4. Winona has 80 hours to divide between leisure and labor. Her utility function is u(r,c) =f(r) + c, when r represents hours of leisure, c represents dollars of consumption, and fisstrictly concave. Winona's wage is wo = $15/hr. initially, then it rises to wi = $20/hr.(i) Explain what happens to Winona's labor supply when the wage rises, and why.(ii) Explain how the answer to (i) would change if Winona were to win a lottery.

In the question above, it is given that : 80 hours are divided between leisure and labor. Utility…

Answered: 4. Winona has 80 hours to divide…

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter21: The Theory Of Consumer Choice

Section: Chapter Questions

Problem 9PA

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Winona has 80 hours to divide between leisure and labor. Her utility function is u(r,c) = f(r) + c, when r represents hours of leisure,c represents dollars of consumption, and f is strictly concave. Winona’s wage is w0= $15/hr. initially, then it rises to w1= $20/hr. (i) Explain what happens to Winona’s labor supply when the wage rises,and why. (ii) Explain how the answer to (i) would change if Winona were to win a lottery.
3. John's utility function is U(C, L) = C1/2L!/2. The most leisure time he can consume is 110 hours. His wage rate is $10. Find John's optimal amount of consumption and hours for leisure and work.
A) Ana decides every day how many hours to work and how much beef to consume. She spends all income earned from work each day on consumption of beef. Her utility function for free time (t, 24 hours minus hours worked) and consumption (y) is: U(t, y) = 2t + y The price per unit of beef consumed is 4 and her hourly wage is 1. • Using a diagram and appropriate algebra, explain what Ana's optimal number of hours work and units of beef consumed are each day. Ana reads a book about the impact of beef consumption on climate change and realises that there is a cost to society of her beef consumption. She takes account of this impact on society in her own decisions, incorporating a disutility of -0.03y per unit of beef consumed. She still only consumes beef and spends all income earned each day on this consumption. • Explain, using a diagram and appropriate algebra, how recognition of the impact of her consumption choice on climate change impacts on Ana's daily free time and beef consumption…
Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 168 hours. Her utility function is U ( C, L) = C x L. This functional form implies that Cindy’s marginal rate of substitution is C/L. Cindy receives $630 each week from her great-grandmother—regardless of how much Cindy works. What is Cindy’s reservation wage?
(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?
A. Consider a consumer whose preferences can be represented by Cobb-Douglas utility function u(x₁, x₂) = xx where ₁ and 2 are the quantities of good 1 and good 2 she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote her income. 1. Derive the consumer's Marshallian demand functions. 2. Derive the consumer's Hicksian demand functions. 3. Derive the consumer's expenditure function. 4. Let m = 20, P₁ = 2, and p2 = 1. Suppose that the price of good 1 drops to p₁ = 1. Find the following (a) Compensating variation (CV) (b) Equivalent variation (EV) (c) Change in consumer surplus (ACS) (d) Compare CV, ACS, and EV. 5. Let m = 120, P₁ = 1, and p2 = 1. Suppose that the price of good 1 increases to P₁ = 2. Find the following (a) Compensating variation (CV) (b) Equivalent variation (EV) (c) Change in consumer surplus (ACS) (d) Compare CV, ACS, and EV.
5. A consumer's utility function over leisure and consumption is given by u(L, Y) = LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effect.
Suppose the wage rate for labor is $20 an hour and the rental rate for capital is $50 per hour. Based on this information, please answer the questions appearing below the graph. 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 1,000 cases Labor Draw an (approximate) is-cost line associated with an hourly budget of $1,000. Hint: Find the intercept points first. If you were to shift this line out, what is the approximate least-cost combination of labor and capital when packaging 1,000 cases of fruit juice?
Rebecca's wage is $10 per hour, and she can work up to 60 hours per week. The table and the budget constraint graph show the trade-off that she faces between income and leisure in one week of potential work at this wage. Her manager raises her wage to $15 per hour. Change the graph below to illustrate her new income-leisure budget constraint. The line and the individual endpoints are movable. Assume that nothing else changes. Hours Leisure time Income ($) (hours) worked at $10/hour 0 200 400 600 0 20 40 60 60 40 20 0 Income ($) 1000 900 800 700 600 500 400 300 200 100 0 0 10 20 30 40 50 60 70 80 90 Leisure (hours)
1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y)=LY+2L a. b. C. Calculate the demand function for L and show it on a graph (L vs W). Calculate the labor supply (H) and show it on a graph (H vs W). What will happen to L, Y and H if the wage per hour (W) will decrease? =
Sharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ per hour of working (W>0) and has the following utility function: U (L, Y) =LY 4Y. a.Calculate the demand function for L. and show it on a graph (L. vs W). b. Calculate the labor supply (H) and show it on a graph (H vs W). c.What will happen to L. Y and H if the wage per hour (W) will decrease?
4) Consider the following scenario: Juliet faces 200 Total Hours to devote to Labor or Leisure. She faces a wage of $10 and has no non-labor income. Her preferences are given by the utility curve U(C,L)=C¾ L¼ a. What are her optimal hours worked and consumption choice? b. What is Juliet's reservation wage? c. Now assume the government is offering a "take-it-or-leave-it" grant of $625 for anyone who isn’t working. What is her optimal hours worked and consumption choice in this scenario? d. Now assume instead the government is offering $625 for non-working individuals, but taxes it away at a rate of 50% for each dollar earned. Graph the budget constraint and find the new optimal hours worked and consumption choice. e. Between (a), (b), and (c) which scenario has Juliet the most well-off? Between (b) and (c) which scenario is most costly (in terms of grants paid) to the government?

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