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Fiscal Multipliers
Government’s fiscal operations affect the equilibrium level of national income depending on the multiplier effects of fiscal operations. Government expenditure (with no taxation) increases the equilibrium level of national income. The overall effect of the government expenditure on the national income depends on the value of government multiplier. On the other hand, taxation (with no government expenditure) causes a reduction in the national income. The overall effect of taxation depends on the tax multiplier. In practice, however, both the fiscal operations (government spending and taxation) go side by side. If the government adopts a balanced budget policy, It spends only as much it taxes. In that case, the overall effect of government and tax multipliers. In this section, we describe the method of working out the expenditure multiplier, tax multiplier and the balanced budget multiplier. Let us discuss first the government expenditure multiplier.
The government expenditure multiplier
To explain and derive the government expenditure multiplier, let us assume (i) that the government spends its money on the goods and services only, i.e. there is no transfer expenditure, (ii) that I, G and T are constant, and (iii) consumption function is given.
To work out the government expenditure multiplier, i.e. G-multiplier and its effects with all other factors given, let us recall all the three-sector equilibrium reproduced below:
Y = [1/(1 – b)] (a –bT + I + G) (eq.1)
Let us now suppose that the government expenditure increases by ∆G causes an increase in the aggregate demand and, therefore, a rise in the equilibrium level of income by, say, ∆Y. the equilibrium level of the national income with ∆G can be expressed by modifying (eq.1):
Y + ∆Y = [1/(1 – b)] (a –b) (a – bT + I + G + ∆G) (eq.2)
By subtracting eq.1 from 2, we get ∆Y resulting from ∆G.
∆Y = 1/1- b (∆G) (eq.3)
The government expenditure multiplier (Gm) can then be obtained as:
Gm = ∆Y/∆G = 1/1 – b (eq.4)
The tax multiplier
A tax is withdrawl from the circular flow of the income. Therefore, a tax has a negative effect on the equilibrium level of the national income. Tax multiplier refers to the negative multiple effect of a change in tax on the national income. To analyse the effect of change in tax and to work out tax multiplier, we will confine to only two kinds of taxation systems:
(a) Lump sum income tax, and
(b) Proportional income tax.
a change in lump sum income tax or a change in proportional income tax affects the equilibrium level of national income differently. Therefore, tax multiplier in the two kinds methods of taxation is different. The effect of a lump sum tax and that of the proportional income tax have the sake of completeness, we show here the computation of the tax multipliers of a rise in the lump sum tax.
Increase in lump sum tax and tax multiplier
In order to find out the impact of a change in the lump sum tax, let us introduce ∆T into the equilibrium equation. Let us recall again the national income equilibrium with a given lump sum tax (T). The equation reads as:
Y = [1/(1 – b)] [a – bT + I + G] (eq.5)
Let us now introduce a change in tax by ∆T. a change in tax, ∆T, changes the national income by ∆Y. when ∆T and ∆Y are incorporated into the national income equilibrium eq. 5, it takes the following form:
Y + ∆Y = 1/(1 – b) [a – b (T + ∆T) + I + G] (eq.6)
= [1/(1 – b)] [a – bT - b∆T + I + G]
The effect of ∆T on the equilibrium level of national income, i.e. ∆Y, can now be obtained by subtracting eq.5 from eq.6. thus, we get,
∆Y = [1/(1 – b)] [-b∆T]
∆Y = -b∆T/(1 – b) (eq.7)
Now, tax multiplier ™ can be obtained by dividing both sides of eq.7 by ∆T.
Tm = ∆Y/∆T = (-b/1) – b
Note that ∆T, that is, a rise in tax, has a negative effect o the equilibrium level of the national income. Increasing tax by ∆T, decreases equilibrium level of national income by a multiple of ∆T. and, as a corollary of it, a tax cut (-∆T) results in a rise in the equilibrium level of the national income.
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The government expenditure multiplier
To explain and derive the government expenditure multiplier, let us assume (i) that the government spends its money on the goods and services only, i.e. there is no transfer expenditure, (ii) that I, G and T are constant, and (iii) consumption function is given.
To work out the government expenditure multiplier, i.e. G-multiplier and its effects with all other factors given, let us recall all the three-sector equilibrium reproduced below:
Y = [1/(1 – b)] (a –bT + I + G) (eq.1)
Let us now suppose that the government expenditure increases by ∆G causes an increase in the aggregate demand and, therefore, a rise in the equilibrium level of income by, say, ∆Y. the equilibrium level of the national income with ∆G can be expressed by modifying (eq.1):
Y + ∆Y = [1/(1 – b)] (a –b) (a – bT + I + G + ∆G) (eq.2)
By subtracting eq.1 from 2, we get ∆Y resulting from ∆G.
∆Y = 1/1- b (∆G) (eq.3)
The government expenditure multiplier (Gm) can then be obtained as:
Gm = ∆Y/∆G = 1/1 – b (eq.4)
The tax multiplier
A tax is withdrawl from the circular flow of the income. Therefore, a tax has a negative effect on the equilibrium level of the national income. Tax multiplier refers to the negative multiple effect of a change in tax on the national income. To analyse the effect of change in tax and to work out tax multiplier, we will confine to only two kinds of taxation systems:
(a) Lump sum income tax, and
(b) Proportional income tax.
a change in lump sum income tax or a change in proportional income tax affects the equilibrium level of national income differently. Therefore, tax multiplier in the two kinds methods of taxation is different. The effect of a lump sum tax and that of the proportional income tax have the sake of completeness, we show here the computation of the tax multipliers of a rise in the lump sum tax.
Increase in lump sum tax and tax multiplier
In order to find out the impact of a change in the lump sum tax, let us introduce ∆T into the equilibrium equation. Let us recall again the national income equilibrium with a given lump sum tax (T). The equation reads as:
Y = [1/(1 – b)] [a – bT + I + G] (eq.5)
Let us now introduce a change in tax by ∆T. a change in tax, ∆T, changes the national income by ∆Y. when ∆T and ∆Y are incorporated into the national income equilibrium eq. 5, it takes the following form:
Y + ∆Y = 1/(1 – b) [a – b (T + ∆T) + I + G] (eq.6)
= [1/(1 – b)] [a – bT - b∆T + I + G]
The effect of ∆T on the equilibrium level of national income, i.e. ∆Y, can now be obtained by subtracting eq.5 from eq.6. thus, we get,
∆Y = [1/(1 – b)] [-b∆T]
∆Y = -b∆T/(1 – b) (eq.7)
Now, tax multiplier ™ can be obtained by dividing both sides of eq.7 by ∆T.
Tm = ∆Y/∆T = (-b/1) – b
Note that ∆T, that is, a rise in tax, has a negative effect o the equilibrium level of the national income. Increasing tax by ∆T, decreases equilibrium level of national income by a multiple of ∆T. and, as a corollary of it, a tax cut (-∆T) results in a rise in the equilibrium level of the national income.
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