Economics 331b The neoclassical growth model

PlusMalthus

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Agenda for today

Neoclassical growth modelAdd MalthusDiscuss tipping points

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Growth trend, US, 1948-2008

0.0

0.4

0.8

1.2

1.6

2.0

50 55 60 65 70 75 80 85 90 95 00 05

ln(K)ln(Y)ln(hours)

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

/dK dt K sY K

/ n = exogenousL L

; / ; / ;L EL y Y L k K L

n (population growth)

Wage rate (w)

0

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Exoogenous pop growth

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1. Economic dynamicsg(k) = g(K) – g(L) = g(K) – n = sY/K - δ – n = sLf(k)/K - δ – n

Δk = sf(k) – (δ + n)k2. 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.

, ( , )

/ ( )

with equilibrium condition:

( ) ( ) *

Y F K EL F K L

y Y L f k

s f k n k

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k

y = Y/L

y = f(k)

(n+δ)k

y*

i* = (I/Y)*

k*

i = sf(k)

* ( *) ( ) *k k sf k n k

Now introduce better demography

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What is the current relationship between income and population

growth?

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-1

0

1

2

3

4

5 6 7 8 9 10 11

ln per capita income, 2000

Pop

ula

tion

gro

wth

, 200

7 (%

per

yea

r)

n (population growth)

Per capita income (y)

0

y* = (Malthusian or subsistence wages)

n=n[f(k)]

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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)

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( ) [ ( ) ]

with long-run or steady state equilibrium (k*)

0 *

( *) [ ( *) ] *

k sf k n f k k

k k k

sf k n f k k

k

y = Y/L

y = f(k)

i = sf(k)

n[f(k)]k

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* ( *) [ ( *) ] *k k sf k n f k k

k

y = Y/L

y = f(k)

k***

i = sf(k)

k**k*

Low-level trap

n[f(k)]k

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High-level equilibrium

* ( *) [ ( *) ] *k k sf k n f k k

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 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

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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.

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Hysteresis loops and Tipping Points for Ice Sheets

17Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,” Computers & Geosciences, April 2006, Pages 316-325

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.

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k

y = Y/L

y = f(k)

k***

i = sf(k)

The Big Push in Economic Development

{n[f(k)]+δ}k

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