C Yd is zero, C is Ca. In
C = Ca + b.Yd
Where, C = consumption expenditure,
Ca = autonomous consumption expenditure,
b = a positive constant,
Yd = consumers’ disposable income, which is equal to the excess of income over Net Direct Taxes (direct taxes less transfer payments). [Direct taxes (T) refer to personal taxes such as income tax paid and transfer payments (R) refer to unilateral transactions such as old-age pensions received by the individuals. Net Direct Taxes are thus equal to T-R.] = Y – (T – R)
= Income consumers feel free to dispose off any way they like.
Graphically, the relationship in equation (4.1) is portrayed as in Figure 4.1. Disposable Income Yd is measured on horizontal axis and consumption expenditure (C) on vertical axis. When Yd is zero, C is Ca. In a two sector model, disposable income, Yd = Y, as tax and transfer payments are nonexistent due to absence of government sector.
The graph is a straight line with an intercept on the vertical axis. For the consumption function in question. Average Propensity to Consume (APC) can be defined as the consumption expenditure incurred per unit of income, i.e.,
APC = Consumption expenditure (C) / Income (Y)
Thus, APC = b, when Y =?; and APC > b, when Y has finite values. In general, APC ? b
In like manner. Marginal Propensity to Consume (MPC), defined as an increase in the consumption expenditure per unit increase in income of the consumers, can be expressed as
MPC = Increase in consumption expenditure (?C) / Increase in income (?Y)
= ?C / ?Y or dC / dY
MPC can thus be obtained for this consumption function through simple differentiation of C with respect to Y.
MPC = dC / dY
= 0 + b
Alternatively, let initial and final levels of consumption be C1 and C2 at income levels of Yl and Y2 respectively. Then,
C1 = Ca + bY1 and
C2 = Ca + bY2
C2 – C1 = b (Y2 – Y1)
?C = b ?Y
?C / ?Y = b
For this consumption function, therefore,
APC ? MPC. (From equations 4.2 and 4.3)
2. Long-Run Consumption Function or Proportional Consumption Function:
In the long run, consumption expenditure is proportional to the income of the consumers. It may be given as:
C = bY
Consumption expenditure, in this case, is zero when income is zero. Average and marginal propensities can be shown to be identical for this type of consumption function.
APC = C/Y
= bY / Y = b
In like manner,
MPC = ?C / ?Y = b
The autonomous consumption (Ca) in this case is zero. This type of consumption function relates to the long-run tendency of consumption expenditure (Fig. 4.2).
3. Non-Linear Consumption Function:
This type of consumption function is quasi-linear (partly linear and partly non-linear). It represents pattern of consumption in advanced countries or of affluent sections. The algebraic expression may take the following form:
C = Ca+ bY + cY2
None of the APC and MPC is constant. Each one is a function of income. For instance,
APC = Ca/Y + b + cY
MPC = b + 2cY
MPC is a linear function of Y while APC is a parabolic function of it. Fig. 4.3 portrays the nature of the curve represented by equation 4.7.