RESEARCH APPLICATIONS

Vasileios Zikos

Chapter 9 in Essential Mathematics for Economics:A Student's Guide to Key Mathematical Techniques, 2026, pp 161-196 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After completing this chapter, students will be able to:Understand how the techniques of partial differentiation, total differentiation, and unconstrained optimization can be used in research applications.Appreciate the applications of mathematics in both theoretical and empirical research in economics.We have seen that the techniques of differentiation and optimization are useful for analyzing the decisions of economic agents, such as consumers and firms. In this chapter, we will explore how these techniques can be applied in two settings from my own research. The first example comes from the field of industrial organization, which uses concepts from game theory to study strategic interactions between agents. These agents can be thought of as players in a game that involves one or more stages of strategic interaction. A player’s optimal strategy at any stage depends on the optimal strategies of the other players. As we will see, the study of such interactions relies primarily on two techniques: differentiation and optimization…

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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