Consider a utility function with one consumption good qi and one type of leisure q2 U(q1 , 92)= q;" 95 1/3 1/3 a) Derive complete labour supply function. b) Under what condition the labour supply curve will be negatively sloped.
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Q3. Consider a utility function with one consumption good q1 and one type of leisure q2
c) Show mathematically and diagrammatically the decomposition of total
effect.
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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.Using the utility function and wage constraint in the problem, please complete the utility maximization problem using the substituion and Lagrangian method. If you can not do both, I would prefer the substitution method.Suppose a firm produces according to the production function Q = 2L0.6K0.2, and faces wage rate ₵10, a rental cost of capital ₵5, and sells output at a price of ₵20. a. Obtain and expression for the factor demand functions. b. Compute the profit-maximizing factor demands for capital and labour
- 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 FALSESuppose that a salesperson earns a basic monthly salary of $800 plus a commission rate is 15% and the possible bonuses are lump-sum amount of $1000 if her monthly sales exceed $10,000 and a further lump-sum of $2,500 if her monthly sales exceed $15,000. Find the function that relates sales to earnings for this salesperson and graph it. At which points is the function discontinuous? Interpret the incentives created by this pay scheme?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/L
- 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?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 a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of $1,500. a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in the long run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph as part a, graphically show the impact of the minimum wage on the optimal level of employment in the long run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price of capital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts the optimal levels of employment and capital in the long run. Clearly identify the resulting scale and substitution effects caused by the lower cost of capital.
- 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.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.Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.