When income rises, how much more do people spend? The answer drives the multiplier in the next lesson. It is a rate of change: the change in spending per dollar of change in income. Consumption is the largest part of GDP.
Key idea
$$MPC = \dfrac{\Delta C}{\Delta Y} \qquad MPS = \dfrac{\Delta S}{\Delta Y} \qquad MPC + MPS = 1$$ Here $Y$ is disposable (after-tax) income. The MPC is the share of an extra dollar that is spent; the MPS is the share that is saved.
Why it works
Each extra dollar of disposable income can only be spent or saved, so the two shares add to 1. If you spend 80 cents of an extra dollar, you save 20 cents: MPC = 0.8, MPS = 0.2. The word "marginal" means "extra": it is about the change, not the total. A family can spend 95% of its whole income but only 80% of a raise. On a graph of consumption against income, the MPC is the slope.
Worked examples
Worked example: From changes
When income rises from \$500 to \$600 a week, spending rises from \$470 to \$545. Find the MPC and MPS.
- $\Delta Y = 100$ and $\Delta C = 75$.
- $MPC = \dfrac{75}{100} = 0.75$; $MPS = 1 - 0.75 = 0.25$.
- Not $\dfrac{545}{600} \approx 0.91$: that is the share of total income spent (the average propensity to consume).
Answer: MPC 0.75, MPS 0.25
Worked example: Using the MPC
The MPC is 0.9 and disposable income rises by \$200 billion. How much do consumption and saving rise?
- $\Delta C = 0.9 \times 200 = 180$ billion dollars.
- $\Delta S = 0.1 \times 200 = 20$ billion dollars. Check: $180 + 20 = 200$.
Answer: C up \$180 billion; S up \$20 billion
Common mistake
Computing the MPC as total spending over total income. The MPC uses changes: $\Delta C \div \Delta Y$. Check: the MPC must be between 0 and 1, and MPC + MPS must equal exactly 1.