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Two‐Sector Stochastic Growth Models

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  • P.M. HARTLEY
  • L.C.G. ROGERS

Abstract

This paper develops the study of two‐sector growth models of the form introduced by Arrow and Kurz (1970). We extend their deterministic model by allowing the population process to become random and by allowing the population to choose their level of effort. We find that under suitable conditions the government is able to tax and borrow in such as way as to induce the private sector to invest and consume along the path which the government considers optimal. Moreover, we also find that in some important cases the model can be solved explicitly in closed form, to the extent that we can write down expressions for tax rates and interest rates. This leads to new one‐factor interest rate models, with related taxation policies; numerical examples show very reasonable behaviour.

Suggested Citation

  • P.M. Hartley & L.C.G. Rogers, 2005. "Two‐Sector Stochastic Growth Models," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 322-351, December.
    • Handle: RePEc:bla:ausecp:v:44:y:2005:i:4:p:322-351
    DOI: 10.1111/j.1467-8454.2005.00272.x
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    References listed on IDEAS

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    1. Fisher, Walter H & Turnovsky, Stephen J, 1998. "Public Investment, Congestion, and Private Capital Accumulation," Economic Journal, Royal Economic Society, vol. 108(447), pages 399-413, March.
    2. Lucien Foldes, 1978. "Optimal Saving and Risk in Continuous Time," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 39-65.
    3. Thomas Christiaans, 2001. "Economic Growth, the Mathematical Pendulum, and a Golden Rule of Thumb," Volkswirtschaftliche Diskussionsbeiträge 94-01, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
    4. Edward F. Denison, 1961. "United States Economic Growth," The Journal of Business, University of Chicago Press, vol. 35, pages 109-109.
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    Cited by:

    1. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
    2. Reiß, Markus & Bethmann, Dirk, 2003. "Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth," SFB 373 Discussion Papers 2003,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Jaime Casassus & Pierre Collin-Dufresne & Bryan R. Routledge, 2005. "Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology," NBER Working Papers 11864, National Bureau of Economic Research, Inc.

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