70 250 375 500 50 70 90 (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference curves. (You will need these to answer part (d) of this problem.) III (b) You have 95 hours a week available for work and leisure combined, and you earn $21.45/hour. Write an equation in terms of I and s which represents this constraint. constraint: (c) Graph this constraint with your graph of the indifference curves. (d) Estimate from the graph what combination of leisure hours and income you would choose under these circumstances. leisure hours = weekly income = What is the corresponding number of hours per week you would work? work hours =
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