Geography, Health, and Demo-Economic Development

Theorem 1. There exists a non-empty set of preference and technology parameters for which
a locally stable equilibrium of low income and high population growth exists in a geographically
unfavorable environment but not in a geographically favorable environment.

Example: The calibration for the U.S. shown in Figure 4 and gA = 1/2 percent, β = 1/3,
and α = 0.8 renders the equilibrium unstable. Keeping U.S. parameters of preferences and
technology the equilibrium becomes locally stable for location parameters b ≤ 0.003.

7. Delayed Demographic Transition

Given limited space on earth, any equilibrium with perpetually high population growth ap-
pears to be implausible from a very long-run perspective. Yet, for unfavorably located regions a
successful demographic transition may be so exceedingly slow that it is almost invisible within
a time-window of, for example, 50 or 100 years. Because it is visually indistinguishable, the
situation may mistakenly be identified as poverty trap. Furthermore, even if demo-economic
development is observable its pattern can look very differently for unfavorably located regions
compared to the experiences of the Western world.

In order to demonstrate these results, we consider the following experiment. Suppose there
are three countries sharing the parameters of preference for consumption, family size, and child
expenditure with the U.S. calibration from Figure 4. Assume identical technologies for all
three countries: α = 0.84, β = 1/3 and gA = 0.001. Given the low rate of technological
progress, population grows initially at a low equilibrium rate of 0.6 percent everywhere. The
three countries differ in their fundamental child survival rates, parameterized by b.

For purpose of comparison we normalize time so that all countries share a common onset
of the demo-economic transition. At time t = 0 the countries experience a permanent shock
of productivity growth towards gA = 0.005. The new steady state of stagnation would be
at gL = 0.0317 and does not exists for all three countries. Thus, every country undergoes a
demographic transition with fundamental child survival converging towards π = a. Eventually
all countries display the fertility rate, child expenditure, savings rate, and income growth rate
implied by the U.S. calibration. Their ways taken towards this balanced growth path, however,
are different.

Consider first the geographically favorably located country represented by b = 0.004 and solid
lines in Figure 5. Driven by technological progress and human capital accumulation the economy

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