The National Income Identity

As useful as the Circular Flow Diagram is for providing a framework for macroeconomic analysis, it is a bit cumbersome. Fortunately, the relationships between the concepts that appear in the table and the diagram can also be represented more efficiently by an equation - the National Income Identity. In its simplest form this equation states that Supply = Demand. Firms produce a given amount of goods and services which they sell in the output market. The value of this output is defined as Gross Domestic Product (Q). The buyers for this output come from the household, government, business, and foreign sectors. Demand originating in these four sectors is defined respectively as: Consumption spending (C); Government spending (G); Investment spending (I); and Export spending (X). Given the nature of the accounting procedures, some of the expenditures by these buyers will be for Imports (M) defined as goods and services produced outside of the U.S. For this reason the level of import expenditures is subtracted from total expenditures to arrive at total demand for domestic production. This relationship can be represented with the Aggregate Supply = Aggregate Demand [equation (1)].

(1) Q = C + I + G + X - M

Aggregate Supply = Aggregate Demand

An alternative approach to the national income identity is described in equation 2. There is no new information in this equation, it is simply a repackaging of the initial information. This approach is often referred to as the Injections = Withdrawals approach. Rather than looking at output demand and supply, this approach focuses on the allocation of income. To explain the equation Injections = Withdrawals fully, we can begin in the output market and trace the flow of income generated in the production of goods and services. Along the way through the system, some of the income leaves the system and does not get back to the firms in the form of demand for output. To simplify, let us assume all the income is paid to the household sector. Some of this income, however, goes to the government in the form of taxes (TA) and some comes back to households in the form of transfer payments (TR). The difference is net taxes (T = TA - TR).  The remainder, defined as disposable income, is allocated by the household sector to buy goods and services which we call Consumption expenditures (C). Some disposable income goes to the purchase of things such as stocks and bonds and deposits in bank accounts which we call Saving (S). This currency is taken out of the flow of income. Some of the goods that are purchased however, are produced abroad resulting in some of the income flowing out of the country to pay for imports (M). The total level of withdrawals from the system would be:

Withdrawals = S + M + T

Offsetting these leakages / withdrawals from the system are the injections of spending. The government buys currently produced goods and services (G) with income that comes from net tax receipts ( TA - TR) and borrowing from the capital market. Similarly there is Investment spending (I) by the business sector on currently produced goods and services to be used in the production of future goods and services that can be financed by retained earnings and borrowing from the capital market. The third injection is Export demand (X) and net foreign payments (NFP), the injection of spending on currently produced goods and services by foreigners. [To make things a bit easier I will set NFP = 0 so we will not need to continue using this term]. Thus, the total level of injections into the system would be:

Injections = I + X + G

If this flow was sustainable, if the income generated in the production process eventually returned to the producers in the form of demand, then injections would need to balance the withdrawals. The equality of Injection = Withdrawals [equation (2)] is therefore simply a restatement of the Supply = Demand condition. 

(2) I + G + X = M + S + T

Injections = Withdrawals

There is a third formulation of the identity which has become quite useful in recent years. This formulation, described in equation 3, focuses attention on the interdependence between the trade deficit (TDEF = X - M), the budget deficit (BD = G + TR - TA) , and the balance between private savings and investment (I - S).

(3) (S - I) = - TDEF + BDEF

In the U.S., for example, it is widely recognized that the savings rate is quite low (low S) and that substantial investment spending (large I) holds the key to future growth. If we add to this the fact that the government is running a substantial deficit (BDEF>0), then the only way to sustain this situation is if the country runs a substantial foreign trade deficit (X  -M < 0). In Japan, on the other hand, a high savings rate has traditionally produced savings that were more than enough to finance investment spending (S > I) and offset any budget deficit (G + T >0). Given these domestic imbalances, Japan will run a trade surplus. Thus the trade and budget deficits are inextricably interrelated, although not in a direct relationship where a change in one will necessarily involve an adjustment in the other. What we can expect is that American leaders will continue to blame the trade deficit with Japan on restrictive trade policies while the Japanese will continue to blame the imbalance on the low saving rate and the high budget deficits in the US.