## Wednesday, January 29, 2014

### The National Income Balance

In this post, Dissecting Money will build the equation used to calculate a nation's GDP.

GDP is the simple sum of all measured components of all participants in the economy.

GDP can be calculated from two perspectives, spending and income.  These two perspectives can be considered as evaluating two economic participants, or,  as establishing the income and expenditures of a single participant as might be found on a financial balance sheet.

The balanced version of the equation is

(0)   C + I + G + (X – M) = C + S + T

Where C represents Consumption, I is Investment, G is Government expenditures, X is eXports,  M is iMports, S is Savings and T is Taxes (government revenue).  These terms will be used consistently throughout this post.

Equation 0 is known as the National Income Identity or sometimes as the National Income Balance.  The idea here is that the left side of the equation is expenditures and the right side is how the expenditures are redeployed by recipients.  The two sides are equal but each side describes a different mix of distribution.

We would like to build Equation 0 from the ground up.  We can begin by assuming that spending upon consumption is received by the consumption supplier who immediately redeploys the money  As a receiver of money, the supplier will consume and probably save some of the money.   We could write the resulting equation as

(1)      C = CS + S

where CS is secondary consumer spending..  Equation 1 has the defined assumption that the left hand spender is NOT the right hand spender.

We may wish to consider only ONE participant.  If we consider that all spenders must first receive income, then we can reduce the number of participants from two to one.  We can consider the participant as an accounting unit with income and expenses carefully recorded.  Equation 1 would still apply to the one participant situation.

After studying Equation 1 for a while, we might consider that savings would be spent at some time.  In fact, the spending of the left side of Equation 1 could all come from previous savings.  More importantly, consumers are not considered as having the ability to create money.  As a result, all consumer spending MUST come from previous savings unless earned and then re-spent within the measurement period.

With this limitation on money creation in mind, we would abandon Equation 1 and substitute

(2)    C + I = C + S

where consumption is identical on both sides of the equation.  Equation 2 makes clear that Investment is equal to Savings.  Unfortunately, the building of Equation 2 highlights a strange problem.

Consumers can not create money so all money spent upon savings must first be saved!  The simple logic of savings as the result of deferred consumption found in Equation 1 has been replaced in Equation 2 with the logic that all savings must first exist and will always be equal to investment!  Where might the money identified as Savings (and Investment) come from?

There is a second logical difference between Equations 1 and 2.  Equation 1 is a flow equation and Equation 2 is an accounting equation.  We would evaluate the terms in Equation 2 by simply counting each savings and consumption event within a measurement period.  Equation 2 has no information as to the source of money used in the transactions.

Bank loans as a money source can be considered at this point in the discussion.  Bank loans result in bank deposits held by third parties.  As a result, every loan can be considered as an Investment by the bank and Savings by the current third party holder of the dynamic deposit. Bank loans will result in both sides of Equation 2 increasing equally.

After studying equation 2 for a while, we might want to split consumption between private and government.  We could then add government spending (G) on the left side and government receipts (T) on the right side to get

(3)    C + I + G = C + S + T

We can re-arrange and simplify equation 3 to read

(4)    S = I + G - T

Notice that G - T is the government deficit.  We therefore see that S = I + government deficit.

We can also re-arrange equation 3 to read

(5)    I = S + T - G = S - (G - T)

Equation 5 is confusing because a deficit is shown as a negative investment.  The confusion is mitigated with the observation that S is increased by the amount of the deficit. A government deficit is considered as if it was an Investment.

From Equation 4, we see that a government deficit has increased Savings which is the identical effect we previously attributed to bank loans.  Economist usually consider increases in Savings as an increase in money supply.  The exact definition of money supply remains a controversial subject.

After studying Equation 3 for a while, we might want to add the export sector.  We can do this by writing

(6)   C + I + G + (X - M) = C + S + T

which is the beginning Equation 0.