What is the definition of the exchange economy?

The “American Heritage College Dictionary” defines an exchange economy as, “an economy in which goods are traded using money or exchanged for other goods.”  In the “exchange economy,” goods and services are produced here and there and elsewhere.  The goods arrive into the general market and get traded for other goods.  The goods could also be exchanged for other cargo or services.  For example, I am a teacher, so I do some tutoring after school.  I have a student that I work with whose mother is a hair stylist.  Instead of me getting money from her for the “exchange” of services for her son, she cuts my hair.  I also exchange services with another lady for my nails, and I tutor a boy whose father owns a gym.  I get to use the gym in exchange for my tutoring services.  This system is also called a “bartering system.”  In a pure exchange economy goods and services are “exchanged” -- for other goods and services or for pieces of paper called stocks or bonds.   Through the passage of time gold and “money” became the most commonly used exchange for all other goods.  A specific amount of money has become the unit of account in the exchange-economy contracts.