Illustration 32
Presume the consumption function is C = 100 + 0.8Yd and investment is I = 200 millions. The government expenditure at $ 180 millions where as the tax function is a proportional income tax function where T = 0.10Y.
- Find the equilibrium level of income in an economy
- Find the revenue from taxes at the equilibrium level of income. Is the government budget balanced?
- Suppose there is an increase in investment from 200 to 240 million dollars, what is the equilibrium level income
- What is the revenue from taxes at the new equilibrium level of income? Is there a balanced government budget?
Solution
- The equilibrium condition is given as Y = C + I + G
- The revenue from taxes at the equilibrium level of income.
- When there is an increase in investment from $200 millions to $240 millions,
- The revenue from taxes at the new equilibrium level of income is
T = 0.10 (1,857.14)
= 185.714 million dollarsHence, the revenue from taxes at the equilibrium level of income is $ $185.714 millions whereas the government expenditure is at 180 million dollars. Therefore, there is a budget surplus of $5.714 millions. Due to the higher income level, there are larger tax revenues leading to a budget surplus.
Here,
C = 100
+ 0.8Yd
C = 100 + 0.8(Y – T)
C = 100 + 0.8(Y – 0.10Y)
C = 100 + 0.8(0.9Y)
C = 100
+ 0.72Y
Thus,
Y = 100
+ 0.72Y + 200 + 180
Y – 0.72 Y = 100 + 200 + 180
0.28Y = 480
Y = 480 / 0.28
The equilibrium level of income is $1,714.28 millions.
The tax function is a proportional income tax function where T = 0.10Y
Thus, T = 0.10(1,714.28) = 171.42 million dollars
Hence the revenue from taxes at the equilibrium level of income is at $171.42 millions where as the government expenditure is at $180 millions. Therefore, there is a budget deficit of $8.58 millions.
Y = 100 + 0.72Y + 240 + 180
Y – 0.72Y = 100 + 240 + 180
0.28Y = 520
Y = 520 / 0.28
The equilibrium level of income is 1,857.14 million dollars.
Illustration 33
In an economy, C = 100 + 0.8Yd, I = $200 millions government expenditures is at $100 millions whereas T = $40 millions.
- Find the equilibrium level of income in an economy.
- Find the equilibrium level of consumption and saving at the equilibrium level of income.
- Depict the injections leakages equality at the equilibrium level.
Solution
1. The equilibrium condition in an economy is given as Y = C + I + G
Here, C = 100 + 0.8Yd
C = 100 + 0.8(Y – T)
C = 100 + 0.8(Y – 40)
C = 100
+ 0.8Y – 32
Thus,
Y = 100
+ 0.8Y – 32 + 200 + 100
Y – 0.8Y = 368
0.2Y = 368
Y = 368 / 0.2
The equilibrium level of income is $1,840 millions.
2. When the equilibrium level of income is $1,840 millions,
Equilibrium level of consumption:
C = 100 + 0.8Yd
C = 100 + 0.8(Y – T)
C = 100 + 0.8(Y – 20)
C = 100 + 0.8(1,840) – 32
C = 100 + 1472 – 32
C = 1,540
The equilibrium level of consumption is $1,540 millions.
Equilibrium level of saving:
S = Y – C – T
S = 1840 – 1540 – 40 = 260
The equilibrium level of saving is $260 millions.
3. Injections = I + G
Leakages = S + T
Injections = 200 + 100 = 300
Leakages = 260 + 40 = 300
This depicts the injections leakages equality at the equilibrium level.
Illustration 34
For a closed economy, the following data is given
Consumption, C = 100 + 0.8Yd
Investment, I = 140
Government Expenditure, G = 400
Transfer Payments, TR = 200
Rate of income tax, t = 0.2
- Write the reduced form of equation for equilibrium income
- Find out equilibrium income
- What is the value of tax multiplier?
Solution
1. Reduced form of the equation for equilibrium income is
Y = 1 (a
+ bTR + I + G)
1 – b
+ bt
2. Substituting the values of parameters in the above equation for the equilibrium income, we have
Y = 1 (100
+ 0.8*200 + 140 + 400)
1 – 0.8
+ 0.8*0.2
= 1 (100
+ 160 + 140 + 400)
1 – 0.64
= 1 (800)
0.36
= 2,222
Thus, the equilibrium income is 2,222
Tax
multiplier = 1
1 – b
+ bt
= 1
1 – 0.8
+ 0.8*0.2
= 1 = 1
1 – 0.64 0.36
= 2.77
Illustration 35
Presume we have an economy characterised by the following functions:
C = 200 + 0.8Yd
Ī = 200
Ḡ = 200
Ť = 200
Values are in million dollars.
- Find the equilibrium level of income.
- How much increase in income will take place if government expenditure on goods and services increases by $120 millions?
- Find the tax multiplier and balanced budget multiplier
- Find the equilibrium level of national income if T = Ť + tY = 200 + 0.25Y
Solution
1. Equilibrium Y = C + Ī + Ḡ
Y = a + bYd + Ī + Ḡ
Y = a + b(Y – Ť) + Ī + Ḡ
Substituting the values of a, b, Ť, Ī and Ḡ we have,
Y = 200
+ 0.8(Y – 200) + 200 + 200
= 200 + 0.8Y – 160 + 200
+ 200
Y – 0.8 Y = 440
0.2Y = 440
Y = 440
/ 0.2
Y = 2,200
2. Government expenditure multiplier Gm = 1
1 – b
= 1 = 5
1 – 0.8
Increase in national income if government expenditure increases by $120 millions.
Δ Y = Gm * DG
= 5 * 120 = 600
3. Tax Multiplier,
Tm = -
b
1 – b
= -
0.8 = - 0.8 = -
4
1 – 0.8 0.2
=
Balanced Budget Multiplier
Gm + Tm
5 + (- 4) = 1
4. The equilibrium level of national income when,
T = 200 + 0.25Y = Ť + tY
Y = 1 (a
- bTR + I = G)
1 – b
+ bt
= 1 (200
- 0.8*200 + 200 + 200)
1 – 0.8
+ 0.8*0.25
= 1 (440)
1 – 0.8
+ 0.2
= 1 (440)
0.4
= 1,100
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- Accelerator theory of Investment
- Average Propensities, Marginal Propensity to Save
- Camouflaged Redundancy
- Classical Vs. Keynesian Models of income and Employment
- Concept of multiplier
- Consumption Function
- Criticisms of Keynesian Thesis
- Drift Theory of Consumption
- Foreign Trade Multiplier
- Government Expenditure
- Investment Function
- Jorgenson's Neoclassical Notion of Investment
- Keynesian Postulations and Underdeveloped Countries
- Keynesian Theory of Income, Output and Employment
- Model of National Income Determination
- Principle of Acceleration and the Super Multiplier
- Principle of Acceleration and the Super Multiplier - Part I
- Thrift, Marginal Competence of Capital
- Saving Function
- Saving and Investment Equality
- Saving - Investment Parity
- Some New Theories of Investment
- Theory of Consumption Function
- Unemployment and Full Employment
