Imagine the following:

- the US mints all close, so that no new \$1 bills are ever generated
- none of the bills ever wears out

If these two things held true, the total number of \$1 bills in
the world would *never change*. That is, they would be
**conserved**.

DEFINITION

If something is **conserved**, the total
number (or amount) never changes.

If \$1 were conserved, then you could easily keep track of how many where in your wallet (or bank account) by simply comparing how much comes in versus how much comes out (we will ignore interest for now).

If both IN and OUT were the same number (or the same
*rate* (for example, dollars per hour)), then the total
amount of money in your account would always be the same. If IN is
bigger than out, you are *accumulating* dollars; if OUT is
bigger you are *depleting* your supply (which we will call a
negative accumulation).

What we have just done is a simple *balance* on dollars,
using the following balance equation:

ACCUMULATION = IN - OUT

DEFINITION

A **balance equation** is a tool used to
account for where things come/go and how their total number (or
amount) changes.

If we now consider interest, it is possible for the total amount
in your account to increase without you putting any money in
yourself. We will call this *generation*, similarly the bank
might change you something for having an account (so the total
amount decreases without your taking any out), so that some is
*consumed*.

A more general balance equation then, is given as

ACCUMULATION = IN - OUT + GENERATION - CONSUMPTION

OUTCOME:

Define the term balance equation and give examples of things that might be balanced

NOTE:

A balance need not be done **only** on conserved
quantities.

NOTE:

In fact, if a material is truly **conserved**
generation and consumption must both be zero. In other words, a
balance on total dollars in this example could not have generation
and consumption. Our example did involve generation and consumption
because we were doing a **specific** balance on your money (not
total money) so you "generated" dollars by taking them from someone
else and "consumed" them by giving them to someone else.