S-159
interactive activity
Appendix
11
Deriving the Multiplier
Algebraically
1. Complete the following table by calculating the value of the multiplier and iden-
tifying the change in Y* due to the change in autonomous spending. How does
the value of the multiplier change with the marginal propensity to consume?
MPC
Value of
multiplier
Change in
spending
Change in
Y*
0.5 ?DC = + $50 million ?
0.6 ?DI = − $10 million ?
1. The value of the multiplier increases with an increase in the marginal propensity
to consume.
MPC
Value of
multiplier
Change in
spending
Change in
Y*
0.5 1/(1 − 0.5) = 2DC = + $50 million + $100 million
0.9 1/(1 − 0.9) = 10 DC = − $2.5 million − $25 million
Solution
WORK IT OUT Interactive step-by-step help with solving this
problem can be found online.
2. In an economy without government purchases, transfers, or taxes, and
without imports or exports, aggregate autonomous consumer spending is
$500 billion, planned investment spending is $250 billion, and the marginal
propensity to consume is 0.5.
a. Write the expression for planned aggregate spending as in Equation 11A-1.
b. Solve for Y* algebraically.
c. What is the value of the multiplier?
2. a. In an economy without government purchases, planned aggregate spending
equals the aggregate consumption function plus planned investment spending:
b. In an economy without taxes or government transfers, GDP equals disposable
income. The economy will be in income–expenditure equilibrium when GDP
equals planned aggregate spending:
c. The value of the multiplier is 1/(1 − 0.5) = 2.
Solution