Labor Economics – Assignment 5

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Labor Economics – Assignment 5

Consider the basic, two period, search model we discussed in class. We focus on the decisions of a worker that nds himself unemployed at the beginning of our analysis. At the beginning of period 1, an unemployed worker observes a wage o er of w. The o er is random – that is, it depends on many factors outside the control of the worker, luck included –. Assume that wages are drawn from a Uniform distribution on the (0, 30) interval. Assume that workers have a career that lasts for two periods, that they get exactly one o er per period with probability equal to 1. If they take the job, they stop the search and cease to obtain job o ers. Assume that the chance that he is red (or the rm that he works for cease to exist) is zero. Assume that wages do not grow over time, and the rate of time discount is one (that is, dollars have the same value over time). The worker aims to maximize the expected value of his earnings, and the choices at his disposal to achieve that are only whether to accept or to turn down an o er at any point in time he obtains one.

Review Questions

a) In this setting, what is the de nition of the reservation wage

b) In the last period, what is the worker reservation wage Why

c) What is the key opportunity cost of taking a job in period one Is it the same as the opportunity cost of taking a job that we obtained when we study the standard theory of labor supply Explain

d) What is the condition that characterizes the reservation wage

Question 1

a) Find the worker’s reservation wage in period one.

b) Find the probability that an unemployed worker in period one will nd a job.

c) Find the average wage of workers that decide to take a job in period one. Compare that with the mean of the distribution of wage o ers and the mean of the distribution of wages of workers that take jobs in period two. Discuss their di erences and similarities.

Question 2 Assume now that the government introduces unemployment

bene ts. Assume unemployment bene ts are paid to unemployed workers 1

at every period, and the value of unemployment bene ts is set at 10 dollars per period.

a) Find the worker’s reservation wage in period 2.

b) Find the worker’s reservation wage in period 1.

c) Find the probability that a worker in period one will nd a job. Is it higher than the one without the unemployment bene ts

d) Find the average wage of workers that decide to take a job in period one. Compare it with the one that would prevail without unemployment bene ts.

e) Thinking about a period of unemployment as an investment in job search that has opportunity costs (foregone wages) and bene ts; what is the change that unemployment bene ts introduce in this environment

Question 3 Assume now, instead, that workers need to pay a fee to apply for jobs. Assume that the fee is 5 dollars per period and that the worker can only obtain a job o er if he pays the costs of searching for the job.

a) Find the worker’s reservation wage in period 1.

b) Find the probability that a worker in period one will nd a job. Is it higher than the one without the job application fee

c) Find the average wage of workers that decide to take a job in period one. Compare it with the one that would prevail in the environment in which the costs of searching for a job was smaller (equal to zero).

e) Thinking about a period of unemployment as an investment in job search that has opportunity costs (foregone wages) and bene ts; what is the change that the introduction of a job application fee creates in this environment

Question 4 Assume that the economy now entered a period of growth and, as a result, rms are o ering higher wages in general. Assume that all wages are 5 dollars higher than they would have been had the economy stayed in its original state. That is, wages are now drawn from a Uniform distribution on the (5,35) interval.

a) Find the worker’s reservation wage.

b) Do the wages of workers that nd jobs in period one grow by 5 dollars Why

c) Find the chance that an unemployed worker nds a job in period 1.

Question 5 Assume that the economy now entered a recession and, as a result, worker’s are nding it harder to obtain job o ers. Assume that,

at every period in which a worker is searching for a job, he only obtains an o er with a probability of .75. Provided that he is lucky enough to get an o er, the wage he obtains is still a random draw from a uniform distribution on the (0,30) interval.

a) Find the worker’s reservation wage in period 1.

b) Find the expected value of the wage of workers that nd jobs in period one.

c) Find the chance that an unemployed worker nds a job in period 1. It is smaller than the chances that he would nd a job in normal times By how much Why

Question 6 Consider the basic Markov chain framework of understand- ing the employment unemployment dynamics. The adult population consists of workers in two distinct states: employment and unemployment. At every year, employed workers have a separation rate of 10%, while unemployed workers have a job nding rate of 85%. Assume that at the end of 2018, the employment rate is 75%.

a) Assuming that the job nding rate and the separation rate stay the same, nd the employment rate (e) and the unemployment rate (u) that is predicted to prevail in 2019, 2020, and 2021.

b) Find the long run equilibrium rates of employment and unemploy- ment.

c) Now, assume that advancements in technology increased the displace- ment of workers by computers, automation, and robots. As a result, the job nding rate decreases to 75% and the separation rate increased to 20%. Assume that the economy has an employment rate of 90% at the moment that these changes take place. Find the predicted levels of employment and unemployment one year, two years, and three years after these changes take place. Plot them in a graph (one graph for the employment level, another one for the unemployment level).

d) Add to the graph the long-run equilibrium level for employment and unemployment rates after these changes take place.