Transcript Economics 157b Economic History, Policy, and Theory Short

Malthusian economics
Basic propositions:
1. It may safely be pronounced, therefore, that population, when unchecked, goes on
doubling itself every twenty-five years, or increases in a geometrical ratio.
2. It may be fairly pronounced, therefore, that, considering the present average state
of the earth, the means of subsistence, under circumstances the most favourable to
human industry, could not possibly be made to increase faster than in an
arithmetical ratio.
3. Taking the whole earth … and, supposing the present population equal to a
thousand millions, the human species would increase as the numbers, 1, 2, 4, 8,
16, 32, 64, 128, 256, and subsistence as 1, 2, 3, 4, 5, 6, 7, 8, 9. In two centuries the
population would be to the means of subsistence as 256 to 9 ; in three centuries as
4096 to 13, and in two thousand years the difference would be almost incalculable.
4. In this supposition no limits whatever are placed to the produce of the earth. It may
increase for ever and be greater than any assignable quantity; yet still the power
of population being in every period so much superior, the increase of the human
species can only be kept down to the level of the means of subsistence by the
constant operation of the strong law of necessity, acting as a check upon the
greater power.
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Economics 331b
Malthusian Economics
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Review of basic production theory
Classical production model.
Aggregate production function (for real GDP, Y)
(1) Y = F( K, L)
Standard assumptions: positive marginal product (PMP),
diminishing returns (DR), constant returns to scale (CRTS):
CRTS: mY = F( mK, mL)
PMP: ∂Y/∂K>0; ∂Y/∂L>0
DR: ∂2Y/∂K2<0; ∂2Y/∂L2<0
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The simplest Malthusian model
Production function:
(1)
Yt = F(Lt )
(1M)
Yt = F(Lt ) = 1 + ln2 (Lt)
Where L = population, B = births, D = deaths, wt = wage rate.
Income:
(2)
wt  Y / Lt
Population dynamics (3) and subsistence assumption (4):
(3)
(3)(4)
Lt / Lt   Lt / t  / Lt  Bt / Lt  Dt / Lt  g (wt )
LLt // LLtg(w
L),t / 
t  *)
/ Lt 0, B
/ Lt 0 Dt / Lt  g (wt )
g (w
g t'(w) 
t
t
t
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Demographic transition
G.T. Miller, Environmental Science
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Dynamics
1. Long-run equilibrium when population is constant:
(5) P = P* → w = w* → wages at long run subsistence wages.
2. What happens if productivity increases?
-
If productivity takes a jump, then simply increase P (next
slide)
More complicated if have continuous population growth,
then can have a growth equilibrium.
Even more complicated if have demographic transition:
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MPL, Real wage (w)
Neoclassical distribution of
Sshort-run output/income
Slongrun
w*
MPL’
MPL
L
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Malthus with continuous growth
Assume Cobb-Douglas production function:
(6) Yt  At Lt
(7)
gY  g A   g L  g A   g ( wt )
> 0 if T.C. strong enough
This is the major reservation to the Malthusian population
model: technological change can outstrip population growth
even in the subsistence version.
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Modern Malthusians
Left-wing neo-Malthusians: This school that believes we are
heading to low consumption because we are exhausting our
limited resources (alt., climate change, …). See Limits to
Growth.
Right-wing neo-Malthusians: This school believe that the
“underclass” is breeding us into misery due to overly
generous welfare programs. See Charles Murray, Losing
Ground: American Social Policy 1950–1980.
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