Understanding the Multiplier Effect - New Learner
Today’s menu: i) Understand the multiplier effect.
Understanding the Multiplier Effect
ii) Demonstrate the multiplier effect using savings and investment curves.
iii) Calculate the value of the spending multiplier. iv) Calculate the impact of the multiplier on income. v) Understand the relationship between spending multiplier, the MPC and the MPS.
Calculating the “Multiplier”
Definitions
If government spending increases...
Keynesian Cross 1600 AE
Multiplier Effect: describes the fact that expenditures of money will tend to be re-spent, thus increasing GDP by a larger amount than the initial expenditure.
…then our equilibrium level of income will also increase!
1400 1200 1000
Spending Multiplier: the amount by which a change in an autonomous expenditure will be multiplied to determine an overall change in equilibrium expenditure / real GDP
X=Y
800
C G
600
AD
400 200
Velocity of Money: describes the average number of times that each unit of money will change hands within a given period of time. (Determines how fast the multiplier effect will occur.)
Round of Spending
Keynesian Cross AE 1400 1200 1000 X=Y
800
This relative change in income is expressed by the “multiplier”, which is the change in income divided by the change in investment!
C G
600
AD
400 200 0 0
500
Y
200
1000
1500
0
2000 Real GDP
Investment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Y = AE
=
100
1 =
2.0
MPS
1
1 =
= 10 20
500
1000
1500
2000 Real GDP
The Multiplier Process
Calculating the “Multiplier” 1600
0
However, because money is re-spent in the economy, a given increase in government spending (or investment, or any injection into the economy) will lead to a larger increase in net domestic income (i.e. real GDP)!
= 0.5
2.0
100.0000 80.0000 64.0000 51.2000 40.9600 32.7680 26.2144 20.9715 16.7772 13.4218 10.7374 8.5899 6.8719 5.4976 4.3980 3.5184 2.8147 2.2518
AE X
Total Round of Total Round of Total Investment Investment Spending Spending Spending Spending Spending 100.00 180.00 244.00 295.20 336.16 368.93 395.14 416.11 432.89 446.31 457.05 465.64 472.51 478.01 482.41 485.93 488.74 490.99
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1.8014 1.4412 1.1529 0.9223 0.7379 0.5903 0.4722 0.3778 0.3022 0.2418 0.1934 0.1547 0.1238 0.0990 0.0792 0.0634 0.0507 0.0406
1 MPS
= 100.00 X
492.79 494.24 495.39 496.31 497.05 497.64 498.11 498.49 498.79 499.03 499.23 499.38 499.50 499.60 499.68 499.75 499.80 499.84
1 0.2
= 100.00 X 5 = 500.00
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
0.0325 0.0260 0.0208 0.0166 0.0133 0.0106 0.0085 0.0068 0.0054 0.0044 0.0035 0.0028 0.0022 0.0018 0.0014 0.0011 0.0009 0.0007
499.87 499.90 499.92 499.93 499.95 499.96 499.97 499.97 499.98 499.98 499.99 499.99 499.99 499.99 499.99 500.00 500.00 500.00
Thus, a $100.00 investment into the economy multiplies out to 500.00 of economic growth!
1
The Multiplier Process Round of Spending 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Round of Total Round of Total Investment Investment Spending Spending Spending Spending Spending
Investment 100.0000 80.0000 64.0000 51.2000 40.9600 32.7680 26.2144 20.9715 16.7772 13.4218 10.7374 8.5899 6.8719 5.4976 4.3980 3.5184 2.8147 2.2518
100.00 180.00 244.00 295.20 336.16 368.93 395.14 416.11 432.89 446.31 457.05 465.64 472.51 478.01 482.41 485.93 488.74 490.99
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1.8014 1.4412 1.1529 0.9223 0.7379 0.5903 0.4722 0.3778 0.3022 0.2418 0.1934 0.1547 0.1238 0.0990 0.0792 0.0634 0.0507 0.0406
492.79 494.24 495.39 496.31 497.05 497.64 498.11 498.49 498.79 499.03 499.23 499.38 499.50 499.60 499.68 499.75 499.80 499.84
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
0.0325 0.0260 0.0208 0.0166 0.0133 0.0106 0.0085 0.0068 0.0054 0.0044 0.0035 0.0028 0.0022 0.0018 0.0014 0.0011 0.0009 0.0007
499.87 499.90 499.92 499.93 499.95 499.96 499.97 499.97 499.98 499.98 499.99 499.99 499.99 499.99 499.99 500.00 500.00 500.00
S
8
We’re actually just calculating the multiplier by calculating the sum of a geometric progression. You may have learned this in Algebra as: =
a 1-r
Where:
a = 1st term (amount of money spent) r = common ratio (percentage of a that is re-spent)
Thus, r = MPC, and therefore 1 – r would be the MPS. Ergo, a over the MPS will calculate the sum of a geometric progression for an amount of money that is spent, then saved, then re-spent, for an infinite number of terms (terms = no. times the money is spent and re-spent.) [Note: This only works for “convergent” sums.]
2
Understanding the Multiplier Effect
ii) Demonstrate the multiplier effect using savings and investment curves.
iii) Calculate the value of the spending multiplier. iv) Calculate the impact of the multiplier on income. v) Understand the relationship between spending multiplier, the MPC and the MPS.
Calculating the “Multiplier”
Definitions
If government spending increases...
Keynesian Cross 1600 AE
Multiplier Effect: describes the fact that expenditures of money will tend to be re-spent, thus increasing GDP by a larger amount than the initial expenditure.
…then our equilibrium level of income will also increase!
1400 1200 1000
Spending Multiplier: the amount by which a change in an autonomous expenditure will be multiplied to determine an overall change in equilibrium expenditure / real GDP
X=Y
800
C G
600
AD
400 200
Velocity of Money: describes the average number of times that each unit of money will change hands within a given period of time. (Determines how fast the multiplier effect will occur.)
Round of Spending
Keynesian Cross AE 1400 1200 1000 X=Y
800
This relative change in income is expressed by the “multiplier”, which is the change in income divided by the change in investment!
C G
600
AD
400 200 0 0
500
Y
200
1000
1500
0
2000 Real GDP
Investment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Y = AE
=
100
1 =
2.0
MPS
1
1 =
= 10 20
500
1000
1500
2000 Real GDP
The Multiplier Process
Calculating the “Multiplier” 1600
0
However, because money is re-spent in the economy, a given increase in government spending (or investment, or any injection into the economy) will lead to a larger increase in net domestic income (i.e. real GDP)!
= 0.5
2.0
100.0000 80.0000 64.0000 51.2000 40.9600 32.7680 26.2144 20.9715 16.7772 13.4218 10.7374 8.5899 6.8719 5.4976 4.3980 3.5184 2.8147 2.2518
AE X
Total Round of Total Round of Total Investment Investment Spending Spending Spending Spending Spending 100.00 180.00 244.00 295.20 336.16 368.93 395.14 416.11 432.89 446.31 457.05 465.64 472.51 478.01 482.41 485.93 488.74 490.99
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1.8014 1.4412 1.1529 0.9223 0.7379 0.5903 0.4722 0.3778 0.3022 0.2418 0.1934 0.1547 0.1238 0.0990 0.0792 0.0634 0.0507 0.0406
1 MPS
= 100.00 X
492.79 494.24 495.39 496.31 497.05 497.64 498.11 498.49 498.79 499.03 499.23 499.38 499.50 499.60 499.68 499.75 499.80 499.84
1 0.2
= 100.00 X 5 = 500.00
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
0.0325 0.0260 0.0208 0.0166 0.0133 0.0106 0.0085 0.0068 0.0054 0.0044 0.0035 0.0028 0.0022 0.0018 0.0014 0.0011 0.0009 0.0007
499.87 499.90 499.92 499.93 499.95 499.96 499.97 499.97 499.98 499.98 499.99 499.99 499.99 499.99 499.99 500.00 500.00 500.00
Thus, a $100.00 investment into the economy multiplies out to 500.00 of economic growth!
1
The Multiplier Process Round of Spending 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Round of Total Round of Total Investment Investment Spending Spending Spending Spending Spending
Investment 100.0000 80.0000 64.0000 51.2000 40.9600 32.7680 26.2144 20.9715 16.7772 13.4218 10.7374 8.5899 6.8719 5.4976 4.3980 3.5184 2.8147 2.2518
100.00 180.00 244.00 295.20 336.16 368.93 395.14 416.11 432.89 446.31 457.05 465.64 472.51 478.01 482.41 485.93 488.74 490.99
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1.8014 1.4412 1.1529 0.9223 0.7379 0.5903 0.4722 0.3778 0.3022 0.2418 0.1934 0.1547 0.1238 0.0990 0.0792 0.0634 0.0507 0.0406
492.79 494.24 495.39 496.31 497.05 497.64 498.11 498.49 498.79 499.03 499.23 499.38 499.50 499.60 499.68 499.75 499.80 499.84
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
0.0325 0.0260 0.0208 0.0166 0.0133 0.0106 0.0085 0.0068 0.0054 0.0044 0.0035 0.0028 0.0022 0.0018 0.0014 0.0011 0.0009 0.0007
499.87 499.90 499.92 499.93 499.95 499.96 499.97 499.97 499.98 499.98 499.99 499.99 499.99 499.99 499.99 500.00 500.00 500.00
S
8
We’re actually just calculating the multiplier by calculating the sum of a geometric progression. You may have learned this in Algebra as: =
a 1-r
Where:
a = 1st term (amount of money spent) r = common ratio (percentage of a that is re-spent)
Thus, r = MPC, and therefore 1 – r would be the MPS. Ergo, a over the MPS will calculate the sum of a geometric progression for an amount of money that is spent, then saved, then re-spent, for an infinite number of terms (terms = no. times the money is spent and re-spent.) [Note: This only works for “convergent” sums.]
2
