7. The multiplier and the MPC Consider two closed economies that are identical except for their marginal propensity to consume (MPC). Each economy is currently in equilibrium with real GDP and aggregate expenditure equal to $100 billion, as shown by the black points on the following two graphs. Neither economy has taxes that change with income. The grey lines show the 45-degree line on each graph. The first economy's MPC is 0.5. Therefore, its initial aggregate expenditure line has a slope of 0.5 and passes through the point (100, 100). The second economy's MPC is 0.75. Therefore, its initial aggregate expenditure line has a slope of 0.75 and passes through the point (100, 100). Now, suppose there is a decrease of $20 billion in investment in each economy. Place a green line (triangle symbol) on each of the previous graphs to indicate the new aggregate expenditure line for each economy. Then place a black point (plus symbol) on each graph showing the new level of equilibrium output. (Hint: You can see the slope and vertical axis intercept of a line on the graph by selecting it.) 140 MPC-0.5 45-Degree Line New AE Line + ?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

2

7. The multiplier and the MPC
Consider two closed economies that are identical except for their marginal propensity to consume (MPC). Each economy is currently in equilibrium with
real GDP and aggregate expenditure equal to $100 billion, as shown by the black points on the following two graphs. Neither economy has taxes that
change with income. The grey lines show the 45-degree line on each graph.
The first economy's MPC is O.S. Therefore, its initial aggregate expenditure line has a slope of 0.5 and passes through the point (100, 100).
The second economy's MPC is 0.75. Therefore, its initial aggregate expenditure line has a slope of 0.75 and passes through the point (100, 100).
Now, suppose there is a decrease of $20 billion in investment in each economy.
Place a green line (triangle symbol) on each of the previous graphs to indicate the new aggregate expenditure line for each economy. Then place a
black point (plus symbol) on each graph showing the new level of equilibrium output. (Hint: You can see the slope and vertical axis intercept of a line
on the graph by selecting it.)
180
140
MPC+0.5
45-Degree Line
New AE Line
•+
?
Transcribed Image Text:7. The multiplier and the MPC Consider two closed economies that are identical except for their marginal propensity to consume (MPC). Each economy is currently in equilibrium with real GDP and aggregate expenditure equal to $100 billion, as shown by the black points on the following two graphs. Neither economy has taxes that change with income. The grey lines show the 45-degree line on each graph. The first economy's MPC is O.S. Therefore, its initial aggregate expenditure line has a slope of 0.5 and passes through the point (100, 100). The second economy's MPC is 0.75. Therefore, its initial aggregate expenditure line has a slope of 0.75 and passes through the point (100, 100). Now, suppose there is a decrease of $20 billion in investment in each economy. Place a green line (triangle symbol) on each of the previous graphs to indicate the new aggregate expenditure line for each economy. Then place a black point (plus symbol) on each graph showing the new level of equilibrium output. (Hint: You can see the slope and vertical axis intercept of a line on the graph by selecting it.) 180 140 MPC+0.5 45-Degree Line New AE Line •+ ?
Aplia Homework: Aggregate Demand
AGGREGATE EXPENDITURE (Billions of dollars)
200
180
160
120
***
REAL GDP (Billions of dollars)
40 60 80 100 120 140 160 180 200
20
0
Multiplier =
AE Line
0 20
MPC=0.5
8
45-Degree Line
40 60
100 120 140 160 180 200
REAL GOP (Billions of dollars)
I
AGGREGATE EXPENDITURE (Billions of dollars)
Ô
New Equilibrium
+.
New AE Line
New AE Line
Using the same method, the multiplier for the second economy is
+
New Equilibrium
Change in Equilibrium Output Change in Aggregate Expenditure x Multiplier
Now, confirm your graphical analysis algebraically using the formula for the simple spending multiplier:
-4
In the first economy (with MPC-0.5), the $20 billion decrease in investment causes equilibrium output to decrease by S billion. In the second
economy (with MPC-0.75), the $20 billion decrease in investment causes equilibrium output to decrease by S billion. Therefore, a lower MPC
is associated with a
multiplier.
45-Degree Line
For the first economy with an MPC of 0.5, the effect of the $20 billion decrease in investment becomes the following:
MPC=0.75
Transcribed Image Text:Aplia Homework: Aggregate Demand AGGREGATE EXPENDITURE (Billions of dollars) 200 180 160 120 *** REAL GDP (Billions of dollars) 40 60 80 100 120 140 160 180 200 20 0 Multiplier = AE Line 0 20 MPC=0.5 8 45-Degree Line 40 60 100 120 140 160 180 200 REAL GOP (Billions of dollars) I AGGREGATE EXPENDITURE (Billions of dollars) Ô New Equilibrium +. New AE Line New AE Line Using the same method, the multiplier for the second economy is + New Equilibrium Change in Equilibrium Output Change in Aggregate Expenditure x Multiplier Now, confirm your graphical analysis algebraically using the formula for the simple spending multiplier: -4 In the first economy (with MPC-0.5), the $20 billion decrease in investment causes equilibrium output to decrease by S billion. In the second economy (with MPC-0.75), the $20 billion decrease in investment causes equilibrium output to decrease by S billion. Therefore, a lower MPC is associated with a multiplier. 45-Degree Line For the first economy with an MPC of 0.5, the effect of the $20 billion decrease in investment becomes the following: MPC=0.75
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