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Optimal consumption and investment in the economy with infinite number of consumption goods


  • Kliber, Pawel


In the article we present some extension for the classical problem of dynamic investment optimization. We take the neoclassical model of growth with one product and many consumption goods. The number of consumption goods can be infinite and the consumption bundle is defined on some abstract, measurable space. The instantaneous social utility of consumption is measured as the integral of individual utilities of the consumption goods. The process of transforming product into consumption goods is described by another measure. The performance of the economy is measured by current value of the total utility in some planning horizon. We show that the problem of choosing optimal consumption paths for each good can be decomposed into 1) problem of choosing optimal aggregate consumption, which can be solved using standard methods of optimal control theory, 2) problem of distribution aggregate consumption into consumption of specific goods.

Suggested Citation

  • Kliber, Pawel, 2014. "Optimal consumption and investment in the economy with infinite number of consumption goods," MPRA Paper 53636, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:53636

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    References listed on IDEAS

    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    2. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, August.
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    More about this item


    optimal growth; golden rule; optimal control; multiple consumption goods; optimal consumption plans;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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