Accounting equation: does income really decrease equity?

Question

I am new to using [double-entry bookkeeping](https://en.wikipedia.org/wiki/Double-entry_bookkeeping_system) for personal finances. [GnuCash](https://en.wikipedia.org/wiki/GnuCash) uses a variant of [the accounting equation](https://en.wikipedia.org/wiki/Accounting_equation) that has five variables, and which seems to be known colloquially as an "expanded" or "extended" accounting equation: assets - liabilities = equity + (income - expenses) This can be re-arranged as: equity = assets - liabilities - income + expenses Rearranging it in this way shows that, all other things being unchanged, **an *increase* in income results in a *decrease* in equity**. Conversely, **an *increase* in expenses results in a *increase* in equity**. To me, this is totally counter-intuitive. I would have expected (if all else remains unchanged): increased income to *increase* equity; and increased expenses to *decrease* equity. My question is: have I misunderstood the equation or the meaning of the terms; and if so, what is the correct interpretation; or if not, then why is this the correct interpretation?

Answer 1

In the original equation, which is often called the basic accounting equation, Assets = Liabilities + Equity.

These three variables can be re-arranged to solve for each variable as follows:

Assets = Liabilities + Equity

Liabilities = Equity - Assets

Equity = Assets - Liabilities

All three of these are permanent accounts; they aren't closed at month or period end. They will be reported at period end on the balance sheet as of a specific date in time.

Ending Equity in the above formula incorporates several temporary accounts that are closed to it prior at period end. We can expand Ending Equity or Equity as follows:

Ending Equity = (Beginning Equity + Income - Expenses + Owner Contributions - Owner Withdrawals)

Mathematically, we now have two different types of variables in this formula: permanent and temporary ones. Therefore, we would need to incorporate parentheses around the computation of temporary accounts values. Once we solve for ending equity, we again only have permanent accounts and the formula can be manipulated to solve for any of the three variables.

Simple proof:

Assets = 100

Liabilities = 50

Beginning Equity = 1

Income = 74

Expenses = 25

Ending Equity = 1 + 74 - 25 = 50

Assets = Liabilities + Equity (ending)

100= 50+ 50

Assets = Liabilities + (beginning equity + income - expenses) <-- Note that Ending equity isn't explicitly present; it's the sum of the parenthetical components

100 = 50 + 1 + 74 - 25

Answer 2

Net income ( the difference between income and expense ) increases equity. A loss would decrease equity.