1. Economic Growth, Population, and Human Capital
June 4, 2005
Beijing, China
China Center for Economic Research
Gary S. Becker
University of Chicago

2. GDP per Capita China, France, Japan, Germany, United Kingdom and United States 1820 - 2000
Source: Madison, Angus. The World Economy: Historical Statistics. OECD, 2003.

3. Gross School Enrolment in Secondary and Tertiary Education China 1990, 2001
Secondary Education
48.7
67.2
Tertiary Education
2.9
12.7
Source: World Development Indicators, The World Bank.

4. The China/West European Dichotomy 1–2001 AD
Population
(millions)
Per Capita GDP
(1990 int. $)
GDP
(billions 1990 int. $)
China
West Europe 1
59.6
24.7
450
26.8
11.1
1000 59
25.4
400
26.6
10.2
1300
100
58.4
600
593 60
34.6
1400 72
41.5
676
43.2
28.1
1500
103
57.3
771
61.8
44.2
1820
381
133
1,204
228.6
160.1
1913
437.1
261
552
3,458
241.3
902.3
1950
546.8
304.9
439
4,579
239.9
1,396.2
2001
1,275.4
392.1
3,583
19,256
4,569.8
7,550.3
Source: Madison, Angus. The World Economy: Historical Statistics. OECD, 2003.

5. Malthusian Economy D D’ Income per Capita S I* S D’ D Population N* N’
Population Growth

6. Malthusian Model
ln n(t) = a + b ln w(t)
ln w(t) = α - β ln N(t)
SS: ln n(t) = 0, n* = 1
ln w* = - a/b
ln N* = α/β + a/(bβ)
Dynamics
ln n(t) = ln N(t+1) – ln N(t) = a + b ln w(t)
... ln N(t+1) = a + bα + (1 – bβ) ln N(t)
Since, b, β > 0, 1 – bβ < 1
Stable, although requires also bβ < 2
β << 1, so sufficient if b < 2

7. Total Fertility Rate China, England and Wales, France, Japan, Sweden and United States 1800 - 2000
Sources: Chesnais, Jean Claude. The Demographic Transition. Oxford: Oxford University Press, World Development Indicators, World Bank, The Reader's companion to American history

8. Fertility Rates for Nations with below Replacement Fertility 1970 – 2000
Source: World Development Indicators, The World Bank.

9. Knowledge Revolution: Modern Economy
Per Capita Income Growth
(ΔI) D
ΔI’ S
ΔI* D S
Population N* N’
Population Growth

10. Modern Model
p(t) = ln [N(t+1)/N(t)] = a – b ln[I(t+1)/I(t)] + c(I(t)) ln I(t)
with c(I) → 0 as I → ∞
ln[I(t+1)/I(t)] = α + β ln N(t) + γ ln I(t)
if γ = 0,
SS: p(t) = p* = 0
ln [I(t+1)/I(t)] = g* = a/b
ln N* = (a/bβ) – (α/β)
if γ ≠ 0,
differentiate growth equation at SS
0 = β p* + γ g*
or p* = - γ g*/β < 0 as γ g* > 0
= 0 as γ g* = 0
> 0 as γ g* < 0
a – b g* = p*, or g* = a / (b - γ/β)

11. Stability of Growth
ln N(t+1) – ln N(t) = a – b [α + β ln N(t) + γ ln I(t)] + c ln I(t)
ln N(t+1) = ln N(t) = a – b α + (1-bβ) ln N(t) + (c-bγ) ln I(t)
if c > bγ, force raising population over time
if c = γ ≈ 0
Stability bβ > 0, same as Malthusian
although now have growth in income and change over time in population