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Income Determination
A three sector or a closed economy model is constructing by adding government sector to the two sector or simple economy model. The government influences the level of economic activities in a variety of ways through its economic activities, fiscal policy (government expenditure and taxation policies), monetary and credit policy, growth policy, industrial policy, labour policy, wage policy, employment policy, control and regulation of monopolies, export and import policies, environment policy etc. however, the closed model of the Keynesian income determination theory confines to the effects government expenditure (including transfer payments) and taxation. Thus, inclusion of the government sector into the simple economy model introduces three new variables to the model, viz, taxes (T), government expenditure (G) and transfer payments (GT). The inclusion of the government complicates the analysis by bringing in the complex system of taxation, expenditure and transfer payments. In our simplified system, the government makes only the following fiscal operations:
(i) It imposes only direct taxes on the households;
(ii) It spends money on buying factor services from the household sector and goods and services from the private business sector; and
(iii) It makes transfer payments in the form of pensions and subsidies.
Capturing the effects of all the three variable-taxes, expenditure and transfer payments-on the equilibrium of the national income in a simple model is a difficult proposition at this stage of our analysis. Therefore, for convenience sake, the effects of these variables on the equilibrium level of income will be discussed in a sequence of four models-Model I, Model II, Model III and Model IV- each being the extension of the previous model while Model I analysis the lump sum tax and government expenditure on the equilibrium level of income. Model II analysis the effect of transfer payments, Model III extends the analysis to the effect of proportional tax system, Model IV combines the three models and presents a comprehensive analysis.
Income determination with government spending and tax:
Model I is an extension of the two-sector model presented, it includes two additional variables-the government spending on purchases (G), and income tax (T). model I is based on the following assumptions:
(i) There is no transfer payment;
(ii) There is only one form of tax, i.e. a lump sum income tax, determined exogenously; and
(iii) The government spending is too exogenously determined.
Let us also assume, for the sake of simplicity that the government follows a balanced budget conditions, Model I has been elaborated under (i) AD-AS approach, and S-I approach.
AD-AS approach
Under AD-AS approach, the variables of the aggregate demand (AD) and aggregate supply (AS) of the three-sector model can be specified as:
AD = C + I + G (eq.1)
And, AS = C + S + T (eq.2)
The Keynesian condition for the equilibrium of the national income may now be written as:
C + I + G = Y = C + S + T (eq.3)
Thus at equilibrium,
Y = C + I + G (eq.4)
In three-sector model, variable C in eq.4 needs to be redefined. With tax imposition, consumption function (C) is redefined as:
C = a + bYd
Where Yd = Y – T, (disposable income)
Where T = tax (lump sum)
By substituting Y – T for Yd, consumption function in a three-sector model can be written as:
C = a + b(Y – T) (eq.5)
By substituting eq. 5 for C in eq.4, the equilibrium level of national income can be written as:
Y = a + b (y – T) + I + G (eq.6)
By rearranging the variables in eq.6, we get the equilibrium level of income (Y) as:
Y = a + bY – bT + I + G
Y (1 – b) = a – bT + I + G
Y = 1/1 – b (a – bT + I + G) (eq.7)
Eq. 7 gives a formal model for the equilibrium level of national income. If consumption function and the values of constants (I, G and T) are known, the equilibrium level of the national income can be worked out.
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(i) It imposes only direct taxes on the households;
(ii) It spends money on buying factor services from the household sector and goods and services from the private business sector; and
(iii) It makes transfer payments in the form of pensions and subsidies.
Capturing the effects of all the three variable-taxes, expenditure and transfer payments-on the equilibrium of the national income in a simple model is a difficult proposition at this stage of our analysis. Therefore, for convenience sake, the effects of these variables on the equilibrium level of income will be discussed in a sequence of four models-Model I, Model II, Model III and Model IV- each being the extension of the previous model while Model I analysis the lump sum tax and government expenditure on the equilibrium level of income. Model II analysis the effect of transfer payments, Model III extends the analysis to the effect of proportional tax system, Model IV combines the three models and presents a comprehensive analysis.
Income determination with government spending and tax:
Model I is an extension of the two-sector model presented, it includes two additional variables-the government spending on purchases (G), and income tax (T). model I is based on the following assumptions:
(i) There is no transfer payment;
(ii) There is only one form of tax, i.e. a lump sum income tax, determined exogenously; and
(iii) The government spending is too exogenously determined.
Let us also assume, for the sake of simplicity that the government follows a balanced budget conditions, Model I has been elaborated under (i) AD-AS approach, and S-I approach.
AD-AS approach
Under AD-AS approach, the variables of the aggregate demand (AD) and aggregate supply (AS) of the three-sector model can be specified as:
AD = C + I + G (eq.1)
And, AS = C + S + T (eq.2)
The Keynesian condition for the equilibrium of the national income may now be written as:
C + I + G = Y = C + S + T (eq.3)
Thus at equilibrium,
Y = C + I + G (eq.4)
In three-sector model, variable C in eq.4 needs to be redefined. With tax imposition, consumption function (C) is redefined as:
C = a + bYd
Where Yd = Y – T, (disposable income)
Where T = tax (lump sum)
By substituting Y – T for Yd, consumption function in a three-sector model can be written as:
C = a + b(Y – T) (eq.5)
By substituting eq. 5 for C in eq.4, the equilibrium level of national income can be written as:
Y = a + b (y – T) + I + G (eq.6)
By rearranging the variables in eq.6, we get the equilibrium level of income (Y) as:
Y = a + bY – bT + I + G
Y (1 – b) = a – bT + I + G
Y = 1/1 – b (a – bT + I + G) (eq.7)
Eq. 7 gives a formal model for the equilibrium level of national income. If consumption function and the values of constants (I, G and T) are known, the equilibrium level of the national income can be worked out.
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