ECONOMIC DYNAMICS AND FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS

Vasileios Zikos

Chapter 8 in Essential Mathematics for Economics:A Student's Guide to Key Mathematical Techniques, 2026, pp 133-159 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After completing this chapter, students will be able to:Understand the concept of a first-order linear differential equation.Solve differential equations with a constant coefficient and a constant term.Solve differential equations with a variable coefficient and a variable term.Verify the solutions of different types of differential equations.Appreciate how differential equations can be useful in understanding the dynamics of certain economic variables, including market prices.In Chapter 7, we developed tools for economic analysis related to integral calculus. We are now ready to tackle problems involving differential equations. In this chapter, we will study the time path of a variable to determine whether, given sufficient time, it converges to a specific equilibrium value. Unlike Chapters 5 and 6, where we focused on static optimization problems, we will not assume that an equilibrium exists a priori. Instead, we will begin by considering a pattern of change that describes the behavior of a variable over time. We will then examine the adjustment process toward a specific value and determine whether an equilibrium exists.

Keywords: Microeconomics; Applied Microeconomics; Optimization; First-order Conditions; Second-order Conditions; Equality Constraints; Inequality Constraints; Concavity; Convexity; Matrix Algebra; Determinants; Differential Calculus; Integral Calculus; First-order Linear Differential Equations; Utility Maximization; Profit Maximization; Research Applications (search for similar items in EconPapers)
JEL-codes: C01 C02 C61 D00 (search for similar items in EconPapers)
Date: 2026
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