KEYNESIAN THEORY AND POLICY AT A GLANCE
DERIVATION OF THE INVESTMENT MULTIPLIER
The notion of an investment multiplier is most relevant when (1) the economy is functioning somewhere below
its full-employment level and (2) market forces, which normally impinge on prices, wages and the interest rate,
are (for some reason) not working. In these circumstances, a (Keynesian) macroeconomic equilibrium (one
involving a substantial amount of economywide unemployment) is achieved through changes in the levels of
spending and income.
When the level of investment increases by some amount,
Ä
I, the equilibrium level of income will increase
by some multiple amount,
Ä
Y. The ratio of
Ä
Y to
Ä
I is called the investment multiplier. It can be derived, as
follows, from the equilibrium condition (Y = C + I + G) together with the consumption equation (C = a + bY).
1.
Y = C + I + G
where C = a + bY
2.
Y = a + bY + I + G
3.
Y +
Ä
Y = a + b(Y +
Ä
Y) + I +
Ä
I + G
4.
Y +
Ä
Y = a + bY + b
Ä
Y
+ I +
Ä
I + G
5.
Y
= a + bY
+ I
+ G
_________________________________________
6.
Ä
Y =
b
Ä
Y
+
Ä
I
7.
Ä
Y - b
Ä
Y =
Ä
I
8.
(1 - b)
Ä
Y =
Ä
I
9.
Ä
Y =
Ä
I
or 10.