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The Malthusian Model
After reviewing the key development and growth facts, it is clear that we need a theory
that can generate a period of constant living standards, followed by a transition period
with modest increases in the living standard, followed by a period of modern economic
growth.
We already have a model that can account for the period of modern economic
growth; the Solow Model with technological change generates constant growth of per
capita output.
It is true that the Solow Model can generate a steady state with a constant
level of per capita output.
This is the Solow Model absent technological change.
One
possibility is to interpret the pre1700 era of constant livings standards as the steady state
of the Solow Model absent technological change.
The problem with this interpretation is
that technology was not stagnant before 1700.
Joel Mokyr a noted economic historian at
Northwestern University has documented in his book The Lever of Riches that numerous
and important technological innovations occurred well before 1700.
In light of the historical record on technological change, we proceed to alternative
theory and model of this pre1700 era.
This is the Malthusian model that goes back to
David Ricardo and the classical economists.
There are two key components of the
model.
The first is a production function with a fixed factor of production. By fixed, we
mean that its supply cannot be changed over time.
Labor and capital are not fixed
factors as both can be increased over time.
In the Malthusian model, the fixed factor is
land. The second key component is a population growth function that is an increasing
function of per capita consumption.
These two elements ensure that the steady state is
characterized by a constant living standard even when there is technological change.
We first proceed by studying the Malthusian model with no capital and absent
technological change to help develop intuition for the model.
We solve the equilibrium
of the model graphically. We then follow this up with an algebraic study of the
Malthusian model with capital accumulation and exogenous technological change.
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Figure (1) below is a plot of per capita income from 3000 BC to 2000 AD. The
feature of the plot is that the standard of living displayed no trend for the first 4800 years
(this period includes Malthusian and PostMalthusian regimes) and then exploded
subsequent to 1800 (Modern regime). These notes are concerned with a theory of the
period prior to 1800.
Figure 1
I. Model with No Capital or Technological Change
People.
Initially, there are N
0
people alive.
We use N
t
to denote the number of people in
the economy at date t.
People prefer more consumption to less.
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 Fall '08
 Villamil
 Steady State, technological change, per capita consumption

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