Savings Income MPC MPS

Marginal Propensity to Consume and Save (MPC / MPS)

In Keynes’s consumption function, what you spend depends on your disposable income: C = a + b·Y. Here b is the marginal propensity to consume, the MPC. Every extra unit of income you get is either spent or set aside, nothing in between, which is why MPC + MPS = 1 and therefore S = (1 − b)·Y − a.

The MPC is what gives you the Keynesian fiscal multiplier k = 1 / MPS = 1 / (1 − MPC). Friedman’s permanent income hypothesis and Modigliani’s life-cycle model add a wrinkle: households try to keep their spending steady against the income they expect over their whole lives (expected lifetime income), so a one-off shock barely moves the short-run MPC. In Brazil the MPC tends to run high, and it climbs higher the poorer the household, which is exactly why cash transfers like Bolsa Família and Auxílio Brasil carry a bigger multiplier.

Applications

It shows up when you size a fiscal stimulus package or design a cash-transfer programme, when you forecast aggregate consumption from wage data, and when you calibrate IS curves and DSGE models. It also helps gauge how a minimum-wage hike or a round of 13th-salary payouts will ripple through retail sales.

FAQ

Why must MPC + MPS equal 1? By definition, disposable income goes either to consumption or to saving, so the two marginal shares have to add up to the full extra unit of income.

What is a typical MPC range? Most empirical estimates land somewhere between 0.5 and 0.9. Poorer households, along with anyone who can’t easily borrow, tend to sit near the top of that range.

Does the multiplier always equal 1/MPS? That clean version only holds in a closed economy with no taxes and no imports. Once you bring in a tax rate t and an import propensity m, the multiplier becomes k = 1 / (1 − b(1−t) + m).