Application of Partial Derivatives in Marginal Analysis of Economic Functions

Abstract

These applications of the partial derivative to the marginal analysis of economic functions demonstrate the role of the partial derivative in economic reasoning analysis. They are more concerned with the examination of the economic variables' impact on outcomes with other variables as constants. The article presents a relatively brief history of the concept, attributing credit to work by the great mathematicians Euler, Lagrange, and Leibniz. The a priori argument presented in the article constitutes the basis upon which the operations of addition, subtraction, multiplication, and division in arithmetic are performed on one unit of money in microeconomics. Microeconomics makes use of economics to compare marginal costs and marginal benefits generated through an additional unit of activity. Partial derivatives make it possible to identify the marginal productivity of factor of production as well as factor savings. The marginal utility hypothesis is also tested out to prove how the consumers optimize their satisfaction through spending on certain products and services. The use of mathematical optimization, the article provides a proper demonstrative example of using the method of partial derivatives of derivative functions to maximizing profit in a specific set of relevant situations. Partial derivatives are an important tool of marginal analysis, contributing significantly to increasing the efficiency and profitability of the economy. CZU: 330.4:338.3; JEL: C02, C30