Labor Economics Assignment 5 Fall 2020 Due Date October 29

Labor Economicsassignment 5fall 2020due Date October 29 Must Be Uplo

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. 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 ï·1() = ï²1» All individuals are equally productive in occupation 2, and the wage paid there is ï·2() = ï²2 The objective of each individual is to maximize their income. 1. If ï²1 = 10 and ï²2 = 5» find the proportion of the population working in occupation 1. 2. If ï²1 = 10 and ï²2 = 5» find the average wage in occupation 1. 3. Answer both (a) and (b) when ï²1 = 8 and ï²2 = 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, ï¹ï´ = 2 for all ï´ï€º 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 ï¹1» 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, ï¹1» 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 ï¹2 will be realized she will be paid that amount. To summarize, the output distributions in any period ï´ are given by Probability distribution of output by type of job Output Level “Bad» job “Good» job ï¹ï´ = 1 0 0» ï¹ï´ = 2 1 0 » ï¹ï´ = 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, ï¹Ì„1 and ï¹Ì„2» 3. An individual lives 3 periods, and seeks to maximize ï·1 −ï£1 + ï·2 −ï£2 + ï·3 −ï£3» where ï·ï´ is the wage in period ï´ and ï£ï´ is the cost paid to find a new job in period ï´ï€º Whenever the individual wants to find a new job (including period 1), she must pay a cost of ïƒ = 3 (so that ï£1 = 3 for all individuals; if they kept that same job in periods 2 and 3» then ï£2 = ï£3 = 0). Whenever an individual finds a job, their wage ï· 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 ï…ï· = 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 ï·2» For what values of ï·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 ï·1» For what values of ï·1 would the individual decide to find a new job in period 2? 3. Determine the average wage in the population in period ï´» ï·Ì„ï´» ï´ = 1» 2» 3» ¼. 4. Determine the proportion of people finding new jobs in period ï´» ﴻ 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?

Paper For Above instruction

This comprehensive analysis delves into the dynamics of labor economics through its multi-part exploration of occupational choices, productivity, and wage determinants across different periods. It combines theoretical modeling with practical implications to provide insights into human capital allocation and job mobility decisions within labor markets.

Part 1: Occupational Choice and Wage Distribution

In the initial scenario, individuals are characterized by a uniform distribution of ability, , on the interval [0, 1]. The wage income in occupation 1 is directly proportional to ability, expressed as ï·1() = ï²1 , where ï²1 is the wage coefficient. For occupation 2, productivity is constant across individuals at ï²2, resulting in a fixed wage ï·2 = ï²2. The individuals aim to maximize income, leading to a strategic occupational choice based on their ability level.

To find the proportion of individuals working in occupation 1 when ï²1 = 10 and ï²2 = 5, individuals with ability  exceeding a certain threshold will prefer occupation 1 since their wage ï·1() surpasses wage in occupation 2. Setting ï·1() = ï·2 yields:

ï²1  = ï²2 ⇒  = ï²2 / ï²1 = 5 / 10 = 0.5

Thus, all individuals with  > 0.5 choose occupation 1, and those with  ≤ 0.5 choose occupation 2. The proportion in occupation 1 is therefore 1 - 0.5 = 0.5, or 50%.

The average wage in occupation 1 is computed as the expected value of ï·1() over  in [0.5, 1], which is:

E[ï·1()] = ∫_{0.5}^{1} ï²1  f() d = ï²1 ∫_{0.5}^{1}  d = ï²1 [^2 / 2]_{0.5}^{1} = ï²1 ( (1)^2 / 2 - (0.5)^2 / 2 ) = 10 ( (1/2) - (0.125) ) = 10 (0.375) = 3.75

When ï²1 = 8 and ï²2 = 6, the threshold  becomes:

ï²2 / ï²1 = 6 / 8 = 0.75

Therefore, 25% of individuals with  > 0.75 choose occupation 1, leading to a proportion of 1 - 0.75 = 0.25, or 25%. The average wage in occupation 1 is:

E[ï·1()] = ï²1 ∫_{0.75}^{1}  d = 8 [^2 / 2]_{0.75}^{1} = 8 ( (1)^2 / 2 - (0.75)^2 / 2 ) = 8 (0.5 - 0.28125) = 8 (0.21875) = 1.75

Part 2: Sequential Job Mobility and Wage Expectations

The second scenario investigates job switching decisions over two periods, considering uncertainty about job quality (good or bad matches). Matches are equally likely, with bad matches consistently producing two units of output, and good matches producing three units with high probability (0.9) or one unit with low probability (0.1). Observations at the end of period one inform the worker’s decision to stay or seek a new job in period two.

The optimal turnover decision depends on the output received in period one. If the output is low (e.g., 1), the worker infers a likely bad match and may decide to switch. Conversely, high output (e.g., 3) suggests a good match, favoring retention.

The expected earnings in period two determine whether the worker finds it beneficial to stay or move. Given the expected output ratios and the probabilities for good matches, the worker assesses whether the expected future wage exceeds the value of continuing at the current employer, considering the costs and expected benefits.

Optimal Decision Rules

If the worker’s output in period one is 3 (indicating a good match), the high likelihood of continued good performance incentivizes staying. If the output is 1 (indicating a bad match), switching is optimal due to the low expected return from staying. For intermediate outputs (such as 2), the decision hinges on the comparison of expected future wages, which might be computed explicitly using Bayesian updating of the match quality based on observed outputs.

Expected Average Wages

The population’s average wage in each period can be calculated by considering the distribution of job types and the realized output. In period one, since no prior information is available, the average wage aligns with the expected output over all matches:

E(wage) = P(good) × E[wage|good] + P(bad) × E[wage|bad] = 0.5 × E[wage|good] + 0.5 × 2

In a good match, earnings are based on the output level, which depends on the probability distribution, but the expected output per period is:

E[output | good] = 0.9 × 3 + 0.1 × 1 = 2.8 units

Correspondingly, wages are proportional to the output, so in expectation, wages mirror the productivity. In the bad match, the wage is fixed at 2 units of output. Calculations indicate that average wages align with these expected outputs, adjusted for the match probabilities.

Interpretation of Job Switching and Wage Investment

The decision to switch jobs after period one depends critically on the observed output. High output suggests a good match, leading to continued employment. A low output indicates poor productivity, increasing the likelihood that switching yields better future wages. Bayesian updating informs this decision by refining the probability that a given output indicates a good or bad match.

Part 3: Multi-Period Job Search with Costs and Wage Uncertainty

This section considers an individual’s strategic decision-making over three periods, balancing expected wages, search costs, and the benefits of job stability versus mobility. The individual's objective function incorporates the wages in each period discounted by the search costs incurred when switching jobs. The wages are drawn uniformly on [0, 10], with an expected value of 5. The decision to switch depends on current wages, potential future wages, and the associated costs.

Decision Rules for Job Switching

The critical value for deciding to change jobs in period 3 after observing ï·2 is derived by comparing current wages against the expected benefit of switching, net of costs. If the current wage ï·2 exceeds a threshold calculated as (expected future wages minus the period-specific search costs), the individual prefers to stay; otherwise, switching is optimal. Similar logic applies to decisions in period 2 based on wages ï·1 and the expected gains in period 3.

Average Wages and Labor Market Dynamics

Average wages across the three periods are derived by integrating the uniform distribution expectations with the decisions made at each stage. The proportion of individuals switching jobs in each period depends on current wages and the anticipated benefits of alternative employment. The longer tenure may influence wage levels due to factors like increased skills or employer-specific investments, though the random wage draws suggest an other-wise independent wage process in this simplified model.

Impact of Job Tenure on Wage Increases

While longer job tenure can sometimes lead to higher wages due to accumulated skills or firm-specific human capital, in this model, the wages are independently drawn distributions at each period. Therefore, observed increases are primarily driven by individual decisions based on wage comparisons rather than direct effects of tenure. The analysis implies that wage growth observed over periods is more attributable to strategic Iocation of employment rather than the duration at a particular firm, consistent with the concept of wage convergence and labor mobility effects discussed in labor economics literature.

Conclusion

The multi-part analysis underscores key principles in labor economics related to occupational choice, job mobility, productivity measurement, and wage determination. The models demonstrate how individual ability and productivity uncertainties influence employment patterns, wages, and strategic decisions about job switching, all within broader labor market dynamics. These insights contribute to understanding the incentives and constraints faced by workers in real-world labor markets, emphasizing the importance of information, mobility costs, and skills accumulation in shaping economic outcomes.

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