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Algebraic Optimization: Marginal Analysis without Calculus

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  • Joseph G. Eisenhauer

Abstract

Teaching students to conduct marginal analysis before they have studied calculus is a major challenge in introductory economics courses. This paper offers a simple algebraic approach to optimization that allows students to extract explicit marginal revenue and marginal cost functions from quadratic total revenue and total cost functions. For first- or second-degree polynomials, the algebraic results are identical to those derived from differential calculus. The technique offers students a deeper understanding of the profit maximization process than can be obtained from spreadsheets and other conventional teaching methods. The resulting functions can be used to develop related insights regarding issues such as deadweight loss and competitive market adjustments. Numerical examples of monopoly and perfect competition are used to illustrate the algebraic optimization technique.

Suggested Citation

  • Joseph G. Eisenhauer, 2018. "Algebraic Optimization: Marginal Analysis without Calculus," Journal for Economic Educators, Middle Tennessee State University, Business and Economic Research Center, vol. 18(1), pages 16-27, Spring.
    • Handle: RePEc:mts:jrnlee:v:18:y:2018:i:1:p:16-27
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    File URL: http://capone.mtsu.edu/jee/2018/pp16-27MS218.pdf
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    References listed on IDEAS

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    1. Lewis Davis, 2014. "How to Generate Good Profit Maximization Problems," The Journal of Economic Education, Taylor & Francis Journals, vol. 45(3), pages 183-190, September.
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    More about this item

    Keywords

    algebraic optimization; marginal analysis; profit maximization;
    All these keywords.

    JEL classification:

    • A22 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Undergraduate
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General

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