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The interrelationships between NI, GNP and PI form the basis for accounting identities or definitions.

Circular flow of income tells us that national product = national income = national expenditures. National product is a monetary measure of all currently produced final goods and services.

National income is the sum of all factor earnings. Factor earnings are then used for consumption and investment.

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National expenditures are, thus, sum of all private consumption and investment expenditures as well as government expenditure. National product is, thus, identically equal to national income which is identically equal to national expenditures. These are called accounting identities.

**In deriving these accounting identities, we make the following assumptions for making our analysis simple: **

We assume that (i) there is no governmental activity, (ii) no foreign trade exists, (iii) depreciation costs are nil. We refer to national income and national output interchangeably.

In this imaginary economy, we symbolise GNP by Y. GNP has two elements in this simplified two-sector economy: consumption (C) and investment (I). We want to show the first identity: output produced equals output sold. Thus,

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Y = C + I … (2.1)

(since G = O, and net export [ X – M] = 0)

In other words, all output produced is consumed and invested.

This output is partly allocated for consumption and partly for saving.

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**Thus, we can write **

Y = C + S ‘ -.. (2.2) since T = 0

Now, we can combine identities (2.1) and (2.2). Since national product and national income are identically equal, C + I must be equal to C + S.

**That is, **

C + I = Y = C + S … (2.3)

The left-hand side of identity (2.3) shows the components of national product or aggregate demand or aggregate expenditure and the right-hand side shows the distribution of income between consumption and saving. This equation shows that output produced is equal to output sold. The value of output produced is equal to income received and income received is partly spent on consumption and partly saved.

**Slightly arranging equation (2.3), we obtain saving- investment identity: **

I = Y – C = S or I = S -…(2.4)

This means that in a two-sector economy— where governmental sector and foreign trade are absent—investment is identically equal to saving. In other words, accounting identity or definitional identity states that actual saving or ex-post saving is always equal to actual investment or ex-post investment. However, ex-ante saving or planned saving is not necessarily identically equal to ex-ante investment or desired investment.

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To make our discussion a realistic one, we introduce government sector and foreign trade sector. Once government is introduced into the picture, we see that government both spends (G) and collects taxes (T) as revenues. Further, the government, like individuals, can also save. Government saving occurs when revenue exceeds expenditure of the government.

Once international trade is introduced, there may also occur saving in the foreign trade sector. Whenever exports (X) exceed imports (M), saving in the foreign sector emerges. Thus, we have three kinds of savings personal saving (S), government saving (T – G), and foreign saving (X – M). In this economy,

S = Y – C – T … (2.5)

We know that

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Y = C + I + G + X- M … (2.6)

Putting the value of (2.6) into (2.5) we obtain S = (C + I + G + X-M)-C-T … (2.7)

**Arranging equation (2.7) and solving for I, we find that all three types of savings become equal to investment: **

I = S + (T – G) + (X – M) … (2.8)

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Thus, investment and savings are equal.

**Ignoring external sector, we can write the following identity: **

Y – T = C + S … (2.9)

**We can write (2.9) as **

Y = C + S + T … (2.10)

**In the absence of external sector, we have **

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Y = C + I + G … (2.11) Combining (2.10) and (2.11), we get

C + I + G = Y = C + S + T … (2.12)

**Cancelling (C) on both sides of (2.12), we can rewrite this fundamental identity as **

I + G = S + T … (2.13) (closed economy)

I + G + X = S + T + M … (2.14) (open economy)