The Multiplier

Given an equilibrium level of income, the multiplier indicates the size of the change in aggregate income resulting from a permanent increase in the level of any autonomous spending component,

that is DY = m x DI

where DY = change in aggregate income

m = the multiplier

DI = change in investment

Note: the same formula applies to a change in government spending (DG) or a change in

the level of autonomous consumption (DC_o).

The formula for the multiplier is:

m = 1 / 1 - MPC

or

m = 1 / MPS

The easiest way to work a multiplier problem is to find the MPS, convert it to a fraction,

and then take the reciprocal.

Special Note: If the problem gives you the MPS, stay there. If it gives you the MPC,

then convert to the MPS, recalling that

1 - MPC = MPS.

Practice Problems

1) Given: MPC = .8

DI = +10 bil

DY = ?

2) Given: MPS = .25

DI = -5 bil

DY = ?

3) Given: C = 20 + .8Y

DI = + 15 bil

DY = ?

4) Given: S = -18 + .4Y

DC_o = + 5 bil

DY = ?

5) Given: Consumers are spending 80% of their incomes to buy goods and services. Now, the level of investment increases by $8.2 billion. What will this do to the level of aggregate income in the economy? Explain!

Hint: How, exactly, is the MPC defined?

Do we have those elements present

in the given of this problem?

6) If a $10 billion increase in autonomous consumption raises the level of aggregate income by $40 billion, then it may be concluded that the MPS in that economy is ___________. Explain.