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 7 = 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.) (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 7 and 8 which represents this constraint. constraint: III 9- (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 7 = 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.) (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 7 and 8 which represents this constraint. constraint: III 9- (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 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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, 1, 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
I
II III
II
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.)
(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:
III
(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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