Labor Economics & Human Capital
Labor economics analyzes how labor markets determine wages and employment. Firms hire workers up to the point where the marginal revenue product of labor (MRP$_L$) equals the wage, treating labor demand as a derived demand from the product market. Workers choose between labor and leisure based on wages and preferences. Human capital theory (Becker, Mincer) argues that education and training raise productivity and wages — the Mincer earnings equation quantifies returns to schooling empirically. Labor market failures include minimum wages, monopsony power, discrimination, and search frictions.
Labor Demand, Supply & Wages
$$MRP_L = MP_L \times MR$$
For a price-taking firm: $MRP_L = MP_L \times P$. Profit-maximizing labor demand condition:
$$MRP_L = w \implies MP_L \times P = w \implies w/P = MP_L$$
The real wage equals the marginal product of labor.
The log-linear relationship between wages and human capital:
$$\ln(w) = \alpha + \beta_1 S + \beta_2 \text{Exp} + \beta_3 \text{Exp}^2 + \varepsilon$$
$S$ = years of schooling, $\text{Exp}$ = years of work experience. $\beta_1$ estimates the private return to one additional year of education — typically $7$–$12\%$ in developed countries.
$$u = \frac{U}{L} \times 100\%, \quad L = E + U$$
- Frictional: Normal job search time. Always present.
- Structural: Skill/geographic mismatch. Long-lasting.
- Cyclical: Below-potential output. Targeted by stabilization policy.
Natural rate $u^* = $ frictional $+$ structural; NAIRU $\approx u^*$.
A single buyer of labor sets $w < MRP_L$, creating a wedge and employment below the competitive level. The monopsonist's labor cost (marginal factor cost) is:
$$MFC = w + L\frac{dw}{dL} > w$$
Profit max: $MFC = MRP_L$. A minimum wage can increase both wages and employment in a monopsony (unlike competitive markets).
Jobs with undesirable characteristics (risk, discomfort, inflexibility) must pay a wage premium to attract workers, all else equal. This wage gap compensates for non-monetary costs and is called a compensating differential.
$MP_L = 50 - 2L$ (in units), product price $P = \$4$, wage $w = \$80$. How many workers are hired?
- $MRP_L = (50-2L)(4) = 80 \implies 50-2L = 20 \implies L = 15$.
$\ln(w) = 1.5 + 0.09S + 0.04\text{Exp} - 0.001\text{Exp}^2$. Compare wages for $S=12$ vs $S=16$, both with Exp $= 0$.
- $S=12$: $\ln(w)=1.5+1.08=2.58$, $w=e^{2.58}\approx\$13.20$/hr.
$S=16$: $\ln(w)=1.5+1.44=2.94$, $w=e^{2.94}\approx\$18.92$/hr.
4 extra years of college raise wages by $\approx43\%$.
Practice Problems
Show Answer Key
1. $200-10L=50 \Rightarrow L=15$.
2. $\partial\ln(w)/\partial\text{Exp}=0.04-0.002\text{Exp}=0 \Rightarrow \text{Exp}=20$ years.
3. $U=11\text{M}$; $u=11/175\approx 6.3\%$.
4. Firms hire until wage equals $MRP_L$; at any given wage, the quantity of labor demanded is where $w=MRP_L$ — so the $MRP_L$ schedule is the demand curve.
5. $MFC=5+0.2L$. Set $MFC=MRP_L$: $5+0.2L=50-0.4L \Rightarrow 0.6L=45 \Rightarrow L=75$. $w=5+0.1(75)=\$12.50$. Competitive wage would be $50-0.4(75)=\$20$ — monopsony pays less.
6. Employment falls (demand curve slopes down) and a surplus of labor (unemployment) emerges above the competitive level.
7. Each additional year of schooling raises log wages by 0.11, i.e., raises wages by approximately 11.6\%.
8. General human capital (reading, math) is portable — workers bear the training cost and reap returns via wages. Firm-specific capital (proprietary systems, internal processes) is not portable — firms share costs and returns, creating mutual lock-in.
9. $MRP_L = 30 \times \$0.90 = \$27 > w = \$25$. The firm should hire more workers.
10. Compensating differentials — the wage premium compensates for the undesirable (dangerous) working conditions. Workers require higher pay to accept identical non-wage conditions.