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Economics 331b The neoclassical growth model Plus Malthus. Agenda for today. Neoclassical growth model Add Malthus Discuss tipping points. Growth trend, US, 1948-2008. 3. Growth dynamics in neoclassical model*. Major assumptions of standard model
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Economics 331b The neoclassical growth model Plus Malthus
Agenda for today Neoclassical growth model Add Malthus Discuss tipping points
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,
Exoogenous pop growth n (population growth) Wage rate (w) 0
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.
y* y = f(k) y = Y/L (n+δ)k i = sf(k) i* = (I/Y)* k k*
What is the current relationship between income and population growth?
Unclear future trend of population in high-income countries Endogenous pop growth n (population growth) n=n[f(k)] Per capita income (y) 0 y* = (Malthusian or subsistence wages)
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)
y = f(k) n[f(k)]k y = Y/L i = sf(k) k
y = f(k) n[f(k)]k y = Y/L Low-level trap i = sf(k) High-level equilibrium k k* k** k***
“TIPPING POINT” k k* k** k***
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
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.
Hysteresis loops and Tipping Points for Ice Sheets 17 Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,” Computers & Geosciences, April 2006, Pages 316-325
Policy Implications • (Economic development) If you are in a low-level equilibrium, sometimes a “big push” can propel you to the good equilibrium. • (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. • (Climate) Policy needs to ensure that system does not move down the hysteresis loop from which it may be very difficult to return.
The Big Push in Economic Development y = f(k) y = Y/L {n[f(k)]+δ}k i = sf(k) k k***