Economics 331b Population dynamics in economics

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Course logistics

The enrollment in the course is full. You can participate if you received an email from me.

There are always appeals for special cases. There is no waiting list.

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Schedule

Wednesday (today): Malthus and CohenFriday: No class. Nordhaus lecture on Economics of

Climate Change, Yale Climate Institute, 12:00 – 1:15, Kroon Hall

Monday: no classWednesday: Solow model with deomgraphy; tipping

pointsFriday: Kremer model

Presentations: any volunteers for Kremer, demography, or Cohen would be welcome (Wed and Fri of next week)

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Importance of population

Obviously important part of social sciences

In environmental economics, part of the stress on natural systems. Can see in the “Kaya identity”:

Pollution ≡ Pop * (GDP/Pop) * (Pollution/GDP),

This equation is often used for energy, CO2, and other magnitudes.

Warning: It is an identity, not a behavioral equation. It doesn’t explain anything.

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Different world views on population

1. Malthus-Cohen: population bumping against resources.

2. Solow-Demographic transition: Need to make the big push to get out of the low-level Malthusian trap.

3. Kremer: people are bottled up and just waiting to be the next Mozart or Einstein.

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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.

[This theory led to Darwin, social Darwinism, poorhouses, and many other social ideas.]

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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

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:

Population dynamics (3) and subsistence assumption (4):

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(3) / / / / / ( ) t t t t t t t t tL L L t L B L D L g w

/ ( ), ( *) 0, '( ) 0t t tL L g w g w g w (4)

(3) / / / / / ( )t t t t t t t t tL L L t L B L D L g w

(2) /t tw Y L

Demographic transition

G.T. Miller, Environmental Science 9

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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L

MPL, Real wage (w)

MPL

Neoclassical distribution of output/income

w*

Sshort-run

Slongrun

MPL’

Malthus with continuous growth

Assume Cobb-Douglas production function:

This is the major anti-Malthus theorem: Rapid technological change can outstrip population growth even in the subsistence version.

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(6)

(7) ( )

> 0 if T.C. strong enough

t t t

Y A L A t

Y A L

g g g g g w

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, P Ehrlich, The Population Bomb

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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Carrying Capacity

Basic idea from ecology: the maximum number of individuals that the environmental resources of a given region can support.

Demographers have sometimes assumed this applies to the upper limit on human populations that the earth can support. (maximum supportable human population).

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Source: J. Cohen, “Population Growth…,” Science, 1995.

Alternative methods for estimating carrying capacity

1. Just assume a maximum population density2. Extrapolate population trends. 3. Single factor model (e.g., food supply)4. Single factor as function of multiple inputs 5. Multiple factor constraints (P < β water; P < γ food;

…) 6. Multiple dynamic and stochastic constraints (P(t) < β water(t) + ε(t) ; P(t) < γ food(t) +ς(t) ;

…]

[Source: As described in Cohen]

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Carrying Capacity from Cohen

Basic idea is that there is an upper limit on the population that the earth can support.

This is a variant of Malthus as follows:

Not clear how to interpret (9). One possibility is the maximum L at subsistence wages, which would be MPL(Z)=w*, or in C-D framework:

Which means that carrying capacity grows at

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(8) / [ ], where is the earth's carrying capacity.t t t t tL L r Z L Z

(9) , where is a productivity parameter.t tZ L

1/(1 )(10) / * / *t t t tY L w Z A w

(11) [1 / (1 )] [1 / (1 .67)] 3 2 6% per year!!! A Ag g

Economic interpretation of carrying capacity theories

Carrying capacity is a concept foreign to economic demography. Is it a normative concept? A descriptive concept?

As descriptive, it seems related to Malthusian subsistence wage.• Carrying capacity changes over time with technological change.• Basic trends in U.S. and rest of world outside of Africa is that technological shifts

have outweighed diminishing returns. I.e., clear evidence that because of technological change, carrying capacity has increased over time.

As normative, it seems inferior to concept of optimum population.• This would be some social welfare function as U(C, L), maximized over

L• However, introducing L gives serious difficulties to Pareto criterion,

which is central normative criterion of economics

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