Labor Economics – Assignment 5

发布时间：2022-04-14

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Labor Economics – Assignment 5

Consider the basic, two period, search model we discussed in class. We focus on the decisions of a worker that ﬁnds himself unemployed at the beginning of our analysis. At the beginning of period 1, an unemployed worker observes a wage oﬀer of w. The oﬀer 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 oﬀer per period with probability equal to 1. If they take the job, they stop the search and cease to obtain job oﬀers. Assume that the chance that he is ﬁred (or the ﬁrm 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 oﬀer at any point in time he obtains one.

Review Questions

a) In this setting, what is the deﬁnition 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 ﬁnd 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 oﬀers and the mean of the distribution of wages of workers that take jobs in period two. Discuss their diﬀerences and similarities.

Question 2 Assume now that the government introduces unemployment

beneﬁts. Assume unemployment beneﬁts are paid to unemployed workers 1

at every period, and the value of unemployment beneﬁts 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 ﬁnd a job. Is it higher than the one without the unemployment beneﬁts?

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 beneﬁts.

e) Thinking about a period of unemployment as an investment in job search that has opportunity costs (foregone wages) and beneﬁts; what is the change that unemployment beneﬁts 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 oﬀer 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 ﬁnd 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 beneﬁts; 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, ﬁrms are oﬀering 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 ﬁnd jobs in period one grow by 5 dollars? Why?

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

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

at every period in which a worker is searching for a job, he only obtains an oﬀer with a probability of .75. Provided that he is lucky enough to get an oﬀer, 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 ﬁnd jobs in period one.

c) Find the chance that an unemployed worker ﬁnds a job in period 1. It is smaller than the chances that he would ﬁnd 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 ﬁnding rate of 85%. Assume that at the end of 2018, the employment rate is 75%.

a) Assuming that the job ﬁnding rate and the separation rate stay the same, ﬁnd 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 ﬁnding 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.