1. Economics 331b The neoclassical growth model Plus Malthus 1

2. Agenda for today Neoclassical growth model Add Malthus Discuss tipping points 2

3. 3 3 Growth trend, US, 1948-2008

4. 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: New variables k = K/L = capital-labor ratio; y = Y/L = output per capita; Also, later define “labor-augmenting technological change,” E = effective labor, 4

5. n (population growth) Wage rate (w) 0 5 Exoogenous pop growth

6. 6 1. Economic dynamics g(k) = g(K) – g(L) = g(K) – n = sY/K - δ – n = sLf(k)/K - δ – n Δk = sf(k) – (δ + n)k 2. In a steady state equilibrium, k is constant, so sf(k*) = (n + δ) k* 3. We can make this a “good” model by introducing technological change (E = efficiency units of labor) 4. Then the model works out nicely and fits the historical growth facts.

7. 7 k y = Y/L y = f(k) (n+δ)k y* i* = (I/Y)* k* i = sf(k)

8. Now introduce better demography 8

9. What is the current relationship between income and population growth? 9

10. n (population growth) Per capita income (y) 0 y* = (Malthusian or subsistence wages) n=n[f(k)] 10 Unclear future trend of population in high-income countries Endogenous pop growth

11. Growth dynamics with the demographic transition Major assumptions of standard model 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) 11

12. k y = Y/L y = f(k) i = sf(k) n[f(k)]k 12

13. k y = Y/L y = f(k) k*** i = sf(k) k**k* Low-level trap n[f(k)]k 13 High-level equilibrium

14. k k***k**k* 14 “TIPPING POINT”

15. Other examples of traps and tipping points In social systems (“good” and “bad” equilibria) Bank panics and the U.S. economy of 2007-2009 Steroid equilibrium in sports Cheating equilibrium (or corruption) 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 15

16. 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. 16

17. 17 Hysteresis loops and Tipping Points for Ice Sheets 17 Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,” Computers & Geosciences, April 2006, Pages 316-325

18. Policy Implications 1.(Economic development) If you are in a low-level equilibrium, sometimes a “big push” can propel you to the good equilibrium. 2.(Finance) Government needs to find ways to ensure (or insure) deposits to prevent a “run on the banks.” This is intellectual rationale for the bank bailout – move to good equilibrium. 3.(Climate) Policy needs to ensure that system does not move down the hysteresis loop from which it may be very difficult to return. 18

19. k y = Y/L y = f(k) k*** i = sf(k) The Big Push in Economic Development {n[f(k)]+δ}k 19