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 Queston: Show that the Slutsky equation holds for this worker
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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
Queston:
Show that the Slutsky equation holds for this worker
Step by step
Solved in 4 steps
- 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 Give that the Slutsky equation holds for this worker.Consider worker 1 with non-labor income Y facing a wage offer w and a utility function defined over consumption and leisure U(c,l) = lnC + 4lnl Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Which worker places a higher value on labor market work?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 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 income elasticity. Is leisure a normal or inferior good for this worker?Suppose there are two identical job offers in the same competitive labor market for a software developer position. Both offers have the same salary of $80,000 per year. However, Job A allows the employee to work from home, while Job B requires the employee to commute to the office daily. The average monthly commuting cost for Job B is estimated to be $400. Calculate the compensating differential in this scenario, and determine if it makes economic sense for the employee to choose Job B over Job A. Assume a working year consists of 12 months.Q3. Consider a utility function with one consumption good q1 and one type of leisure q2a) Derive complete labour supply function.b) Under what condition the labour supply curve will be negatively sloped.
- To which of the following job characteristics could the hedonic wage function be applied? a. the degree to which a job involves monotonous work b. the degree to which the area surrounding the job location is safe c. the degree to which a job involves strenuous work d. the probability of being injured on the job e. All of these can be represented with a hedonic wage function.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.A worker has 110 hours available in a week that can be used for leisure (L) or work (h). The utility function is U = (1 - α)ln(C) + α ln(L), where C is consumption. a) The price per unit of consumption is 1, the hourly wage is w, and the worker has a non-labor income of V. Show that the labor supply is: h* = (110(1-a)- (av)/w). Also, find the demand for consumption and leisure. b) What is the effect on labor supply of i) an increase in the hourly wage and ii) an increase in non-labor income? c) Set α = ½. What are C, L, and h when w = 200 and V = 10000? What is the reservation wage? d) What is the effect on labor supply of i) a 30% income tax and ii) a 10% wealth tax (on V)? e) What is the labor supply if V increases to 11600? f) An increase in V to 11600 gives the worker the same utility as w = 250 and V = 10000 (you do not need to show it). What are the income, substitution, and total effects on labor supply of an increase in wage from 200 to 250 while V remains at 10000?…
- Consider a worker who is endowed with T hours of time and investment income V per week, faces a wage rate w per hour, and whose preferences over the consumption of goods, the price of a unit of which is p, and leisure can be represented by the utility function U(C,L) = C1/2L1/2. Find the worker’s labour supply. When is it positive? Will the worker ever work more than half their time endowment? (25%)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.The weekly preferences over consumption (C) and leisure(L) are defined by u(C, L) = √C + 3√L. The person receives a weekly allowance of m from The hourly wage is $18 per hour, and the person can work up to50 hours each week (T = z + L = 50), where z is the number of hours spent working). a)How many hours will the person work if her allowance is m= $450 per week b) What is the smallest allowance m for which the person will stopworking altogether (z∗ = 0) for a wage of w = 18?