Modern Labor Economics: Worker Mobility, Immigration & Human Capital

Understanding Worker Mobility in Modern Labor Economics

In today's globalized economy, worker mobility—encompassing turnover, migration, and immigration—is a central topic in modern labor economics. This tutorial breaks down key concepts from ECON 5850 Problem Set 10, using current trends like remote work and the gig economy to illustrate timeless principles. Whether you're analyzing a family's relocation decision or the macroeconomic effects of immigration, the tools of human capital theory and present value analysis remain essential.

The Determinants of Worker Mobility: A Family Relocation Example

Consider a dual-earner couple deciding whether to move for better job opportunities. Using a discount rate of 6%, we compare the present value of combined salaries at current jobs versus new jobs over three years, minus moving costs of $10,000. This calculation mirrors how workers evaluate mobility investments in practice, similar to deciding whether to accept a remote job offer from a tech hub like Austin or stay in a smaller market.

To compute net present value (NPV):

Year 0: -$10,000 (moving costs)
Year 1: ($83,000 - $80,000) / (1.06) = $2,830
Year 2: ($87,000 - $82,000) / (1.06)^2 = $4,450
Year 3: ($92,000 - $85,000) / (1.06)^3 = $5,875

Total NPV = -$10,000 + $2,830 + $4,450 + $5,875 = $3,155. Since NPV > 0, the move is worthwhile. This example highlights how discounting future earnings is crucial in labor economics, just as investors discount future cash flows.

The maximum mobility costs that still make the investment worthwhile equal the present value of future gains: $2,830 + $4,450 + $5,875 = $13,155. If psychic costs are included, they must be less than this amount.

Psychic costs (e.g., leaving friends, family, familiar environment) are often front-loaded, but psychic benefits (e.g., better climate, cultural opportunities, proximity to hobbies) can accrue over time. For example, moving from a cold region to a warmer one may yield ongoing happiness gains, much like the mental health benefits of relocating to a nature-rich area.

If a worker moves without a job, initial earnings may be lower. Suppose year 1 new salary is only $78,000 (vs. $80,000 current). The NPV becomes: Year 1: ($78,000 - $80,000)/1.06 = -$1,887; Year 2: ($87,000 - $82,000)/1.06^2 = $4,450; Year 3: ($92,000 - $85,000)/1.06^3 = $5,875. Total = -$10,000 - $1,887 + $4,450 + $5,875 = -$1,562, so not worthwhile. The lowest year 1 new salary that yields NPV ≥ 0 solves: NPV = -10,000 + (S1 - 80,000)/1.06 + 4,450 + 5,875 = 0 => S1 = $79,000. This shows the importance of earnings growth in justifying mobility.

It is unlikely both spouses gain equally; one may have better job prospects, leading to tied mover or tied stayer scenarios. For instance, if one spouse works in tech and the other in education, the move may benefit the tech worker more.

The Gain to Society from Mobility

Mobility not only benefits individuals but also increases total output. Consider two labor markets with different marginal product schedules. If workers move from a low-productivity market to a high-productivity one, total output rises. This is analogous to how labor reallocation during the COVID-19 pandemic shifted workers from hospitality to e-commerce and logistics, boosting overall efficiency.

Using a simple example with 6 workers: 3 in Market A and 3 in Market B. If Market A's marginal product declines faster, workers will migrate to Market B until wages equalize. This process continues until the marginal product of the last worker is the same in both markets, maximizing total output. The area under the marginal product curve equals total output, and migration increases this area.

In practice, geographic mobility is often hindered by housing costs, family ties, and information frictions. However, policies that reduce these barriers can generate significant economic gains.

The Consequences of Immigration

Immigration is a hot-button issue in labor economics. Using a simple supply-demand model: native supply LN = 2W, immigrant supply LI = W, and labor demand LD = 20 - 2W. Without immigration, total supply L = LN = 2W, so equilibrium: 20 - 2W = 2W => W = 5, L = 10. With immigration, total supply L = 2W + W = 3W, so 20 - 2W = 3W => W = 4, L = 12. Native employment falls from 10 to 8 (since LN = 2*4 = 8), so 2 native jobs are 'lost' to immigrants. However, native workers' total income drops from 10*5 = 50 to 8*4 = 32, a loss of 18. Firms' profits (producer surplus) increase because they hire more labor at lower wages. Total output (area under demand curve) rises from 0.5*(10+20)*5 = 75 to 0.5*(12+20)*4 = 64? Wait, correct calculation: Before immigration, output = 0.5*(10+20)*5 = 75. After immigration, output = 0.5*(12+20)*4 = 64? That can't be right because output should increase. Let's recalc: Demand: LD = 20 - 2W, so inverse demand: W = 10 - 0.5L. Output is integral of W from 0 to L: ∫(10 - 0.5L)dL = 10L - 0.25L^2. For L=10, output = 100 - 25 = 75. For L=12, output = 120 - 36 = 84. So output increases by 9. Immigrants earn total wages = 4*4 = 16, but their economic rent (willingness to pay for the right to work) is the area above their supply curve: immigrant supply: W = LI (since LI = W), so for LI=4, the supply price is 4, but wage is 4, so rent = 0? Actually, immigrant surplus = wage - supply price = 4 - 4 = 0? That seems off. Let's compute correctly: Immigrant supply: LI = W, so inverse supply: W = LI. At equilibrium, LI = 4, so the last immigrant's reservation wage is 4, but the first immigrant's reservation wage is 0. Total immigrant surplus = ∫(4 - LI)dLI from 0 to 4 = [4LI - 0.5LI^2] from 0 to 4 = 16 - 8 = 8. So immigrants would be willing to pay up to 8 in real terms for the right to work.

A transfer scheme: native workers lose 18 in income, firms gain additional profits (change in producer surplus). Compute producer surplus before: PS = 0.5*(10)*5 = 25? Actually, producer surplus is area above supply but below price. Since supply is native+immigrant, but for firms, it's the same. Better to compute change in profits: Before immigration, profits = total revenue - total wages = output - wages = 75 - 50 = 25. After immigration, profits = 84 - 48 = 36. Increase of 11. So total surplus (native income + profits) before = 50+25=75, after = 32+36+8 (immigrant surplus) = 76. Society gains 1. To compensate natives, firms could transfer 18 to natives, leaving firms with 36-18=18, still better than before? Actually, before firms had 25, so they'd be worse off. Alternatively, a tax on immigrants or firms could fund a wage subsidy for natives. For example, a lump-sum tax on immigrants of 8 (their surplus) and on firms of 10 (part of their gain) could give natives 18, leaving immigrants with 0 and firms with 26 (still better than 25). So it's possible to make everyone at least as well off.

Other effects of immigration not captured include: impact on housing prices, innovation, cultural diversity, and fiscal effects (taxes vs. public services). For instance, immigrants often fill labor shortages in agriculture and healthcare, boosting economic growth.

Migration After a Job Loss

A defense worker earning $60,000 loses job and moves to North Carolina for $50,000. This may seem irrational, but if future earnings growth in North Carolina is higher, the move can be worthwhile. For example, if the new job offers faster promotion or better long-term prospects, the present value of lifetime earnings may exceed staying and searching locally. This does not contradict human capital theory; it highlights that mobility decisions are based on expected future benefits, not just current wage. The worker might also value non-pecuniary factors like lower cost of living or better climate.

Why Women Have Higher Quit Rates

Empirical evidence shows women have higher quit rates and shorter job tenure, often attributed to lower levels of firm-specific training. According to Chapter 5, women are less likely to be offered such training because employers anticipate higher turnover due to family responsibilities or career interruptions. This creates a vicious cycle: less training leads to lower wages and job attachment, increasing quit rates. However, recent trends like remote work and flexible schedules may reduce these gaps, as seen in the post-pandemic labor market where gender equality in work arrangements improved.

In summary, understanding worker mobility and immigration is crucial for analyzing labor markets. Whether you're a student of labor economics or a policymaker, the principles of human capital investment, discounting future earnings, and marginal productivity provide a framework for evaluating these complex decisions.