Solution
1. Complete the following table by calculating the value of the multiplier and identi-
fying 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?
?
?
0.5 ⌬C = + $50 million
MPC
Value of
multiplier
Change in
spending
Change in
Y*
1. The value of the multiplier increases with an increase in the marginal propensity to
consume.
0.5 ⌬C = + $50 million
Value of
multiplier
Change in
spending
MPC
Change in
Y*
2 (= 1/(1 − 0.5))
+ $100 million
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 con-
sume is 0.5.
a. Write the expression for planned aggregate spending as in Equation 11A-1.
Appendix:
Deriving the Multiplier
Algebraically
11 A
CHAPTER
S-162 CHAPTER 11 APPENDIX DERIVING THE MULTIPLIER ALGEBRAICALLY
Solution
2. a. In an economy without government purchases, planned aggregate spending
equals the aggregate consumption function plus planned investment spending:
AEPlanned = C + IPlanned
AEPlanned = $500 billion + 0.5 × YD + $250 billion
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:
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