Economics 282
Fall 2001
B. Ferguson
HANDOUT 5: Derivation of National Income Accounting Identities
I. Simple Case: Private Economy with no Government and no International Trade
Income: In a private economy all income generated is received by households (Y=YD), thus all of Y must be either consumed (C) or saved (S):
|
Y |
(This it true by definition: it holds as an identity) |
Expenditure: There are only two types of expenditure: consumption (C) and investment (I').
Note for the identities I' is accounting investment which includes all changes in inventories; the ' distinguishes it from planned investment (I), which does not include any unplanned change in inventories. The behavioral models we develop in the course (starting next week) will concern planned I, not I' (i.e. planned I does not include unplanned changes in inventories).
At the aggregate level accounting income = accounting expenditure, thus:
|
Y |
or S |
This is true because we defined the terms to make it true; it is an identity.
II. Economy with Government and International Trade
Income: Taxes (TA) and transfers (TR) now distinguish total income (Y) from disposable income (YD):
|
YD |
Disposable income can still
only be consumed or saved: YD = C+S; Does Y = C+S? Why or why not? Does
S 
I'? Why or why not?
Expenditure: Aggregate accounting expenditure now is: C+I'+G+NX, where G is government spending on goods and services (does this include transfers? why or why not?) and NX is net exports, or exports (X) minus imports (Q).
With income = expenditure, by accounting definition: Y / C+I'+G+NX
(Note this implies that NX = Y-(C+I'+G); what does this tell you?)
|
and |
YD = Y-TA+TR = C+I'+G+NX-TA+TR = C+S |
Cancel the C's, move the I' to the right side, and rearrange the remaining right hand terms to get:
|
S-I' = (G+TR-TA) + NX |
What is (G+TR-TA)?
What does this identity tell you?
What can it not tell you? Must S=I? Why or why not?