Suppose that a consumer can earn a higher wage rate for working overtime. That is, for the first q hours the consumer works, he or she receives a real wage rate of w1, and for hours worked more than q he or she receives w2, where w2 > w1 . Suppose that the consumer pays no taxes and receives no nonwage income, and he or she is free to choose hours of work. (a) Draw the consumer’s budget constraint, and show his or her optimal choice of consumption and leisure. (b) Show that the consumer would never work q hours, or anything very close to q hours. Explain the intuition behind

Suppose that a consumer can earn a higher wage rate for working overtime. That is, for the first q hours the consumer works, he or she receives a real wage rate of w1, and for hours worked more than q he or she receives w2, where w2 > w1 . Suppose that the consumer pays no taxes and receives no nonwage income, and he or she is free to choose hours of work. (a) Draw the consumer’s budget constraint, and show his or her optimal choice of consumption and leisure. (b) Show that the consumer would never work q hours, or anything very close to q hours. Explain the intuition behind

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.3P

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22. Taro's utility function is U(C, R) = 32√√R+C, where R is the amount of leisure. He has 16 hours a day to divide between work and leisure. He gets $10 an hour no matter how many hours he works, but must pay a 20% tax on his labor income. He has also an income of $40 from non-labor income source. How many hours will he choose to work? A) 4 B) 8 C) 10 D) 12 E) 16
Suppose that a person has 2000 hours to allocate each year between leisure and work. a. Derive the equation of his budget constraint given an hourly wage of $(15)/hour. b) Graph his budget constraint line based on the equation you derived in part a. (Consumption (C) on the vertical axis and leisure (L) on the horizontal axis). Please make sure to include the value for the vertical and horizontal intercepts. c) Now suppose that the local government introduces an income guarantee program for single parents in which the income transfer is $10,000 per year if an individual does not work during that year (this dollar amount represents the benefit guarantee). If the individual decides to work, this transfer program imposes a 100% benefit reduction rate (e. g.. each additional hourly wage earned is reduced by 100%). Derive the new budget constraint equation that corresponds to this scenario. d) Draw the budget line that corresponds to the new scenario on a new graph. (Consumption (C) on the…
Kimo is a parent who has $200 in non-labor income. Kimo can earn $10 per hour working between 0 and 60 hours in a week if he works. Draw and label clearly the potential income constraint diagram faced by Kimo What is the slope of the budget constraint
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1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y) =LY+2L C. vv). e. VS What will happen to L, Y and H if the wage per hour (W) will decrease? d. How would your answer to the previous question (c) will change if Sharon has a fixed amount of money (Wo) that is not connected to W? If Sharon has the following utility function: U= L³+ Y², is it possible that she will choose not to work at all? Explain and show the condition for your result if exists. |||
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? =
Jones, without a job or job prospects, has been on social assistance for the past four months. Social assistance pays a basic benefit of $600 a month with a benefit reduction rate of 75 percent for earned income. Her welfare benefit is given as B = 600 - 0.75E, where E represents monthly earnings. Jones has just been offered a part-time job working 5 hours a day, 5 days a week, earning an hourly wage of $11. Sketch a budget constraint for Jones given the social assistance scheme in place and the wage rate available for part time work. How much income would she earn if she accepted the job? Would Jones still be on social assistance if she took the job? Draw the budget constraint.
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Sharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ 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?
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…
Question 1 Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure. 1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points. 2. What are the person’s marginal utilities for consumption and leisure? What is her marginal rate of substitution between leisure and consumption in terms of C, L, and α? 3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words. 4. Solve for the person’s optimal choices of leisure and consumption, L ∗ and C ∗ , in terms of T, V , w, and α. 5. How does L ∗ change as you increase wage w and non-labor income V ? 6. How does C ∗ change as you…