Fogel 1994a 1994b % 56% 95% = % 198% = % 2. 1 /190-1 = % Fogel 1987

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1 " Ramsey - Lee 1981 Richards 1984 Fogel 1992 Fogel 1991 Fogel and Flout 1994 Fogel 1994a 1994b * wangdihai@ fudan. edu. cn 11&ZD SHKXZD004 B

2 Fogel 1994a 1994b % 56% 95% = % 198% = % 2. 1 /190-1 = % Fogel a Sohn % 1 Baumol 1967 van Zon & Muysken 2001 Boumal 1967 van Zon & Muyskey Strauss & Thomas 1998 Grossman 1972

3 Chakraborty 2004 Bunzel & Qiao 2005 OLG Hemmi et al Sachs 2001 p

4 u. β 0 1 u c t e - βt dt t = 0 u ' > 0 u < 0 y = f k hl y k h l l 1 f 2 Strauss & Thomas 1998 Bloom et al Howitt 2005 Kalemli-Ozcan et al Weil 2007 Barro 1996 van Zon & Muysken Weil 2007 Fogel f h > 0 f k > 0 f hh < 0 f kk < 0 f kk f hh > f 2 hk h k Fogel 1994a 1994b Strauss & Thomas Grossman

5 1972 Fogel 1994a 1994b Strauss & Thomas h = h c h' c 0 h c 0 h c c - > 0 c - h c c c - h c c > c - h' c > 0 c c - h' c = 0 3 k = f k h c - δk - c δ 6 f k h c - δk c k max c k u c t e - βt dt s. t. t = 0 k = f k h c - c - δk k 0 H = u c + λ f k h c - c - δk λ limλke - βt = 0 t λ = u' c + λf h k h c h' c λ = λ β + δ - f k k h c c t k t 1 < f h k h c h' c c t k t 2 8 Ramsey

6 8 λ λ c k λ = u' c / 1 - f h k h c h' c f h k h c h' c h' c 1 - f h k h c h' c λ f h k h c h' c u' c 10 1 f h k h c h' c λ c = u cc 1 - f h k h c h' c + u c f hh k h c h' c 2 + f h k h c h c < 0 [ 1 - f h k h c h' c ] 2 λ k = u c f hk k h c h' c / 12 [ 1 - f h k h c h' c ] 2 > c = - ( λ / λ ) [ c f k k h c - δ - β] - ( λ k / λ ) [ c f k h c - c - δk] c = k = 0 f k h c - c - δk = 0 f k k h c - δ - β = c * k * βh' c * f kh k * h c * f h k * h c * h' c * f kk k * h c * < 0 17 c * k * 1 148

7 y = f k h G k A α h A θ A / A = θ G k A α h G ωk ωa α h = ωg k A α h ω > 0 3 2' G k > 0 G h > 0 G kk < 0 G hh G 0 h = G k 0 = 0 limg i x 1 x 2 = + lim x i 0 2' 18 < 0 G kk G hh > G 2 hk 3' x i + G i x 1 x 2 = 0 i = y^ = y / A α h = G k / A α h 1 g k^ A α h k^ k / A α h g k^ g 0 = 0 limg x = + g' 0 = + limg' x = 0 x g k^ - c^ - δk^ g k k^ = δ + β 2' 3' x 19 3 = ' 3' k^ * c^ * k^ * 2 2' 3' c^ * h^ * h' c * < h c * / c * ε hc c * h' c * / h c * < 1 22 k^ * c^ * h^ * k^ * c^ * h^ * 2 2 σ h ωc = ω σ h c h 0 = 0 h' c 0 h c 0 lim h' c = + lim h' c = 0 c 0 + c + OE 1 5' 珓 k k / A α ~ c c / A α 珘 h h / A ασ k 珓 / 珘 h = k^ c ~ / 珘 h = c^ 珘 h = h c / A ασ = h c / A α = h c ~ 3 5' 3 2' 3' 3 5' h' c k 珓 * 珘 h * c ~ *

8 c ~ / 珘 h c^ * OEB 珘 h = h c ~ 2 c ~ / 珘 h c^ * 珘 h * c ~ * OE 珘 h * c ~ * OEB 1 k 珓 * 珘 h * c ~ * k 珓 * 珘 h * c ~ * k 珓 * 珘 h * c ~ * k k = k珓 k 珓 + α A A = αθ c c = 珓 c c 珓 + α A A = αθ h h = 珘 h 珘 h + ασ A A = ασθ θ 2' x y = y / y = αε yh A / A + ε yh h / h + ε yk k / k = αθ / ( ) ε yh ε yk ε yh + ε yk = van Zon & Muysken Fogel 1994a 1994b % θ > 0 23 x hy = ε yh h 23 / h / ( y / y ) = ε yh σ 24 x ky = ε yk k / k / y ( ) / y = ε yk 25 x solow = [ αε yh A / A + ε yh h / h ] / ( y / y ) = ε yh 26 x hs = ε yh h / h / [ αε yh A / A + ε yh h / h ] = σ σ ε yk 1 /3 2 /3 σ 3 /

9 50% 1 x hy 1 /2 σ 3 /4 x hs 3 /4 Fogel 1994b / BMR BMR Fogel 1994b p. 6 0 c > c h = h c h = 0 h' c 0 - h c 0 lim c c - + h' c = + lim h' c = 0 c + c ' 3' h h' -1 1 / c^ * > h' -1 1 / c^ * / c^ * 28 0 h' - 1 c^ * E 1 E 2 c ~ / 珘 h c^ * E 1 BE 2 珘 h = h c ~ BE 2 B E 1 E 2 B c ~ 1 h' c ~ 1 = 1 / c^ * c ~ 1 = h' -1 1 / c^ * 2 c ~ / 珘 h E 1 1 σ Solow /8 ε yk 1 /8 ε yh 7 /8 σ 4 /7 151

10 c^ * c ~ * 珘 h * E 1 E 2 c ~ * 珘 h * E 1 BE 2 2 h c ~ 1 > c ~ 1 / c^ * h h' -1 1 / c^ * > h' -1 1 / c^ * / c^ * E 1 BE 2 E 1 E 2 2 c ~ * l E 1 OE 2 E 1 E 2 h' c ~ * l < h c ~ * l / c ~ * l E 2 c ~ * h 2 h' c ~ * h < h c ~ * h / c ~ * h 2 E c ~ * l c ~ * l 0 E 1 c ~ * l E 1 E 1 E E 1 4 c ~ * l > c ~ 1 c ~ * l c * l = c ~ * l A α = c ~ * l A 0 e α gt A Romer Lucas 1988 E

11 c ~ * l 4 E 1 E 1 E 1 E 1 4 E a 1994b 2002 Baumol 1967 van Zon & Muysken Fogel 1994a 1994b Baumol 1967 van Zon & Muysken

12 van Zon & Muysken 2001 Arrow-Romer Arrow-Romer Baumol W. J Macroeconomics of Unbalanced Growth the Anatomy of Urban Crisis American Economic Review Barro R. J Health and Economic Growth Paper Presented at the Senior Policy Seminar on Health human Capital and Economic Growth Theory Evidence and Policies Pan American Health Organization and Inter-American Development Bank Washington DC. Bloom D. E. D. Canning and J. Sevilla 2004 The Effect of Health on Economic Growth A production Function Approach World Development Bunzel H. and X. Qiao 2005 Endogenous Lifetime and Economic Growth Revisited Economics Bulletin Chakraborty S Endogenous Lifetime and Economic Growth Journal of Economic Theory Fogel R. W Biomedical Approaches to the Estimation and Interpretation of Secular Trends in Equity Morbidity Mortality and Labor Productivity in Europe Unpublished manuscript University of Chicago. Fogel R. W Second Thoughts on the European Escape from Hunger Famines Chronic Malnutrition and Mortality in S. R. Osmani ed. Nutrition and poverty Oxford Clarendon Fogel R. W. 1994a Economic Growth Population Theory and Physiology The Bearing of Long-term Processes on the Making of Economic Policy American Economic Review

13 Fogel R. W. 1994b The Relevance of Malthus for the Study of Mortality Today Long-run Influences on Health Mortality Labor Force Participation and Population Growth NBER working paper h0054. Fogel R. W Nutrition Physiological Capital and Economic Growth paper presented at the Senior Policy Seminar on Health human Capital and Economic Growth Theory Evidence and Policies Pan American Health Organization and Inter-American Development Bank Washington DC. Fogel R. W. and R. Floud 1994 Nutrition and Mortality in France Britain and the United States Unpublished manuscript University of Chicago. Grossman M The Demand for Health A Theoretical and Empirical Investigation NBER Occasional Paper 119 Columbia University Press. Hemmi N. K. Tabata and K. Futagami 2006 The Long-term Care Problem Precautionary Saving and Economic Growth Journal of Macroeconomics In Press Corrected Proof Available online 22 December Howitt P Health Human Capital and Economic Growth In Health and Economic Growth Findings and Policy Implications edited by G. Lopez-Casasnovas B. Rivera and L. Currais. Cambridge MA MIT Press Kalemli-Ozcan S. H. E. Ryder and D. N. Weil 2000 Mortality Decline Human Capital Investment and Economic Growth Journal of Development Economics Lucas R. E On the Mechanics of Economic Development Journal of Monetary Economics Richards T Weather Nutrition and the Economy The Analysis of Short Run Fluctuations in Births Deaths and Marriages France in T. Bengtsson G. Fridlizius and R. Ohlsson eds. Pre-industrial Population Change Stockholm Almquist and Wiksell Romer P. M Increasing Returns and Long-Run Growth Journal of Political Economy Romer P. M Endogenous Technological Change Journal of Political Economy 98 5 Part II S71 S102. Sachs J. D Macroeconomics and Health Investing in Health for Economic Development Report of the Commission on Macroeconomics and Health Presented to Gro Harlem Brundtland Director-General of the World Health Organization on 20 December Sohn B Health Nutrition and Economic Growth Ph. D. dissertation Brown University. Solow R. M. Technical Change and the Aggregate Production Function Review of Economics and Statistics Strauss J. and D. Thomas 1998 Health Nutrition and Economic Development Journal of Economic Literature van Zon A. H. and J. Muysken 2001 Health and Endogenous Growth Journal of Health Economics van Zon A. H. and J. Muysken 2003 Health as a Principal Determinant of Economic Growth Working paper MERIT- Infonomics Research Memorandum. Weil D. N Accounting for the Effect of Health on Economic Growth Quarterly Journal of Economics Health Human Capital Economic Growth and Poverty Trap Wang Dihai School of Economics Fudan University Abstract Based on Fogel s research this paper studies the relationship between capital accumulation and consumption and discusses the effect of health on economic growth in an extended Ramsey model with assumption that consumption not only bringing agents utility but increasing agents health. The paper has two important features 1 treading health as a simple function of consumption which allows us to study health and growth in an aggregate macroeconomic model 2 the existence of multiple equilibria of capital stock health and consumption which is highly relevant to the reality-rich countries may end up with higher capital better health and higher consumption than poor countries. Key Words Health Human Capital Consumption Economic Growth Poverty Trap JEL Classification D99 E21 I12 155

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<4D6963726F736F667420576F7264202D20A661B0ECAE74B2A7AABAA4A4B0EAB941A7F8B0F2C2A6B1D0A87C2E646F63> Hong Kong Teachers Centre Journal 香港教師心報, Vol. 2 Hong Kong Teachers Centre 2004 地域差異的中國農村基礎教育發展與香港的教育投資援助容萬城香港浸會大學教育學系教育經濟學者們重視教育的經濟價值, 在眾多的