All individuals have the same utility function over consumption, C, and leisure, L, given by U = C1/3L2/3, Denote the wage rate by w. The total time available for labour and leisure is equal to 12. The price of consumption is PC=1. Denote the amount of labour supplied as N. Find the Labour supply function.
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All individuals have the same utility function over consumption, C, and leisure, L, given by U = C1/3L2/3, Denote the wage rate by w. The total time available for labour and leisure is equal to 12. The price of consumption is PC=1. Denote the amount of labour supplied as N.
Find the Labour supply function.
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- 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.The demand curve for labor will shift upward and to the left if labor becomes more productive. TRUE OR FALSE If total utility increases as wealth increases, the first derivative of the utility function is negative. TRUE OR FALSEA 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?…
- 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 an individual whose utility function is U(C, R) = 2C - (4 - R) 2 where R is the amount of leisure the consumer experiences per day. Suppose that the individual normally sleeps T hours a day, and they can spend the remaining hours between work and leisure. The individual receives an hourly wage of w > 0 and has also an income of Y > 0 a day from non - labour sources. The price of consumption goods is p per unit.Consider the labor–leisure budget constraint curve on the graph. This curve shows trade‑offs between income and leisure that must be made over the course of one week. Assume there are no artificial barriers to limits on hours worked and that the wage is $25 per hour. Determine the vertical and horizontal intercepts. vertical intercept: $ horizontal intercept: h
- The production function of a given item is Q = 10(L^½)(K^½) and the factor prices are equal to $20 for wages, and $80 for rent. If Q = 140, determine the Marginal rate of technical substitution. a. (L + 2) / (K - 1) b. K^2L c. (K - 1) /L d. K/LSuppose the wage you are being paid per hour doubles form $15 to $30. Would you decide to work more hours or fewer hours ? Is there an income and substitution effect involved in your decision about how many hours you choose to work? If so, what is being substituted for what?A firm produces at an output level where the marginal product of labor (MPL) is 50 units and the marginal product of capital (MPK) is 10 units. Suppose that the wage rate (PL) is $25 and the rental price of capital (PK) is $40. a.Is this firm maximzing profit? b.What should the firm do if it is not alocating its budget efficiently?
- if leisure is an inferior good, what can you say about the slope of the labor supply curve?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.Illustrate (using a labor-leisure choice diagram) how a firm may induce a typical employee to lengthen his work week voluntarily by paying him premium wage rates for overtime hours.