1. Consider Spence job market signaling model. A worker's type is 0 = {6, 9}, where the probability that 0 = 9 is equal λ = (0, 1). The total number of workers equals N. The productivity of a worker in a job is 0. Each worker chooses a level of education e≥0. The cost of obtaining education level e is 3e/0. Reservation utility is 4 for every worker. All workers are price takers and the price of the final good produced is 1. Assume that firms are risk neutral and employment lasts for one year. Assume that there are two firms that compete by offering wages simultaneously and independently. (a) Find all separating equilibria and identify a Pareto superior separating equilibrium. Do not forget to specify the equilibrium wage scheme. (b) Calculate TS and find the value of society loss (DWL) for the best (Pareto superior) signaling equilibrium. (c) Find all values of λ= (0, 1) under which prohibition of signaling results in a Pareto improvement in comparison with the best (Pareto superior) signaling equilibrium. Explain the result intuitively.

1. Consider Spence job market signaling model. A worker's type is 0 = {6, 9}, where the probability that 0 = 9 is equal λ = (0, 1). The total number of workers equals N. The productivity of a worker in a job is 0. Each worker chooses a level of education e≥0. The cost of obtaining education level e is 3e/0. Reservation utility is 4 for every worker. All workers are price takers and the price of the final good produced is 1. Assume that firms are risk neutral and employment lasts for one year. Assume that there are two firms that compete by offering wages simultaneously and independently. (a) Find all separating equilibria and identify a Pareto superior separating equilibrium. Do not forget to specify the equilibrium wage scheme. (b) Calculate TS and find the value of society loss (DWL) for the best (Pareto superior) signaling equilibrium. (c) Find all values of λ= (0, 1) under which prohibition of signaling results in a Pareto improvement in comparison with the best (Pareto superior) signaling equilibrium. Explain the result intuitively.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 13 Consider a market in which there are two types of workers L and H. Each type of worker has a different level of productivity, but that productivity is unobservable ex ante to potential employers. Before seeking employment at a firm in the market, all workers can (if they choose) get some level of education e. This choice of education e is observable to all, including potential employers. Assume that the market is competitive, so expected profits must be zero in equilibrium. The L-type workers have a productivity of 2 if they work for a firm in the market. They also have an outside option of 2. The utility function of the L-type workers UL - wL- eL, where wl is the wage received and eL is the level of education they obtain. The H type worker has an outside option of 2 and a productivity of 4 if they are employed by a firm in the market. The utility function for a H-type worker is UH=wH - (%)eH, where wH is the wage paid to a H-type and eH is the education they choose to get.…
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