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A note on the three-sector Cobb–Douglas GDP function


  • Muro, Kazunobu


The GDP function chooses the most efficient point on the production possibility frontier with curved surface. We derive a three-sector Cobb–Douglas GDP function including three goods (agriculture, manufacturing, and services) and three factors (capital, labor, and land). It is very difficult to derive the Stolper–Samuelson theorem in the three-sector version. But we derive it numerically. By applying the empirical factor income share across sectors, we show that an increase in the relative agricultural goods price in terms of manufacturing goods decreases the real interest rate and the wage rate while it increases the land rent. On the other hand, an increase in the relative service price in terms of the manufacturing goods decreases the real interest rate while it increases the wage rate and the land rent. The three-sector Cobb–Douglas GDP function with three factors must be useful for empirical studies in structural change.

Suggested Citation

  • Muro, Kazunobu, 2013. "A note on the three-sector Cobb–Douglas GDP function," Economic Modelling, Elsevier, vol. 31(C), pages 18-21.
  • Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:18-21 DOI: 10.1016/j.econmod.2012.11.008

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    References listed on IDEAS

    1. Piyabha Kongsamut & Sergio Rebelo & Danyang Xie, 2001. "Beyond Balanced Growth," Review of Economic Studies, Oxford University Press, vol. 68(4), pages 869-882.
    2. L. Rachel Ngai & Christopher A. Pissarides, 2007. "Structural Change in a Multisector Model of Growth," American Economic Review, American Economic Association, vol. 97(1), pages 429-443, March.
    3. Daron Acemoglu & Veronica Guerrieri, 2008. "Capital Deepening and Nonbalanced Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 467-498, June.
    4. Echevarria, Cristina, 1997. "Changes in Sectoral Composition Associated with Economic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 431-452, May.
    5. Akos Valentinyi & Berthold Herrendorf, 2008. "Measuring Factor Income Shares at the Sector Level," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 820-835, October.
    6. Francisco J. Buera & Joseph P. Kaboski, 2012. "The Rise of the Service Economy," American Economic Review, American Economic Association, vol. 102(6), pages 2540-2569, October.
    7. Donghoon Lee & Kenneth I. Wolpin, 2006. "Intersectoral Labor Mobility and the Growth of the Service Sector," Econometrica, Econometric Society, vol. 74(1), pages 1-46, January.
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