While business and economics are two closely related fields, one (economics) serves to lay the foundation of the other (business) through its various models and underpinnings. The interdependence of these two fields operates much the same way as chemistry to metallurgy or physics to engineering.
Specifically, economics is a social science that studies how societies use resources to produce and distribute goods and services and how the public consumes that which is produced. It analyzes the transfer of wealth among different segments of a society and how both individuals and groups respond to financial incentives. It is primarily concerned with the choices that businesses, governments and other producers make (among labor, technology, finance, etc.) in order to maximize output of a given commodity with scarce or limited means to produce the given object.
Moreover, the broader study of economics can be broken down into subdivisions called micro and macroeconomics. Microeconomics deals with the habits of individual producers and consumers while macroeconomics is focused on larger economies such as state and national governments. The governmental system in which an economy operates (i.e., capitalism versus socialism) can have a drastic effect on the levels of output and costs of production.
Businesses provide the goods and services that those in the economics field study. Knowledge of economic models can help a given business understand how to better control production and distribution costs, maximize efficiency, incentive labor participation, drive output and, ultimately, increase profits.
Business as a discipline involves learning the principles of finance, operations, hiring, management, product development, customer service, marketing, sales and other factors to create commodities that customers find valuable. Economics gives business owners a way to study how all of these things can be used most effectively to achieve that value proposition. In other words, economics studies the allocation of resources to produce the goods and services that drive business decisions in the marketplace.