Economics 331b Spring 2011 Tentative Course Topics. Population dynamics and Malthus’s theory Economics of exhaustible resources Energy policy Discounting Geosciences Impacts of climate change Cost of reducing emissions Integrated assessment climate-economic models Decision making under uncertainty 1

Requirements Course requirements are the following: One term paper at end of course (15 pages) A midterm examination in week 7 or 8 A 3-hour final examination No textbook. All readings are electronic. Be prepared for class. 2

Meeting times Generally, lectures are on Monday and Wednesday. Fridays will be sections, occasional lectures, special topics. You must be available on Fridays to take the course. 3

Prerequisites We will use the following all the time: -Growth theory (neoclassical and advanced) -Theory of externalities -Core micro -Calculus (multivariate, simple integral, logs, simple differential equations, Lagrangeans, NO matrix algebra) Note: you should have access to a textbook on intermediate macro and intermediate micro. 4

First two weeks: The “population problem” -Basics of demography -Malthusian theories -Kremer’s technological story -The “aging society” and its challenges 5

Basics of demography -Birth rates -Mortality rates -Survival rates -Life expectancy -Support ratio 6

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Issues Raised in Malthusian models What are the dynamics of human population growth? What is the demographic transition? The interesting case of a low-level trap, and how to get out of it (a generic multiple equilibrium like bank panics). Are humans doomed to return to the stone age because of resource exhaustion? Why do some people think this is all irrelevant because the problem is population decline and an aging population. 8

Two Views of the Demographic Fate of the World 1.The Malthusian view – population filling up the world. 2.The Aging Society What is your view? 9

10 (1) Malthusian

11 (2) Geezertown

Economics 331b Population dynamics in economics 12

Schedule Wednesday 12: Malthus Friday14: Cohen Monday 17: no class Wednesday 19: Solow model with demography; tipping points Friday 21: Kremer model 13

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. 14

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. 4.Modern demography: With declining populations and low mortality rate, growth fiscal burdens and declining innovation. 15

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.] 16

17 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 ; T t ) Where L = population, T = land (terra), w t = wage rate. Income = wages: Population dynamics (3) and subsistence assumption (4): 18

n (population growth) Wage rate (w) 0 w* (Malthusian subsistence wage) n=n[w] 19

Dynamics 1. Long-run equilibrium when technology is constant: (5) L = L* → 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: 20

21 L Real wage (w) MPL 1 Malthus in the neoclassical production model L1*L1* w* S

22 L Real wage (w) MPL 1 Malthus in the neoclassical production model L1*L1* w* L2*L2* MPL 2 S

Demographic transition G.T. Miller, Environmental Science 23

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. 24

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–

Agenda for today The idea of carrying capacity Cohen’s description Link to Malthus 26

Background on carrying capacity Originates in range/wildlife management. Populations characteristically increase in size in a sigmoid or S- shaped fashion. When a few individuals are introduced into, or enter, an unoccupied area population growth is slow at first..., then becomes very rapid, increasing in exponential or compound interest fashion..., and finally slows down as the environmental resistance increases... until a more or less equilibrium level is reached around which the population size fluctuates more or less irregularly according to the constancy or variability of the environment. The upper level beyond which no major increase can occur (assuming no major changes in environment) represents the upper asymptote of the S-shaped curve and has been aptly called the “carrying capacity” or the saturation level. (Odum, Fundamentals of Ecology) 27

Ehrlichs on human populations The key to understanding overpopulation is not population density but the numbers of people in an area relative to its resources and the capacity of the environment to sustain human activities; that is, to the area’s carrying capacity. When is an area overpopulated? When its population can’t be maintained without rapidly depleting nonrenewable resources (or converting renewable resources into nonrenewable ones) and without degrading the capacity of the environment to support the population. In short, if the long-term carrying capacity of an area is clearly being degraded by its current human occupants, that area is overpopulated. By this standard, the entire planet and virtually every nation is already vastly overpopulated. (Ehrlich and Ehrlich The population explosion. ) 28

Logistic curve Idea is that there is some maximum population, K. Actual approaches as a sigmoid or logistics curve: Where does K come from? Is it static or dynamic? Is r always positive? How do r and K respond to changes in technology? 29

Carrying Capacity Demographers have sometimes assumed this applies to the upper limit on human populations that the earth can support. (maximum supportable human population). Estimates of maximum possible population: 30 Source: J. Cohen, “Population Growth…,” Science, 1995.

Alternative methods for estimating carrying capacity 1.Assume a maximum population density 2.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] 31

Carrying Capacity from Cohen Basic idea is that there is an upper limit on the population that the earth can support. This is Cohen’s interpretation of Malthus with dynamic c.c.: What is economic interpretation here? [This is the art in economic science!] One possibility is the Z = maximum L at subsistence wages, which would be MPL(K)=w*, or in C-D framework: Which means that carrying capacity grows at 32

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 33

Verdict on carrying capacity My economist’s take on this: 1.Useful only in very limited environment (fruit flies in a jar). 2.Particularly limited for human populations: -Because it depends so crucially on technologies -Because human population growth does not respond mechanically and in Malthusian manner to income/resources. 34

Growth dynamics in neoclassical model* Major assumptions of standard model 1. Full employment, flexible prices, perfect competition, closed economy 2. Production function: Y = F(K, L) = LF(K/L,1) =Lf(k) 3. Capital accumulation: 4. Labor supply: * For those who are rusty on the neoclassical model, see handout as well as chapters from Mankiw on the course web site. 35

36 k y = Y/L y = f(k) (n+δ)k y* i* = (I/Y)* k* i = sf(k)