Introductory Mathematics and Statistics for Islamic Finance, + Website

Chapter 9Optimization Theory

Islamic finance is concerned with maximum and minimum problems known as optimization problems. Resources are costly and scarce, with pressing priorities. Optimization reconciles resource scarcity with pressing priorities. Modern “neoclassical marginalism” represents the culmination of optimization theory in economics and finance. Value theory in economics derives demand functions from consumers' optimizing behavior and supply functions from producers' optimizing behavior. The theory of international trade and comparative advantage is also based on the optimization principle. Optimal allocation of resources requires that each country specializes in a product for which it has a comparative advantage; trade takes place when a country exports its product and imports the product of its trading counterpart. Optimization aims at achieving efficient use of resources—maximizing profits, maximizing utility, exploiting price arbitrage opportunities, and enhancing economic growth. Firms or countries that fail to optimize the use of resources and achieve efficiency fall into decay and have problems. This is the case in countries with debt crises, inflation, and stagnation.

Optimization is a key element of Islamic business management. Firms make production, hiring, and investment plans based on the optimization principle. They try to save on expensive resources. For instance, if labor is expensive and highly unionized, a company may resort to mechanization and ...