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.

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| Consider Spence job market signaling model. A worker's type is 0 e{6, 9}, where the probability that
0 = 9 is equal 2 e (0, 1). The total number of workers equals N. The productivity of a worker in a job is . Each
worker chooses a level of education e20.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 1 e (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.
Transcribed Image Text:1. | Consider Spence job market signaling model. A worker's type is 0 e{6, 9}, where the probability that 0 = 9 is equal 2 e (0, 1). The total number of workers equals N. The productivity of a worker in a job is . Each worker chooses a level of education e20.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 1 e (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.
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