Why living standards were flat for millennia: population growth eating every productivity gain.
Warming up the engine…
The pre-industrial growth trap: population grows whenever income exceeds subsistence, but land is fixed, so any productivity gain is eventually eaten by more mouths and living standards return to subsistence.
Income per head falls as population rises (diminishing returns to fixed land); population growth ∝ income − subsistence
For most of human history the model was right: better harvests meant more surviving children, which diluted the gain within a generation or two. The Industrial Revolution broke the trap when technology started improving faster than population could respond, and the demographic transition then severed the income-fertility link entirely.
Malthus is a model of the LEVEL of living standards, not growth: technology shifts income up temporarily, population growth drags it back. Explain why it stopped applying after ~1800 for full marks.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at N 64, F 16.0.
Equilibrium: N* = 64.0, F* = 16.0
Current equations
For most of history, better harvests meant more mouths, not richer lives. Food grows with diminishing returnsdiminishing returnsEach extra unit of an input adds less output than the one before, holding other inputs fixed. (the curve) while each person needs a fixed amount (the line), population always expands until the two meet again.