Consider the standard labor-leisure choice model. Consumer gets utility from consumption (C) and leisure (L). She has H total hours. She works NS hours and receives the hourly wage, w. She has some non-labor income and pays lump-sum tax T. Further suppose (n-T) >0. The shape of utility function is downward-sloping and bowed-in towards the origin (the standard U-shaped case just lke a cobb-douglas function) If this consumer decides to NOT WORK AT ALL, then it must be the case that

Consider the standard labor-leisure choice model. Consumer gets utility from consumption (C) and leisure (L). She has H total hours. She works NS hours and receives the hourly wage, w. She has some non-labor income and pays lump-sum tax T. Further suppose (n-T) >0. The shape of utility function is downward-sloping and bowed-in towards the origin (the standard U-shaped case just lke a cobb-douglas function) If this consumer decides to NOT WORK AT ALL, then it must be the case that

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.2P

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Consider a representative agent with the utility function U = ln(Ct)+ Nt The budget constraint is Ct = wtNt +Dt where wt is the wage and Dt is non-wage income (i.e. a dividend from ownership in the firm). The agent lives for only one period (period t), and hence its problem is static. (a) Derive an optimality condition characterizing optimal household behav- ior. (b) Solve for the optimal quantities of consumption and labor. Plz do fast asap, urgent.
A worker receives a wage rate w and has L hours of leisure every day (the total endowment of hours is 24 hours per day). The government gives a subsidy of rate S of his income. The worker spends all his income. 1. Write a budget constraint of this individual and plot it. 2. Display graphically what is the optimal consumption-leisure choice for this worker. 3. Imagine that instead, the government imposes income tax at rate T . What is the new budget constraint? Display on the same picture. In the new optimum is the consumption higher? Explain the answer in terms of wealth and substitution effects.
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Consider the following labor-leisure choice model. U(C,L) = C^2/3L^1/3 C = wN + π – T H= N+ L Where C: consumptionL: leisureN: hours workedH = 50 : total hoursw = 4 : hourly wageπ = 20 : non-labor income T = 10 : lump-sum tax Suppose the hourly wage changes to w = 5. Perform a decomposition and fill in the table C L N Substitution Effect Income Effect Total Effect
Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure U(c,l) = lnC + 4lnl 1) Provide the functional form of the income effect from a marginal decrease in income. 2) Provide the functional form of the substitution and total income effects of a marginal increase in wage. 3) Show that the Slutsky equation holds for this worker.
How would you demonstrate part c) diagramatically 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day.
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Suppose that the owner of Boyer Construction is feeling the pinch of incrs associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours? (LO2, LO3, LO7)
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Consider the problem of a consumer who chooses between consuming goods and enjoying leisure in the current and future periods. Denote the consumption and leisure in the current period as C and l, and the consumption and leisure in the future period as C′ and l′, respectively. The preference is summarized by the following utility function: U(C,C′,l,l′)=lnC+ψlnl+β(lnC′ +ψlnl′). This individual is endowed with h units of time in each period. Wage rate per unit of labour time is w and w′ in the current and future period. In addition, the consumer receives profit transfer π and π′ and pays lump-sum taxes T and T′ in the current and future periods. Denote the saving in the current period as Sp. Answer the following questions. Derive the life-time budget constraint of this consumer. Set up the consumer’s problem. Solve for consumption (C and C′), leisure (l and l′), and saving (Sp). How does an increase in wage rate w affect C, Sp, and l?
Consider an individual who lives in an economy without a welfare program. They initially work T-L0hours per week, where (T-L0)>0. They earn an hourly wage (W) and no non-labour income. a) Draw a graph that reflects this individual’s income-leisure constraint, utility-maximizing indifference curve (U0), choice of leisure hours (L0) and income (Y0). b) Now, assume that a welfare program has been implemented in this economy. The welfare benefit is smaller than the individual's initial income level (Y0) and there is a 50% clawback on any labour income earned. The individual now maximizes their utility by working and collecting a partial welfare benefit. On the same graph as part a, draw this individual’s new income-leisure constraint, utility-maximizing indifference curve (U1), choice of leisure hours (L1) and income (Y1).
Suppose a person can work up to 80 hours per week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Assume that under these conditions the person maximizes utility by choosing to work 50 hours each week. The government proposes a negative income tax so that everyone receives $300 per week regardless of how much they work. To pay for the negative income tax, the payroll tax would be increased to 50%. Using the labor-leisure model, graphically show whether a person would be better off if the negative income tax is adopted and indicate whether hours worked increases or decreases due to the policy.