Business
Business is the activity of making one's living or making money by producing or buying and selling goods or services. Simply put, it is "any activity or enterprise entered into for profit. It does not mean it is a company, a corporation, partnership, or have any such formal organization, but it can range from a street peddler to General Motors." The term is also often used colloquially (but not by lawyers or public officials) to refer to a company, but this article will not deal with that sense of the word.
Economy
An economy (from Greek οίκος – "household" and νέμoμαι – "manage") is an area of the production, distribution, or trade, and consumption of goods and services by different agents. Understood in its broadest sense, 'The economy is defined as a social domain that emphasizes the practices, discourses, and material expressions associated with the production, use, and management of resources'. Economic agents can be individuals, businesses, organizations, or governments. Economic transactions occur when two parties agree to the value or price of the transacted good or service, commonly expressed in a certain currency. However, monetary transactions only account for a small part of the economic domain.
Business Administration
The technical and commercial functions of a business are clearly defined, but the same cannot be said of the administrative function. Not many people are familiar with its constitution and powers; our senses cannot follow its workings - we do not see it build or forge, sell or buy - and yet we all know that, if it does not work properly, the undertaking is in danger of failure.
Henri Fayol (1900). "Henri Fayol addressed his colleagues in the mineral industry 23 June 1900." Translated by J.A. Coubrough. In: Fayol (1930) Industrial and General Administration. pp. 79-81
Business Administration
To those who run businesses, profits are obviously desirable and losses deplorable. But economics is not business administration. From the standpoint of the economy as a whole, and from the standpoint of the central concern of economics — the allocation of scarce resources which have alternative uses — profits and losses play equally important roles in maintaining and advancing the standards of living of the population as a whole.
Thomas Sowell, Basic Economics (4th ed., 2010)