labor economics assignment 5

Labor Economics

Assignment 5

Fall 2020

Due Date: October 29, must be uploaded on NYU Classes prior to 2:00 p.m. New York

time.

1. In a population of individuals, there is a distribution of “occupation 1” ability, 

which is uniformly distributed on the interval [01] If a type  individual works

in occupation 1, their wage income is

1() = 1

All individuals are equally productive in occupation 2, and the wage paid there is

2() = 2

The objective of each individual is to maximize their income.

1. If 1 = 10 and 2 = 5 find the proportion of the population working in

occupation 1.

2. If 1 = 10 and 2 = 5 find the average wage in occupation 1.

3. Answer both (a) and (b) when 1 = 8 and 2 = 6

2. An individual lives two periods, and their objective is to maximize their lifetime

(sum of two period) income. The productivity of an individual at a given firm is

unknown until she works there, and can only be inferred from the productivity

realizations she has at the firm). There are two types of worker-firm job matches,

“good” ones and “bad” ones, and they are equally represented in the population

(that is, the probability of finding a good match is 05 which is also the probability

of finding a bad match). At a bad match, the individual always produces two units

of output,  = 2 for all  At a good match, the individual produces three units of

output with probability 09 in any period, and produces 1 unit of output in any

period with probability 01 Based on 1 she will attempt to determine whether

the match is good or bad.

At the end of the first period, the individual observes and is paid her productivity

in the period, 1 Based on that observation, she can then decide to try a different

firm in the second period or remain at her first period firm. Whatever she chooses,

at the end of the second period her productivity 2 will be realized she will be

paid that amount. To summarize, the output distributions in any period  are

given by

Probability distribution of output by type of job

Output Level “Bad” job “Good” job

 = 1 0 01

 = 2 1 0

 = 3 0 09

Note that the output realizations are independent over time. If someone in a

“good” job in period 1 drew an output level of 3 they still have a probability of

a draw of 1 next period of 0.1.

1. Describe the optimal turnover decision, that is, determine who would leave

their employer after period 1 and who would stay based on their output

realization.

2. Determine the average wage earned in the population in both periods, ̄1 and

̄2

3. An individual lives 3 periods, and seeks to maximize

1 −1 + 2 −2 + 3 −3 where  is the wage in period  and  is the cost paid to find a new job in period

 Whenever the individual wants to find a new job (including period 1), she must

pay a cost of  = 3 (so that 1 = 3 for all individuals; if they kept that same job

in periods 2 and 3 then 2 = 3 = 0). Whenever an individual finds a job, their

wage  at the job is determined by a draw from the Uniform distribution on the

interval [010] Then the expected value of the wage at a job is given by  = 5

If an individual remains at the same job from one period to the next, then they

receive the same wage as in the previous period.

1. Let the wage that the individual had in period 2 be given by 2 For what

values of 2 would the individual decide to find a new job in period 3?

2. Let the wage that the individual had in period 1 be given by 1 For what

values of 1 would the individual decide to find a new job in period 2?

3. Determine the average wage in the population in period  ̄  = 123

4. Determine the proportion of people finding new jobs in period   where

1 = 1

5. Does length of time at a job, known as job tenure, “cause” the wage increases

observed in periods 2 and 3? Why or why not?

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