Demand and supply are fundamental concepts in microeconomics that influence market decisions. This article aims to explore the application of mathematical models in explaining the interaction between demand and supply in the market for goods and services. Through an economic mathematics approach, we analyze the demand and supply functions, as well as the application of market equilibrium using calculus techniques and function analysis. The proposed mathematical model focuses on how price and quantity are determined in competitive markets, along with the impact of external factors such as consumer income, related goods prices, and production costs. This study also examines applications in economic policy-making to balance the market.