The incidence of subsistence consumption causes a positive effect of income on fertility. As
income rises above subsistence level, current consumption becomes less essential and the desire
to have children becomes more important for young adults.
∂n β3β4 λ(1 — π)c
(8)
∂y φ(β3 — β4)∏y2
The income elasticity of child demand, (∂n∕∂y) = c∕(y — c), is infinite at subsistence level
and decreases towards zero as income goes to infinity. Later, in the macroeconomic model the
survival-effects in (7) are sufficient to explain a delayed demographic transition and slow growth
for geographically unfavorable environments. The subsistence-effect in (8), however, is necessary
to generate a stable equilibrium of stagnation.
4. Correlations of Demo-Economic Development
The rate of population growth, gL := n(y,π(y)) ∙ π(y) — 1, is affected by income through its
impact on fertility and, indirectly, through its impact on health expenditure and child survival.
Thus, the total effect of a marginal increase of income on population growth consists of three
parts:
∂gL ∂n ∂n∂π ∂π
∂y ∂y ∂π ∂y ∂y
(9)
The first term on the right hand side is the subsistence effect originating from the hierarchy
of needs. It is positive because parents want to support a larger family as income rises from
subsistence level. The second term is the quality-quantity substitution effect. It is negative
because higher average income in an economy increases the probability that children survive and
causes parents to substitute fertility with child expenditure. The third term is the demographic
effect. It is positive because more children survive when income rises, both because increasing
average income in the economy improves survival and because parents spend more on each child.
After inserting (1), (6c), (6d), and their respective derivatives into (9) and applying some
algebra we get an easily analyzable expression:
∂gL /
., nπ
∂y
1 ∂π
(10)
У(У — c) 1 — ∏ ∂y
The first term in parentheses results from the subsistence effect. It is infinitely large at subsis-
tence level and vanishes quickly with rising income. The second term comprises the demographic
effect and the quantity-quality substitution effect. Eventually, this term also vanishes as income
10