Now, with decreasing fertility, the familiar Beckerian trade-off in (5b) becomes operative and
parents want to spend more on their children. The increase of h has a positive feedback effect
on the left-hand side of (5c) so that we have to assume β3 > β4 for a consistent solution to exist.
In other words, having a family must be more important than child quality expenditure. This
parameter restriction is assumed to hold henceforth.
Note that the wish to spend more on children when π rises cannot be driven by the motive
to improve child survival because the starting point of the whole chain of effects was that child
health expenditure became less effective with rising π. Thus, it must be driven by the child
quality motive. This lets us conclude that child expenditure changes its character with improving
fundamental survival probabilities. At low π's expenditure is driven by its β3-component, i.e.
health and nutrition, whereas at high n’s it is mainly motivated by the β4-component, i.e.
schooling and education. The downside of this effect is that it holds also vice versa: parents
react to deteriorating child survival by substituting child expenditure with increasing fertility.
Thus, with endogenous health, parents in high mortality environments have a comparative
advantage in child bearing i.e. in producing cheap children.6
From the first order conditions we obtain the following solution.
βιy + (β2 + β3)c
cl =-------Â-------
(6a)
(6b)
(6c)
(6d)
φ
_ β2(1 - c/y)
Φ
= β3β4λ(l - π)(1 - c/y)
φ φ(β3 - β4)π
h = (β3 - β4)∏
h β4λ(1 - π) ,
where φ ≡ β1 + β2 + β3 . From (6b) we see that the savings rate is increasing with economic
development and converges towards a constant as income gets large. As derived intuitively above,
fertility is lower and child expenditure higher under better fundamental survival conditions:
(7a)
(7b)
∂n |
= -β3β4λ(l - c/y) |
∂π |
φ(β3 - β4)π2 |
∂h |
= β3 - β4 > 0. β4λ(1 - π)2 |
∂π |
6I borrowed this expression from Moav (2005) who derives a similar result in a very different setting where well
educated mothers have a comparative advantage in teaching and poorly educated mothers in child bearing.