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The marginal propensity to save (MPS = 1 − MPC) is the fraction of additional disposable income that households save. MPC + MPS = 1 always holds.
Derive MPS from consumption function as 1 − MPC. Work through income shock scenarios showing decomposition into consumption and savings.
From the Keynesian consumption function and your understanding of MPC, you know that each additional dollar of disposable income gets split between consuming and not consuming. The part that is not consumed is saved. The marginal propensity to save is simply the complement: MPS = 1 − MPC. If households spend 80 cents of each additional dollar, they save 20 cents — MPS = 0.2. The identity MPC + MPS = 1 holds by definition, because income must either be consumed or saved; there is nowhere else for a dollar to go (within the simple two-use Keynesian framework).
The reason MPS has its own name and importance is that it plays a central role in the fiscal multiplier. The spending multiplier is 1 / (1 − MPC) = 1 / MPS. A government spending increase of $100 billion in an economy where MPS = 0.2 generates a total output increase of $500 billion, because each round of spending becomes income for someone else, 80% of which gets re-spent, 80% of that gets re-spent again, and so on. A higher MPS means each round of additional income leaks out of the spending cycle faster — savings are a "leakage" — so the multiplier is smaller. An economy where households save 40 cents of every extra dollar has a multiplier of only 2.5, compared to 5 when they save 20 cents. This is why fiscal stimulus is more powerful in economies where households have high MPC (low MPS), and less powerful where households are cautious savers.
The distinction between MPS and the average propensity to save (APS) matters for correctly interpreting data. APS is total saving divided by total income — it describes the fraction of all income that is saved, not just the fraction of the last dollar. MPS describes behavior at the margin. Empirically, higher-income households tend to have both higher APS (they save more of their total income) and higher MPS (they save more of additional income). This means aggregate MPS is not fixed but rises with the income distribution — shifts in income toward higher earners raise aggregate MPS, while redistribution toward lower-income households who have high MPC can increase the fiscal multiplier. Understanding MPS is therefore not just about bookkeeping; it connects saving behavior to the dynamics of income determination and fiscal policy effectiveness.