Human Capital Accumulation & Growth

Assumption §

• ass. Factors of production is only human capital $H$
• ass. Human capital $H$ does not have diminishing marginal returns. The production function is simply:

$$Y=zuH$$

where $u$ is the portion of time spent training, i.e. generating human capital. Namedly:

$$h=\underset{\text{ H.C. Generation }}{\underbrace{(1-u)}}+\underset{\text{ Working }}{\underbrace{u}}$$

• ass. Human capital is generated by $H_{t+1}=b(1-u)H_t$ where $b$ is the learning efficiency, i.e. is there a university, apprehenticship, etc.

Profit Maximization §

Production will occur via profit maximization:

$$\begin{array}{rlr}\underset{u}{\max }\pi & =Y_t-\underset{\text{ wages }}{\underbrace{wu{H}_t}}& \\ & =(z-w)u{H}_t& \\ (z-w)& \stackrel{\text{set}}{=}0& \text{FOC}\\ \therefore z& =w& \end{array}$$

Observe that firms will provide wage that is simply equivalent to productivity $z$, regardless of how many hours worked. The labor market has perfectly elastic demand.

Human Capital Law of Motion §

$$\begin{array}{r}\frac{H_{t+1}}{H_t}=\frac{b(1-u)H_t}{H_t}=b(1-u)\end{array}$$

Observe:

• If $b(1-u)>1$, or $b>\frac{1}{1-u}$ human capital will grow
• No declining ${\text{MP}}_H$. explosive growth.
• Convergence will not happen )