Malthusian Growth

Assumptions §

• ass. Factor of production is just labor $N$ and land $L$; there is no capital $K$
• ass. Nobody saves. There is no way to save, thus there is no investments. All output results in consumption. i.e. $Y=C$
• ass. Law of Motion (Malthusian Population). Population growth is positively correlated to consumption per capita:

$$\frac{N_{t+1}}{N_t}=g\left(\underset{\text{ consumption per cap }}{\underbrace{\frac{C_t}{N_t}}}\right)$$

where

• $g(\cdot )$ is the population growth function wrt consumption per capita
• Note that $\frac{C_t}{N_t}=\frac{Y_t}{N_t}$ Thus we have the population growth formula:

$$N_{t+1}=N_{t}g(z\cdot f(\ell ))$$

where

• $f(\cdot )$ is the production function in intensive form. Note here there is no capital, because capital is not a factor of production Observe.
• Steady state (red point) is achieved when $N_{t+1}=N_t$, thus from the LoM (Pop.) we get $g(zf(\ell ))=1$, the intersection with the $45^{\circ }$ line
• Increase in $z$, causes:
  1. Increase in production per capita $zf(\ell )$
  2. Increase in consumption per capital $C_t$
  3. Increase in population $N_t$
  4. Thus consumption per capita normalizes
  • Visually this is the economy moving to the left

Malthusian Trap §

def. Malthusian Trap. this fact that even when population grows there is not an increase in consumption or production per capita. The ways to escape this trap is:

1. Instead of increasing quantity of children, increase the quality of children, via apprehenticeships, universities, etc.
2. Emergence of capital, i.e. factories, tools, that can accumulate rmk. Charging interest in a Malthusian society is stealing, because nobody can invest, and thus nobody’s capital will grow