Economics 331b The neoclassical growth model Plus Malthus 1

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

3 3 Growth trend, US,

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

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

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

Now introduce better demography 8

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

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

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

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

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

k k***k**k* 14 “TIPPING POINT”

Other examples of traps and tipping points In social systems (“good” and “bad” equilibria) Bank panics and the U.S. economy of 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

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

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

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