acalculator

What is the MPC?

Enter how much consumption and income changed. The MPC calculator divides one by the other for the marginal propensity to consume, and shows the marginal propensity to save and the spending multiplier. Add a tax rate, imports or a change in spending if you need them.

Your numbers

Taxes, imports and a change in spending
Marginal propensity to consume (MPC)
0.8

Consumption changes by $800.00 when income changes by $1,000.00: an MPC of 0.8 and an MPS of 0.2.

Marginal propensity to save (MPS)
0.2
Spending multiplier
5

Marginal propensity to consume (MPC): 0.8. Consumption changes by $800.00 when income changes by $1,000.00: an MPC of 0.8 and an MPS of 0.2.

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

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

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.

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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Change in consumption $800.00, Change in income $1,000.00 gives Marginal propensity to consume (MPC) 0.8, Marginal propensity to save (MPS) 0.2, Spending 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. Change in consumption $700.00, Change in income $1,000.00, Tax rate 10%, Marginal propensity to import (MPI) 0.1, Change in spending $100.00 gives Marginal propensity to consume (MPC) 0.7, Marginal propensity to save (MPS) 0.3, Spending multiplier 2.13, Change in 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. Change in consumption -$450.00, Change in income -$600.00 gives Marginal propensity to consume (MPC) 0.75, Marginal propensity to save (MPS) 0.25, Spending 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. Change in consumption $2,345.67, Change in income $3,000.00, Tax rate 22.5%, Marginal propensity to import (MPI) 0.15, Change in spending $1,000,000.00 gives Marginal propensity to consume (MPC) 0.78189, Marginal propensity to save (MPS) 0.21811, Spending multiplier 1.84, Change in 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

How it works

  • MPC = change in consumption ÷ change in income
  • MPS = 1 − MPC
  • Spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate ÷ 100) − MPI)); with no tax rate or MPI this is 1 ÷ (1 − MPC) = 1 ÷ MPS
  • Change in GDP = spending multiplier × change in spending, shown when you give a change in spending

Rules:

  • The changes in consumption, income and spending may be negative (a fall). Each is at most $1 quadrillion in size. The tax rate is 0% to 100% and the MPI 0 to 1; an empty one counts as 0.
  • The change in income must not be 0; otherwise there is no answer.
  • The multiplier and the change in GDP are shown only when 1 − (MPC × (1 − tax rate) − MPI) is more than 0. When it is 0 or less (an MPC at or above 1 with few leakages), the page shows the MPC and MPS alone.
  • A result too large to show as a number gives no answer. So does a result that is not 0 but too small to show as a number.
  • The arithmetic is exact on the decimals you type. The MPC and MPS show up to 6 decimals (6 significant figures below 0.0001 in size), the multiplier to 2 decimals and money to the cent, with halves rounded up (away from 0).

Assumptions

  • Income is disposable income, after taxes; the tax rate box is only for the multiplier, which starts from total income.
  • The MPC, tax rate and MPI stay the same in every round of spending.

Worked examples by hand

$800 of $1,000. MPC = 800 ÷ 1,000 = 0.8; MPS = 1 − 0.8 = 0.2; multiplier = 1 ÷ 0.2 = 5.

OpenStax's multiplier with taxes and imports. MPS 30% means MPC = 700 ÷ 1,000 = 0.7. Multiplier = 1 ÷ (1 − (0.7 × (1 − 0.10) − 0.1)) = 1 ÷ 0.47 = 2.1277, shown as 2.13. $100 of spending changes GDP by 100 ÷ 0.47 = $212.77 (OpenStax rounds to $213).

A fall in income. Income falls by $600 and consumption by $450: MPC = −450 ÷ −600 = 0.75; MPS = 0.25; multiplier = 4.

Decimals, with every leakage. MPC = 2,345.67 ÷ 3,000 = 0.78189; MPS = 0.21811. Leakages = 1 − (0.78189 × 0.775 − 0.15) = 0.54403525; multiplier = 1 ÷ 0.54403525 = 1.84. $1,000,000 of spending changes GDP by $1,838,116.19.

Other questions people ask

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.