# What is the MPC?

Computes the marginal propensity to consume (MPC) from changes in consumption and income, with the marginal propensity to save and the spending multiplier.

- Page: https://www.acalculator.org/finance/mpc-calculator
- JSON spec: https://www.acalculator.org/finance/mpc-calculator.json
- Version: e8590e1f28e3

## Default answer

Example with the default inputs (Change in consumption $800.00, Change in income $1,000.00): Consumption changes by $800.00 when income changes by $1,000.00: an MPC of 0.8 and an MPS of 0.2.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| dc | Change in consumption | How much consumer spending rose (or fell, as a negative number). |
| dy | Change in income | How much disposable income rose (or fell, as a negative number) at the same time. |
| tax | Tax rate | The share of extra income taken in taxes, for the multiplier. Optional; empty means 0%. |
| mpi | Marginal propensity to import (MPI) | The share of extra income spent on imports, from 0 to 1, for the multiplier. Optional; empty means 0. |
| spend | Change in spending | A change in government spending or investment, to see its effect on GDP through the multiplier. Optional. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mpc | Marginal propensity to consume (MPC) | Change in consumption ÷ change in income. |
| mps | Marginal propensity to save (MPS) | 1 − MPC. |
| multiplier | Spending multiplier | 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)); with no taxes or imports, 1 ÷ (1 − MPC). |
| gdp | Change in GDP | Spending multiplier × change in spending. |

## Method

MPC = change in consumption ÷ change in income. MPS = 1 − MPC. Spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)), shown when the denominator is more than 0. Change in GDP = multiplier × change in spending.

## Assumptions

- Consumption and income change over the same period; income is disposable (after-tax) income for the MPC.
- An empty tax rate or MPI counts as 0, which gives the simple multiplier 1 ÷ (1 − MPC) = 1 ÷ MPS.
- Arithmetic is exact on the typed decimals; the MPC and MPS show up to 6 decimals (6 significant figures below 0.0001 in size), the multiplier to 2 and money to the cent.

## Worked examples

1. dc = $800.00, dy = $1,000.00 gives mpc = 0.8, mps = 0.2, multiplier = 5. Source: OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model: 800 ÷ 1,000 = 0.8.
2. dc = $700.00, dy = $1,000.00, tax = 10%, mpi = 0.1, spend = $100.00 gives mpc = 0.7, mps = 0.3, multiplier = 2.13, gdp = $212.77. Source: OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model: 1 ÷ (1 − (0.7 × 0.9 − 0.1)) = 1 ÷ 0.47 = 2.13 (exact 100/47).
3. dc = -$450.00, dy = -$600.00 gives mpc = 0.75, mps = 0.25, multiplier = 4. Source: OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model.
4. dc = $2,345.67, dy = $3,000.00, tax = 22.5%, mpi = 0.15, spend = $1,000,000.00 gives mpc = 0.78189, mps = 0.21811, multiplier = 1.84, gdp = $1,838,116.19. Source: OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model.

## FAQ

### What is the marginal propensity to consume?

The marginal propensity to consume (MPC) is the share of an extra dollar of income that people spend on consumption. An MPC of 0.8 means 80 cents of each extra dollar is spent and 20 cents saved.

### How do I calculate the MPC?

Divide the change in consumption by the change in income. If income rises by $1,000 and consumption by $800, the MPC is 800 ÷ 1,000 = 0.8.

### What is the marginal propensity to save?

The share of an extra dollar of income that is saved. With no other use for the money, MPC + MPS = 1, so MPS = 1 − MPC: an MPC of 0.8 gives an MPS of 0.2.

### How does the MPC give the spending multiplier?

Each dollar spent becomes someone else’s income, and part of it is spent again. With no taxes or imports the multiplier is 1 ÷ (1 − MPC): an MPC of 0.8 gives 1 ÷ 0.2 = 5, so $100 of new spending can raise GDP by $500.

### How do taxes and imports change the multiplier?

They are leakages: money taxed or spent on imports is not spent again at home. The multiplier becomes 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)). With an MPC of 0.7, a 10% tax rate and an MPI of 0.1, it is 1 ÷ 0.47 = 2.13.

### Can the MPC be more than 1?

For a household, yes, for a time: spending can rise by more than income when people borrow or draw on savings. The MPS is then negative. A multiplier needs leakages above zero, so this calculator shows none in that case.

## Sources

- OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model: the marginal propensity to consume is the share of the additional dollar of income devoted to consumption, the marginal propensity to save the share saved, MPC + MPS = 1 (when income rises by $1,000 with an MPC of 0.8, consumption rises by $800); spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)), with MPS 30%, a 10% tax rate and an MPI of 10% giving 1 ÷ 0.47 = 2.13, so $100 of spending raises GDP by $213. https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model (retrieved 2026-10-19)