We are given a utility function in which a household lives for just one period. hl+1/e u(c, h) = c - 1 + 1/e' where we have picked a utility function where hours worked h enter negatively into the leisure entering positively). The worker earns a real wage w = . But labor income is taxed at rate T, so that in the budget constraint, the labor income is (1-T)wh. The household doesn't have any assets, so c = wh. lity function (rather than Write out the household's optimization problem - utility function and budget constraint. Solve for the household's optimal labor supply h and consumption . How does the tax rate affect labor supply?

We are given a utility function in which a household lives for just one period. hl+1/e u(c, h) = c - 1 + 1/e' where we have picked a utility function where hours worked h enter negatively into the leisure entering positively). The worker earns a real wage w = . But labor income is taxed at rate T, so that in the budget constraint, the labor income is (1-T)wh. The household doesn't have any assets, so c = wh. lity function (rather than Write out the household's optimization problem - utility function and budget constraint. Solve for the household's optimal labor supply h and consumption . How does the tax rate affect labor supply?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.1P

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Suppose that the utility function of an individual is given by U=YL2, where Y is real income and L is leisure time. The marginal utilities are MUL =0.5YL-1/2 and MUy=0.5Y-12L1/2 There are 15 hours available for labour/leisurer the current wage rate is $20 per hour, and the price index for real income is 5. Assume that there is no non-labour income. Show minimal calculation work. a) Determine the budget constraint function? b) Determine the optimal relationship between income and labour hours? C) Calculate the optimal amount of labour hours? d) Calculate the optimal amount of leisure hours? e) Calculate the income level of the individual at the optimal condition? - Calculate the utility level for the individual at the optimal condition?
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1.4 10c44 is the utility function of Fredvick 9 Sales executive at Barclays who maximizes uti lity by combining Leisure (L) with a maket basket of consumptive goods (c) 9 If tredrick does not earn any non -labair income(v estimate his labour supply function in temo of I,P and w. Where P= price, T = Total time wage rate. b) Calculate his reservation wage if T= 24 and P= I Calculate his oLon wage elasticity of labour supply equilibrium- in
The United States has established a progressive income tax system, where a worker’s tax rate onearnings increases as she earns more money. There are 168 hours in a given week. Assume thatfor the first 56 hours worked, the tax rate is t1, which means that the net real wage is w*(1-t1).After working the 56th hour, the worker jumps to a higher tax rate t2. After the 112th hourworked, the individual jumps to an even higher tax rate, t3.(a) During most election years, some politicians argue that a having a flat tax system isbetter. Assume that there is a proposal to institute a flat tax, where all workers pay a taxrate equal to t4, which is greater than t3. On the same set of axes, graph the budgetconstraints associated with the progressive tax system and the flat tax system. Make sureto label all of the slopes.(b) Would moving to this proposed flat tax system likely encourage more or fewer hoursworked for relatively high-wage workers? Make sure to explain your answer (a writtenexplanation…
Suppose Jenny has 16 hours per day to allocate between work and leisure and she earns a wage rate of $25 per hour. If at the utility-maximizing level of employment (1.e., MRSYL = w), Jenny's MUL is 20 utils, what is her MUy? O A 08 utils OB 500 utils OC 1.25 utils OD Cannot be determined with the information provided Assume that b = 0.15% and that l = 0. If the one-year interest rate is 5% and the two- year interest rate is 5.75%, then i is equal to: O A 6 20% OB 5 60% OC 5 15% OD 5.90%
Consider the following labor-leisure choice model. Utility function over consumption (C) and leisure (L) U(C.L) = (1/3L1/3 Total hours: H = 40 Labor hours: NS = H - L Non-labor income: π = 30 Lumpsum tax: T = 10 Hourly wage: w = 4 Suppose the hourly wage changes to w = 3. What is the substitution effect of this change on labor supply? A. +2.65 B. -2.65 C. +3.48 D.-3.48 E. None of the above
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