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Leibnitz Integral Rule and Its Application to the Business Firm's Longevity Problem

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  • James P. Gander

Abstract

The paper takes the Leibnitz Integral Rule (LIR) under variable integration limits and demonstrates how it can be applied to a business firm's dynamic problem of determining its optimum level of investment activity, when the longevity (life span) of the investment is itself a variable determined by the level of investment. Usually, the longevity of an investment is taken as given and fixed. Here, the level of investment activity has a dual effect, determining not only the longevity of the investment, but also the firm's net profit flow (which over the life span of the investment determines the firm's stock of wealth). The chosen application is the investment needed to create and maintain the salesperson-buyer business relationship involving the sale of a given product. The demonstration shows the assumptions needed to fit the LIR to the problem in order to make the fit tractable. The need for empirical research on the form of the longevity-investment function is also discussed.

Suggested Citation

  • James P. Gander, 2020. "Leibnitz Integral Rule and Its Application to the Business Firm's Longevity Problem," Working Paper Series, Department of Economics, University of Utah 2020_01, University of Utah, Department of Economics.
    • Handle: RePEc:uta:papers:2020_01
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    File URL: https://economics.utah.edu/research/publications/2020_01.pdf
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    More about this item

    Keywords

    Leibnitz Integral Rule; Variable Integration Limits; Net Profit Flow; Level of Investment Activity; Dual Effect of Investment; and Longevity-Investment Function.;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • H8 - Public Economics - - Miscellaneous Issues
    • Z0 - Other Special Topics - - General
    • K16 - Law and Economics - - Basic Areas of Law - - - Election Law
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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