Differential calculus for optimizing costs, revenues and profits in jipijapa's entrepreneurial ventures

Abstract

This review aimed to examine how differential calculus can formalize production and pricing decisions in micro-enterprises of the Jipijapa canton, Manabí province. A qualitative approach with exploratory and descriptive scope was adopted through a systematized documentary review of thirteen articles published between 2021 and 2026 in indexed journals, selected according to thematic relevance, verifiability of the digital identifier and proximity to the Ecuadorian context. The literature was organized along three axes: mathematical optimization applied to management, financial determinants of Ecuadorian micro-enterprise profitability, and conditions of the Jipijapa entrepreneurial ecosystem. On that basis, a quadratic model of revenue, cost and profit was built, solved through the first-order condition and verified with the second-order condition, and illustrated with a hypothetical case of a prepared-food business. The exercise yielded an optimal quantity of seven hundred monthly units, a price of 3.60 dollars and a maximum profit of 696 dollars. An increase in fixed cost reduced profit without shifting the optimal output level, whereas a rise in the variable input cost did shift it. Marginal analysis offers local micro-enterprises a verifiable decision criterion with low implementation cost.