Deborah's utility over consumption (C), hours worked (H), and hours spent in commute (S) is: (1) U (C, H) = C¹2-H-S. The maximum number of hours that Deborah can work productively is 10. Thus (2) 0s Hs 10. On the days which Deborah works, she spends 2 hours in commuting from home to work and then back (one hour each way). (3) If H > 0, S = 2. Else if H = 0, S = 0. Assume that C ≥ 0 and S≥ 0. For simplicity, we also assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting. (a) Explain why Deborah's preferences are not strongly monotone in C and H. Use an example to support your answer. (b) Deborah's marginal utility from consumption (C) is strictly decreasing in C. True or False? Explain. Draw an indifference curve in (H, C) space that yields U = 6. Make sure to plot hours worked (H) in horizontal axis and (C) in vertical axis and label at least two points/bundles which give U = 6. (d) Deborah's income is hourly wage (w) times the hours worked (H). Suppose w = $32 per hour and price of C is $1. How many hours would Deborah work to maximize her utility? How much C will Deborah choose? Assume that Deborah has no other sources of income. (e) Deborah has received a new job offer which pays $w* an hour. However, it requires relocation closer to city where prices are at least 30% higher. More concretely, price of C is $1.30 instead of $1. On the plus side, relocation will cut down Deborah's commuting time from 2 hours per day to 30 minutes per day (15 minutes each way). That is, S will decline from S=2 to S=0.5. Deborah is a utility maximizer. Deborah will accept the offer if and only if w* > Fill in the blank. Explain your answer.
Deborah's utility over consumption (C), hours worked (H), and hours spent in commute (S) is: (1) U (C, H) = C¹2-H-S. The maximum number of hours that Deborah can work productively is 10. Thus (2) 0s Hs 10. On the days which Deborah works, she spends 2 hours in commuting from home to work and then back (one hour each way). (3) If H > 0, S = 2. Else if H = 0, S = 0. Assume that C ≥ 0 and S≥ 0. For simplicity, we also assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting. (a) Explain why Deborah's preferences are not strongly monotone in C and H. Use an example to support your answer. (b) Deborah's marginal utility from consumption (C) is strictly decreasing in C. True or False? Explain. Draw an indifference curve in (H, C) space that yields U = 6. Make sure to plot hours worked (H) in horizontal axis and (C) in vertical axis and label at least two points/bundles which give U = 6. (d) Deborah's income is hourly wage (w) times the hours worked (H). Suppose w = $32 per hour and price of C is $1. How many hours would Deborah work to maximize her utility? How much C will Deborah choose? Assume that Deborah has no other sources of income. (e) Deborah has received a new job offer which pays $w* an hour. However, it requires relocation closer to city where prices are at least 30% higher. More concretely, price of C is $1.30 instead of $1. On the plus side, relocation will cut down Deborah's commuting time from 2 hours per day to 30 minutes per day (15 minutes each way). That is, S will decline from S=2 to S=0.5. Deborah is a utility maximizer. Deborah will accept the offer if and only if w* > Fill in the blank. Explain your answer.
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section6.A: Indifference Curve Analysis
Problem 1SQP
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Transcribed Image Text:Deborah's utility over consumption (C), hours worked (H), and hours spent in commute (S)
is:
(1)
U (C, H) = C¹2-H-S.
The maximum number of hours that Deborah can work productively is 10. Thus
(2)
0≤H≤ 10.
On the days which Deborah works, she spends 2 hours in commuting from home to work
and then back (one hour each way).
(3)
If H > 0, S = 2. Else if H = 0, S = 0.
Assume that C ≥ 0 and S≥ 0. For simplicity, we also assume that there are no other costs
(e.g., ticket costs, parking fee) associated with commuting.
(a)
Explain why Deborah's preferences are not strongly monotone in C and H. Use
an example to support your answer.
(b)
Deborah's marginal utility from consumption (C) is strictly decreasing in C.
True or False? Explain.
Draw an indifference curve in (H, C) space that yields U = 6. Make sure to plot
hours worked (H) in horizontal axis and (C) in vertical axis and label at least two
points/bundles which give U = 6.
(d)
Deborah's income is hourly wage (w) times the hours worked (H). Suppose w
= $32 per hour and price of C is $1. How many hours would Deborah work to maximize
her utility? How much C will Deborah choose? Assume that Deborah has no other
sources of income.
(e)
Deborah has received a new job offer which pays $w* an hour. However, it
requires relocation closer to city where prices are at least 30% higher. More concretely,
price of C is $1.30 instead of $1. On the plus side, relocation will cut down Deborah's
commuting time from 2 hours per day to 30 minutes per day (15 minutes each way). That
is, S will decline from S = 2 to S = 0.5.
Deborah is a utility maximizer. Deborah will accept the offer if and only if w* >
Fill in the blank. Explain your answer.
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