Basic Accounting Concepts - what am I missing?

[Tony]

On Mon, 3 Jan 2011 01:28:44 -0500, Jim Smith <jimsmth761 at gmail.com> wrote:

> I have come to understand the Accounting Equation as a function rather
than
> a mathematical equation. It is a function because of the restriction that
> double entry is always required. It doesn't work as a purely mathematical
> equation. Thinking of it as an equation leads to nonsensical results.

The accounting equation is both functional and mathematical.  It's probably
best to understand assets/liabilities/equity as balance accounts (i.e. that
hold amounts) and income/expense as flow accounts (i.e. that show the
transition of balance accounts from time x to time y).

The fundamental equation Assets - Liabilities = Equity holds at all times,
but it is underspecified for the purposes to which you are putting it. 
Better would be to write it as Assets(t) - Liabilities(t) = Equity(t) where
t is some specific point in time.

If we take t=0 to be the beginning of some period and t=1 to be the end of
that period, then the equation trivially gives us (abbreviated):

A(0) - L(0) = E(0)
and
A(1) - L(1) = E(1)

If we define Income(1) and Expense(1) to be the sum of all income and
expense (flows) over the period from t=0 to t=1, then we can arrive at the
equations you are attempting to understand.  We need one more basic fact
(related to the "clean surplus" concept), E(1) = E(0) + NI(1), where NI(1)
= net income over the period = Income(1) - Expense(1).

With these definitions in place, we can see that both formulations that
caused confusion were "correct", but merely underspecified:

We can transform A - L + ( I - Ex) = Eq (note the + sign) into the more
precise:

A(0) - L(0) + ( I(1) - Ex(1) ) = Eq(1)

Similarly, we can transform A - L - ( I - Ex) = Eq (note the - sign) into
the more precise:

A(1) - L(1) - ( I(1) - Ex(1)) = Eq(0)

this last equation manipulates to A(1)-L(1) = Eq(0)+I(1)-Ex(1)

So, in general, the expanded formulations of A-L=Eq that include income and
expenses implicitly reference a beginning and end period, and you just have
to careful about which amounts are measured at the beginning of the period
and which are being measured at the end.

Tony