Sketch of a modeling framework

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Sketch of a modeling framework F ? a LF ß
(e A) (1 ß ) (Food production)   s
LF / L (Definition
of s)   M ? ? LM
(Urban-based manufactures)   m M / L ? ?
( 1 s ) (Per capita manufactures)   d? / dt
? m (Productivity
growth)   n (1/L)dL/dt ? s
(Population growth) Note productivity growth
may allow for diffusion from abroad
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Assume per capita dietary needs are f and that
beyond dietary needs households have zero income
elasticity of demand for food. Assume also that
we begin in a region in which the basic dietary
needs can be met for the entire population.   f
L ? a LF ß (e A) (1 ß )   Thus,   s f
(1/ ß) ? (a/ ß) s (1- ß)/ ß where s e
A / L (arable land in efficiency units,

per
capita)     (1/ s)(ds/dt) (a/ ß) ? ? (s - 1)
(1- ß)/ ß ? s     Depending on initial
conditions, s either approaches 0 (endogenous
growth) or 1 (Malthusian trap)
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The threshold degree of urbanization is t
a ?? / a ?? (1- ß)?   If s gt t
then the economy approaches Malthusian trap If
s lt t then the economy approaches
urban-based endogenous growth     Malthusian
trap is likely under the following
conditions   Low initial technology level ?
Low land per person (A/L) Low efficiency of
land (e.g. tropical ecozone) e Low urban
efficiency (e.g. landlockedness) ? Low degree
of learning by doing ?
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The Transition from Adoption (implementation)
to Innovation High concentration of innovators,
few cases of transition to innovation (exceptiona
l cases include Korea, Taiwan, Singapore,
Israel) Special public institutions play a key
role in the transition