1. Economics 331b Carrying capacity, Malthusian traps, and other stuff 1

2. Heavy energy/environment hitters in the new administration 2 Energy: Steven Chu Environment: Carol Browner Regulation: Cass Sunstein Budget/economics: Peter Orszag Economics and everything: Larry Summers

3. Carrying Capacity Basic idea from ecology: the maximum number of individuals that the environmental resources of a given region can support. Basic idea is that there is an upper limit on the population that the earth can support. (maximum supportable human population). 3 Source: J. Cohen, “Population Growth…,” Science, 1995.

4. Carrying Capacity 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 4

5. Economic interpretation of carrying capacity theories Carrying capacity is an interesting but not obviously interesting economic concept. 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 5

6. 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. 6

7. Vested interests or entrenched ideas? “The ideas of economists and political philosophers, both when they are right and when they are wrong, are more powerful than is commonly understood…. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back. The power of vested interests is vastly exaggerated compared with the gradual encroachment of ideas…. Sooner or later, it is ideas, not vested interests, which are dangerous for good or evil.” [J.M. Keynes, The General Theory] 7

8. Growth dynamics with the demographic transition 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: Now add endogenous population: 4M. Population growth: n = n(y) = n[f(k)] ; demographic transition This leads to dynamic equation (set δ = 0 for expository simplicity) 8

9. Demographic transition G.T. Miller, Environmental Science 9

10. Current demography 10

11. n (population growth) Per capita income (y) 0 y (Malthusian) n=n[f(k)] 11 Unclear future trend of population in high-income countries

12. k y = Y/L y = f(k) k*** i = sf(k) k**k* Low-level trap n[f(k)]k 12 High-level equilibrium

13. k k***k**k* 13 “TIPPING POINT”

14. Other examples of traps and tipping points In social systems Bank panics and the U.S. economy of 2007-2009 Steroid equilibrium Cheating equilibrium Epidemics in public health What are examples of moving from high-level to low-level? In climate systems Greenland Ice Sheet and West Antarctic Ice Sheet Permafrost melt North Atlantic Deepwater Circulation Very interesting policy implications of tipping/trap systems 14

15. Hysteresis Loops When you have tipping points, these often lead to “hysteresis loops.” These are situations of “path dependence” or where “history matters.” Examples: - In low level Malthusian trap, effect of saving rate will depend upon which equilibrium you are in. - In climate system, ice-sheet equilibrium will depend upon whether in warming or cooling globe. 15

16. 16 Hysteresis loops and Tipping Points for Ice Sheets 16 Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,” Computers & Geosciences, April 2006, Pages 316-325

17. k y = Y/L y = f(k) k*** i = sf(k) The Big Push {n[f(k)]+δ}k 17