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A Dual Approach to the Derivation of Feedback Demand Functions for Capital-Accumulating Agents

Author

Listed:
  • Bolin, Kristian

    (Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Caputo, Mikael R

    (Dept. of Economics, Univ. of Central Florida)

Abstract

An optimal control model of a consumer is developed that accounts for the consumption of many goods and services, the accumulation of wealth, a state variable that affects instantaneous preferences and wealth accumulation, and contains several canonical models as special cases. Formulas are provided for the feedback consumption functions in terms of certain partial derivatives of a consumer’s lifetime indirect utility function, thereby obviating the need to solve the necessary conditions of Pontryagin or the Hamilton-Jacobi-Bellman equation. The intrinsic qualitative properties of the optimal control model in differential form are derived, and an example of how to implement the results for econometric purposes is provided as well.

Suggested Citation

  • Bolin, Kristian & Caputo, Mikael R, 2024. "A Dual Approach to the Derivation of Feedback Demand Functions for Capital-Accumulating Agents," Working Papers in Economics 843, University of Gothenburg, Department of Economics.
    • Handle: RePEc:hhs:gunwpe:0843
    as

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    capital stock; feedback solutions; HJB equation; optimal control;
    All these keywords.

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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