The Multiplier and Marginal Propensities

Statement

• The multiplier (k) is the number of times national income expands as a result of an initial injection.
• The marginal propensity to consume (MPC) is the ratio of the change in consumption to a change in income.
• The marginal propensity to withdraw (MPW) is the ratio of the change in withdrawals to a change in income.

Notes

These three terms are defined together because the multiplier is computed from the marginal propensities: $k = \dfrac{1}{1 - MPC} = \dfrac{1}{MPW}$. Each propensity is a value between 0 and 1. The MPW decomposes into the marginal propensities to save, to tax and to import, $MPW = MPS + MPT + MPM$ — the three ways an extra dollar of income leaks out of the domestic circular flow rather than being re-spent. The final change in national income follows from $\Delta Y = k \times \Delta J$, where $\Delta J$ is the initial injection; the process that produces it is the multiplier effect.