Consumption and saving both are functions of money income, therefore, it is possible to establish a relationship between propensity to consume and propensity to save.

The sum of the Average Propensity to Consume (APC) and Average Propensity to save (APS) is always equal to unity, i.e., APC + APS = 1. It is so because the money income can either be spent on consumption or it can be saved. In case, we consider the ratio of consumption to money income, we call it average propensity to consume, (APC), and the ratio of saving to income represents average propensity to save (APS). It is for his reason that the sum of APC and APS equals unity.

Symbolically,

APC = C/Y and  APS = S/Y

We know that Y = C + S

APC = APS = C/Y + S/Y = C+S/Y = Y/Y = 1

Hence    APC + APS = 1

The sum of the Marginal Propensity to Consume (MPS) and Marginal propensity to Save (MPS) is always equal to unity, i.e. MPC + MPS = 1.

It is so because MPC shows the ratio of change inc consumption, i.e., ΔC/ ΔY, whereas MPS shown the ratio of change in saving to change in income, i.e., ΔS/ΔY. Increased income could again be spent either on consumption or can be saved.

Symbolically,

                            MPC = ΔC/ΔY and MPS = ΔS/ΔY
We known that   ΔY = ΔC + ( )S

MPC + MPS = ΔC/ ΔY + ΔS/ΔY = ΔC+ΔS/ΔY

                          = ΔY/ΔY = 1

Hence          MPC + MPS = 1

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