From the Psychological Law of Consumption, savings represent that part of the disposable income of consumers which is not spent on consumption. Thus, savings function can be derived from the consumption function.
Saving = Disposable Income – Consumption
Or, S = Yd – C = Yd – (Ca + bYd)
= Y – Ca – bY
[For a two sector model, Yd = Y]
= -Ca + (1 – b) Y
When Y = 0, S = – Ca. That means savings are negative when income of the consumer is zero. Negative saving is known as dissaving, that is, withdrawing the past savings for current consumption.
When unemployed, a consumer borrows from his accumulated savings to finance his subsistence consumption. In case he has no such reserves, he resorts to borrowing from the available sources and repays such loans from future savings.
The expression, (1 – b) can be identified as (1 – MPC), which represents the Marginal Propensity to Save (MPS), as discussed earlier. MPS is defined as an increase in savings per unit increase in income. Mathematically,
MPS = ?S / ?Y
= Change in the level of savings per unit change in income.
The savings function for an economy with two sectors, namely, the household and the producers’ sectors, has been derived in equation 4.10 above from the relevant consumption function for the economy in question. The same is portrayed in Fig. 4.4.
Recall that the consumption function for an economy with government as the third sector is
C = Ca + bYd
Here, Y’ is disposable income or income at the disposal of the consumer which is obtained after deducting net direct taxes (T – R) from income. Thus,
Yd = Y – (T – R)
= Y – T + R
In absence of the government sector, T = R = 0, and,
Yd = Y