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. 1

Economics 331b Malthusian Economics 2

3 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: ∂ 2 Y/∂K 2 <0; ∂ 2 Y/∂L 2 <0

The simplest Malthusian model Production function: (1) Y t = F(L t ) (1M) Y t = F(L t ) = 1 + ln 2 (L t ) Where L = population, B = births, D = deaths, w t = wage rate. Income: Population dynamics (3) and subsistence assumption (4): 4

Demographic transition G.T. Miller, Environmental Science 5

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: 6

7 L MPL, Real wage (w) MPL Neoclassical distribution of output/income w* S short-run S longrun MPL’

Malthus with continuous growth Assume Cobb-Douglas production function: This is the major reservation to the Malthusian population model: technological change can outstrip population growth even in the subsistence version. 8

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–