Geography, Health, and Demo-Economic Development

dynamics are then determined by the following two-dimensional system.⁸

yt+1 = α(1 - β)(1 + gA) [1 + gL(yt)]^α-1 h(yt)^αxt ,                   (14a)

xt+1 = (1 + gA)(1 + gL(yt))^α-1xt .                                  (14b)

6. Stagnation

From (14) follows that any equilibrium fulfils

дь(у) = дь ≡ (1 + gA)^1/(1-a) - 1 .                            (15)

At an equilibrium, the positive impact of technological progress is neutralized by the negative
impact of population growth (through decreasing returns to scale with respect to the reproducible
factors). For existence of this Malthusian-Iike equilibrium the fertility rate supporting дь* has
to lie in the feasible range of parental preferences, i.e. g_L* ≤ maxg_L(y). Inspection of (15)
shows that existence of an equilibrium becomes increasingly unlikely for any set of preference
parameters when technological progress grows faster or when arable land becomes a less essential
factor in production (i.e. α rises).

Consider, for example, an economy populated by parents with preferences as those underlying
the income correlations in Figure 4 (dotted lines). These parents generate a maximum population
growth rate of 2.8 percent annually implying that an equilibrium exists if (1 + gA)^1/(1-a) — 1 ≤
0.028. For example, if agricultural progress grows at 0.5 percent p.a., an equilibrium exists
for α < 0.82. If gA is rises to one percent per year, existence requires α < 0.64. In other
words, economies particularly susceptible for stagnation are characterized by low agricultural
productivity growth and high dependency on arable land.

Recall from the analysis of Section 3 and Figures 3 and 4 that population growth is higher
in unfavorable locations. Thus, for given parameters of preference and technology, existence
of equilibrium is more likely for unfavorably located economies. For example, with gA = 0.5
percent and α < 0.82 the equilibrium does not exist for the U.S. calibration of Figure 4 (solid
lines) while it exists for the tropically located country (dashed lines).

⁸Because h is bounded from above and below through household behavior, subsequent results are robust for any
positive function f (h). Furthermore, we could introduce technological progress as being determined by the skill
level of the working population -as in Galor and Weil (2000) and Strulik (2004) - without change in qualitative
results.

15

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