Mathematical Relationship between MPC and MPS!

The sum of MPC and MPS is equal to unity (i.e., MPC + MPS = 1).

For sake of convenience, suppose a man’s income Increases by Rs 1. If out of it, he spends 70 paise on consumption (i.e., MPC = 0.7) and saves 30 paise (i.e., MPS = 0 3) then MPC + MPS = 0.7 + 0.3 = 1.

MPC + MPS = I as proved below. We know that income (Y) is either spent on consumption (C) or saved (S).

Symbolically:

Y =C + S

or

∆Y = ∆C + ∆S

By dividing both sides by AY, we get:

∆Y/∆Y = ∆C/∆Y = ∆S/∆Y

or

I = MPC + MPS

From this, the relationship can also be expressed in the following way:

MPC =1-MPS

MPS =1-MPC

Clearly if one is given, we can find out the other because the sum of MPC and MPS is equal to unity, i.e., Incremental (additional) income.

What is the value of MPC when MPS is zero?

The value of MPC is equal to unity (i.e., 1) when MPS is zero since whole of disposable income is spent on consumption. Again, value of MPC cannot he greater than 1 because change in consumption (i.e., additional consumption) cannot be more than change in income (i.e., additional income).

MPC or MPS cannot be negative because MPS is ratio between additional saving (∆S) and additional income (∆Y) and similarly MPC is ratio between additional consumption (∆C) and additional Income (∆Y). Here, additional shows positive (+) value.