2. Assume that individuals have the utility function over consumption (c) and labor (1) given by U (c,1) = 2c+0 log (20 – 1), where 0 is a constant parameter reflecting disutility from work. Suppose the only income that individ- uals have is from labor income. (a) Suppose labor income is taxed at rate T. Solve for utility-maximizing labor supply as a function of w, T, and 0.
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- Emma is employed at a contract where he can vary his labour supply between 0 and 40 hours per week. She derives utility from consumption, c, and leisure, L. Her preferences are represented by the following utility function: U(c,L) = min(c, L). The unit price of consumption is p, and the hourly wage rate is w. (a) Derive an expression for Emma's labour supply. (b) The government contemplates introducing a consumption boosting policy including a monthly transfer of money for which Emma is eligible. At what size of the transfer will Emma decide to not work? Assume that the unit price of consumption is 30 and the hourly wage rate is 50Consider 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 a.Provide the functional form of the income effect from a marginal decrease in income and provide the functional form of the substitution and total income effects of a marginal increase in wage.Suppose that following represents the utility function of the individual U(c,l)=log(c)+log(l) c = consumption level of the individual and l = leisure, while the market wage is 10 and available time is 20. 1) Find and draw the labor supply function. 2) Suppose that the government introduces a cash grant for the labor (who is in the labor force) in the amount of R. Find and draw the labor supply function? Compare it to the labor supply function you have found in a). 3) Discuss the existence of reservation wage in the settings described in a and b? If your answer is : “there are no reservation wages under those settings”, please introduce a change in the policy described in b) to make sure that the reservation wage would exist.
- Consider the following model of labour supply. There is a representative worker with the following utility function: U(C,L) = C + 3L The budget constraint and time constraint are: C = wh + V h = T – L where w = 1,V = 500,T = 100. The notation is the same as question 1. a) Calculate the optimal leisure and consumption. b) Explain why we usually do not use this type of utility function to model the labour supply.Consider worker 1 with non-labour income Y facing a wage offer w and a utility functiondefined over consumption and leisureU(c,l) = lnC + 4lnl1) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Whichworker places a higher value on labour market work?12) Suppose the worker participates in the labour market. Derive worker’s compensated laborsupply function and the compensated labour supply elasticity with respect to wage as a functionof utility level and wage.3) Derive worker’s uncompensated labour supply function (for labour market participants andnon-participants) and the uncompensated labour supply elasticity (for labor market participants)with respect to wage as a function of non-labour income and wage.4) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?5) Provide the functional form of the income effect from a marginal decrease in income.6) Provide the functional form of the substitution and total income…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 a) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Which worker places a higher value on labour market work? b) Suppose the worker participates in the labour market. Derive worker’s compensated labor supply function and the compensated labour supply elasticity with respect to wage as a function of utility level and wage. c) Derive worker’s uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labor market participants) with respect to wage as a function of non-labour income and wage.
- Q1 A representative household receives utility from consumption c and supplying labor l: u(c, 1) = √c+y√√1-1 As usual, is the share of time that the household spends working. The household owns an exogenously determined amount of capital, earns the nominal rental rate R on each unit of its capital holdings, earns the nominal wage W on each unit of labor it supplies, and pays the price P per unit of consumption.. The household's budget constraint is: Pc Wl+ Rk Solve the household's utility maximization problem and select which of the following represents the household's labor supply equation: 1-2 (WP)k +4P 1-2-() 1= 01= l= 1-4(wk) 1+4 W-²(WP) Save AnswerFind the conditional factor demand for factor \(x_2\) if the firm wants to produce \(y\ =\ 25.1\) units of output with the production function \(f(x_1,x_2)\ =\min{(0.5x_1,0.3x_2)}\). Price of output \(p\ =\ 39.1\) and prices of inputs are \(w_1\ =\ 5.3\) and \(w_2\ =\ 8.7\). Hint: 1. Think what is the cheapest way to produce \(y\) units of output given this specific produciton function. 2. Derive demand for \(x_2\) as a function of \(y\), \(w_1\) and \(w_2\) only Type your answer with at least 4 decimal digits! Answer:Suppose that the production of a certain product only requires one input, labor, and that the additional production diminishes by half after the last input. On the other hand, the demand of the good can be described using the equation Q = 10000 – P/10. The total product of the second unit of labor is 3,000 unite. Finally, each additional worker requires P1,000,000. Given the following information, answer the following questions: What is the marginal revenue product of the third unit of labor? Answer: 500 How would you characterize the marginal revenue product of labor? How would you characterize the labor market that this firm faces?
- 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?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 a) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker? b) Provide the functional form of the income effect from a marginal decrease in income. c) Provide the functional form of the substitution and total income effects of a marginal increase in wage.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 Derive worker’s uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labor market participants) with respect to wage as a function of non-labour income and wage.