Saving Function:

The part of income not spent on consumption is saving. Saving is consumption decline. When saving increases, consumption will drop. According to Keynes, the height of saving in the economy, similar to consumption, basically based on income. The relationship between income and saving can mathematically be stated as in equation shown below and it is termed as saving function.

S = -a + by
S = - 4 + .2Y

Here,
S = Saving;
Y = Income;  
-a = dis-savings.

Marginal tendency to Save MPS is the ratio of change in saving into a change in income. Therefore this is the rate of change in the propensity to saving.

Or MPC = ΔS/ΔY

Here,
ΔS = Change in saving and
ΔY = Change in income

With a rise income, when MPC tends to drop, MPS will tend to increase. When MPC stay constant, MPS will too stay constant. Therefore income comprises of consumption and saving.

Therefore Y = C + S

Or,

MPC + MPS = 1
MPS = 1 – MPC or
MPC = 1 – MPS

In an economy wherever people spend less of their extra income, MPC will be less and the CC curve will be less sheer. It will be noted that the constant (-a) is dis-saving since it is autonomous consumption that is not related to income. The autonomous consumption will became zero in long run. That is, households can’t consume without income in long run. Therefore in long run, the consumption purely based on income and the curve C that begins from origin.

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