The Nash bargaining solution between the employer and the worker satisfies the fol- lowing maximization problem: max[W (w) – U]°[J(w) – V]!-8, w where rW (w) = w+ s(U – W) and r.J(w) = y – w + s(V – J). Show that the outcome of this maximization problem is a surplus-sharing rule of the form: W (w) – U = B[W (w) – U + J(w) – V].
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- 3. A firm that is located in country H, where price levels are p = (1,1), needs to send one of its two employees to its branch in country F. However, in country F price levels are p′ ≫ p, so the firm will have to pay additional salary to ensure that its employee is equally well-off in country F as she was in country H. Suppose the utility functions of the two employees are u1(x1, x2) = x1 + x2 and u2(x1, x2) = min {x1, x2}. The two employees are otherwise identical, including current salary. If the firm wants to minimize the additional salary it needs to pay, which employee should it send? Explain.A company called Tramlaw has become the only employer in the local market for retail labor. The marginal value (extra profit before wages) of hiring an additional worker-hour is ?? = 60 − ?, where ?? is marginal value and ? is the hours of labor worked. The supply of workers is given as ? = ? 2 , where ? is the wage (the price of labor). Assume Tramlaw pays all retail workers in this market the same wage. For parts (a) and (b), ignore the numbers and equations (though you could use the equations as hints). a. Explain in words why Tramlaw’s marginal cost of hiring an additional worker-hour is higher than supply, which represents the marginal cost to the worker of providing an additional hour of labor. b. Draw a market diagram of Tramlaw’s local labor monopsony, including marginal value (MV), supply (S), and marginal cost (MC). Graphically indicate the monopsonist’s profit-maximizing quantity of labor ??, wage ??, the efficient quantity of labor ? ∗ , and any deadweight loss (DWL)…A city government is considering renting space in an all‑day parking garage for its 100 employees. The government estimates these employees' demand function for parking spaces is 150 ‑ 50P (P ≥ $1), where P is the per-day price of parking, and the city will pass on the cost. (a) If the city needs not charge each of its employees the same price for a parking space, what is the maximum amount the city could pay for the 100 spaces, and what would be the average cost per space? (b) Assume the employees’ union insists that – per their contract – each employee must be charged the same price for parking, and the city’s response is to intend charging the price that maximizes its parking fee revenue. What price per space would the city charge under this circumstance, and how much less total dollar benefit would the employees receive?
- The market for low-skilled workers is highly competitive, due to the high numbers of low skilled individuals. If the labor supply is given by the equation QS = 10W and measured per hour, and the demand for labor is given by the equation QD = 240 − 20W. Where Q measures the quantity of labor hired (in thousands of hours). Answer the following: (a) At the market equilibrium what is the going wage rate and quantity of low-skilled labor being employed? (b) If the union successfully forces a minimum wage increase of $9 per hour, at the new market equilibrium what will be the new quantity of labor hired and the quantity of any excess (demand or supply) of labor? (c) At the $9 minimum wage how much deadweight loss is created? (d) After the implementation of the $9 minimum wage, in terms of surplus how much better off are low-skilled workers and how much worse off are employers? (e) If the minimum wage is set at $11 rather than $9 how does the deadweight loss and surplus change?The relationship between a worker’s daily wage, w, and her daily output, q, is q = 0.1 w2 - 0.0005 w3 so that the worker’s marginal product with respect to her wage is MPw = 0.2 w - 0.0015 w2. What is the optimal efficiency daily wage for the firm to pay? How much output will the worker produce each day? How much profit does the firm earn on the worker’s output each day if the price of output is fixed at $0.80 per unit?7. What assumption is most important to reach the conclusion that government regulation of risk on the job harms some workers? a. The assumption of perfect information b. The assumption of diminishing marginal returns to safety expen- diture c. The assumption that some firms have market power in the output market d. The assumption that it's costly for firms to reduce risk 8. Holding all else constant, the offer curve in a labor market where there is a trade-off between wages and risk of injury does NOT tell us: a. The possible wage-risk combinations that firms will offer in a labor market. b. The optimal matches between risk-averse workers and firms in a labor market. c. The equilibrium level of employment when risk is present d. The compensating wage differentials for various levels of risk.
- Consider the labour market for farms during the harvest season. Assume the market is perfectly competitive, with a labour demand function QD = 10-P and a labour supply function QS = 3P, where P is the wage. a) What are the consumer (farm owners) surplus and producer (farm workers) surplus in equilibrium? b) What is the price elasticity of demand at the equilibrium? c) Suppose the government subsides the farm owners (consumers) $1 for every unit of labour purchased. Then, compute the quantity of labour traded in the market, the wage received by the workers and the wage paid by the farm owners. d) Calculate the consumer surplus and producer surplus in the presence of the subsidy in part c).describe how the firms sets an efficiency wage above the competitive level. Why are there no market forces forcing the profit-maximizing firm to reduce the wage to the competitive level?a- Start from the initial endowment point Ex A and Ey A for individual A(the commodities in the economy are x and y) and initial endowment point Ex B and Ey B for individual B. Write down the no excess demand condition for both individuals, and write down the collective no excess demand condition for the entire society, if the demands of individual A is XA and YA and the demands of individual B is XB and YB. b-If UA=XA 2/3×YA 1/3 and UB=min(2YB, XB) establish the main equation for the contract curve for the society. Assume that the starting endowment level is Ex A=2 Ex B=4 and Ey A=2 Ey B=1. c-In terms of the MRS`s for the two individuals why is it very hard to guarantee equalization? Graphically represent the situation. d- Compute the competitive equilibrium (prices and quantities) for the exchange economy? e- Does your results in d substantiate the first welfare theorem? Explain why or why not. f- Write down what the second fundamental theorem says about the trade-off between equity…
- Part B: As a policy analyst for the Congressional Budget Office, you have been asked to estimate the potential costs of occupational licensing to the U.S. economy. Using demand analysis, a basic examination of the national costs of licensing could be developed as follows: Suppose that the entire 10 percent wage premium is from market power (as opposed to greater productivity from enhanced human capital), and further assume that labor supply is perfectly elastic and the labor demand elasticity is 0.5. Hypothetically, assume that the Census data suggests that there are approximately 68 million licensed workers in the U.S. Also assume that the average earning is $50,000. Calculate the potential job loss and the annual cost to consumers as a consequence of occupational licensing. Hint: Recall that the movement up the demand curve is the change in wages times the labor demand elasticity times the number of workers. To calculate the costs, what would a license worker make if they were…Consider a competitive economy that has four different jobs that vary by their wage and risk level. The table below describes each of the four jobs.Job Risk ( r ) Wage ( w)A 1/5 $ 3B 1/4 $12C 1/3 $23D 1/2 $25All workers are equally productive, but workers vary in their preferences. Consider a worker who values his wage and the risk level according to the following utility function:u(w, r) = w + 1/r2Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs must become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation?Consider a nonrenewable resource that can be consumed either today (period 1) or tomorrow (period 2) and has a finite supply of 4 units. Assume the inverse demand for the resource in both periods is: P_1 = 30 - 5Q_1 P_2 = 30 - 5Q_2 Assume the marginal cost of extracting the resource is constant at $10 and the social discount rate is 20 percent (r = .2). Assuming the resource is allocated efficiently, what is the consumer surplus in period 1? Please report your answer out to at least two digits (e.g., 3.24).