Consider the Mortensen-Pissarides model described in the lecture. Now suppose that an unemployed worker at the beginning of each period can choose between searching for a job and working as a selfemployed worker during the period. If an unemployed worker searches for a job, then he or she will receive the unemployment benefit, b, and then will be matched with a job randomly in the same way as assumed in the lecture. If an unemployed worker works as a self-employed worker, then he or she will receive z as the income for the current period, will not be able to search for a job within the same period, and will be an unemployed worker again at the beginning of the next period. Answer the following questions. Note: Except for new variables and parameters, the notations of variables and parameters are the same as in the lecture. 1. Define the Bellman equation for an unemployed worker. Notes: - You only need to define the equation rather than solve it. Use the same notations of variables and parameters as in the lecture and the problem statement described above. 2. Assume b = 1, c = 0.7, r = 0.1, y = 3, p=0.3, and λ = 0.05, and also suppose 0 = 1.2 in the steady state. What is the maximum value of z that makes unemployed workers choose to search for a job in the steady state in this case? Note: Assume that if an unemployed worker is indifferent between searching for a job and being self-employed, he or she always chooses to search for a job.
Consider the Mortensen-Pissarides model described in the lecture. Now suppose that an unemployed worker at the beginning of each period can choose between searching for a job and working as a selfemployed worker during the period. If an unemployed worker searches for a job, then he or she will receive the unemployment benefit, b, and then will be matched with a job randomly in the same way as assumed in the lecture. If an unemployed worker works as a self-employed worker, then he or she will receive z as the income for the current period, will not be able to search for a job within the same period, and will be an unemployed worker again at the beginning of the next period. Answer the following questions. Note: Except for new variables and parameters, the notations of variables and parameters are the same as in the lecture. 1. Define the Bellman equation for an unemployed worker. Notes: - You only need to define the equation rather than solve it. Use the same notations of variables and parameters as in the lecture and the problem statement described above. 2. Assume b = 1, c = 0.7, r = 0.1, y = 3, p=0.3, and λ = 0.05, and also suppose 0 = 1.2 in the steady state. What is the maximum value of z that makes unemployed workers choose to search for a job in the steady state in this case? Note: Assume that if an unemployed worker is indifferent between searching for a job and being self-employed, he or she always chooses to search for a job.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the Mortensen-Pissarides model described in the lecture.
Now suppose
that an unemployed worker at the beginning of each period can choose between searching for a job and working as a
selfemployed worker during the period. If an unemployed worker searches for a job, then he or she will receive the unemployment
benefit, b, and then will be matched with a job randomly in the same way as assumed in the lecture. If an unemployed worker
works as a self-employed worker, then he or she will receive z as the income for the current period, will not be able to search for a
job within the same period, and will be an unemployed worker again at the beginning of the next period.
Answer the following questions.
Note: Except for new variables and parameters, the notations of variables and parameters are the same as in the lecture.
1.
Define the Bellman equation for an unemployed worker.
Notes:
- You only need to define the equation rather than solve it. Use the same notations of variables and parameters as in the lecture and
the problem statement described above.
2.
Ө
Assume b = 1, c = 0.7, r = 0.1, y = 3, ¢ = 0.3, and X = 0.05, and also suppose 0 = 1.2 in the steady state. What is the
maximum value of z that makes unemployed workers choose to search for a job in the steady state in this case?
Note: Assume that if an unemployed worker is indifferent between searching for a job and being self-employed, he or she always
chooses to search for a job.
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