Explain that sum total of MPC and MPS equal to 1 ?

Answer : 

We know that:

MPS = ∆S / ∆Y

MPC = ∆C / ∆Y

We also know that:

(Additional income is either used in increasing consumption or saving)

∆Y = ∆C +∆ S

(Dividing both sides of the equation by ∆Y)

∆Y / ∆Y = ∆C / ∆Y + ∆S / ∆Y

1 = MPC + MPS

So that,

MPC + MPS = 1

Or, MPC = 1 – MPS

Or, MPS = 1 – MPC

MPC is generally less than unity and greater than zero. It means that a part of increase in income is consumed and the other part is saved.

So, the aggregate MPC and MPS must be equal to unity. Thus, if half of the increase in income is spent on consumption, the other half must be saved.

So that when MPC = 1/ 2 (half), then MPS = 1/ 2(half) also implying that

MPC + MPS = 1 always.