Profit Maximization in Monopoly Markets: Economic Optimization Using Derivatives

Abstract

This study examines the system of profit maximization in monopoly markets, focusing on how monopolists determine optimal output and price levels through calculus-based on selecting. The essential problem addressed is the internal output limiting by monopolies, which contrasts with the higher output level observed in competitive markets. Using linear demand and cost functions, the research is applicable first and second order requirements of calculus to derive the profit-maximizing quantity (Q*) and price (P*). Key findings confirm that monopolies produce less than socially optimal quantities, resulting in deadweight loss—the measurement of reduced producer and consumer welfare. The analysis is contextualized with the real-world applications, especially in pharmaceutical and technology markets, where monopolistic structures such as patent-protected drugs, dominant operating systems are prevalent. This research will also contribute to understand monopoly inefficiency by formally conformation the optimal output level through mathematical derivation, strengthening the needs for antitrust regulation to reduce benefit losses.