ForHosting KIT · Finance & money

Spending multiplier calculator

With a marginal propensity to consume of 0.8 the multiplier is 5, so an injection of 100 lifts equilibrium output by 500. Enter the spending change and the MPC to check a problem set or sketch a stimulus effect. Free in your browser.

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Worked example

If you enter

Spending: 100
Mpc: 0.8

You get

Mps: 0.2
Multiplier: 5
Output change: 500

The Keynesian spending multiplier converts a one-time injection of autonomous spending into the larger change in equilibrium output that follows when households re-spend a fraction of each extra unit of income. That fraction is the marginal propensity to consume, or MPC: the share of an extra unit of disposable income that is spent rather than saved. In the simple closed-economy model with no income tax and no imports, the multiplier equals one divided by one minus MPC, and the change in output equals the injection times that multiplier. Students checking problem sets, instructors grading fiscal-impulse items, and analysts sketching a first-pass stimulus effect all need the same deterministic arithmetic: given a spending injection and an MPC, return the multiplied output. This calculator accepts a finite spending amount and an MPC between zero and one (including zero, excluding one), and it rejects an out-of-range MPC instead of returning an infinite or negative multiplier.

What the spending multiplier is and how the geometric series sums

The simple Keynesian spending multiplier is the factor by which an autonomous change in spending is multiplied to obtain the change in equilibrium national output. Households consume a fraction MPC of each extra unit of disposable income and save the complementary fraction, the marginal propensity to save. The first round of spending becomes someone else's income; that recipient spends MPC of it; the next recipient spends MPC of that remainder, and the chain continues.

The infinite geometric series one plus MPC plus MPC squared plus MPC cubed and so on sums to one over one minus MPC whenever the absolute value of MPC is less than one. Therefore the change in output, written Delta Y, equals the initial spending injection times one over one minus MPC. If MPC is zero point eight, the multiplier is five, so a one-hundred-unit injection raises equilibrium output by five hundred units.

If MPC is zero point five, the multiplier is two. If MPC is zero, nobody re-spends and the multiplier is one: output rises only by the original injection. If MPC were one, the series would not converge and the formula would divide by zero, which this calculator treats as invalid input rather than Infinity.

The identity is the closed-economy, lump-sum-tax, no-import version taught in principles of macroeconomics. Real economies also leak through taxes and imports, which shrink the effective multiplier; those extensions need extra parameters and are out of scope here. This capability implements only the two-input workhorse: spending and MPC in, multiplier and output change out.

What you can do with it

Homework and exam multiplier checks

Students enter a spending injection and an MPC from a problem set and verify ΔY = spending × 1/(1 − MPC) against textbook keys.

First-pass fiscal output sketches

Convert an announced spending package and a published household MPC into a first-pass output change before adding taxes or imports.

FAQ

What is the formula for the spending multiplier?

The simple multiplier is 1/(1 − MPC). The change in output is ΔY = spending × 1/(1 − MPC).

Why must MPC be between 0 and 1?

MPC is a share of extra disposable income spent.

What happens if the spending injection is negative?

A negative spending value is a spending cut.

Is this the money multiplier or the tax multiplier?

No. This tool is the Keynesian spending multiplier from an injection and MPC. The money multiplier uses the reserve ratio; the tax multiplier uses −MPC/(1 − MPC). Those are different searches.

Why does this multiplier leave out taxes and imports?

It uses the simple closed-economy model from principles of macroeconomics, with no income tax and no imports. In real economies those leaks shrink the multiplier, and modeling them needs extra inputs that this calculator does not take.

Related tools

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/fin/spending-multiplier

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/fin/spending-multiplier \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"spending":100,"mpc":0.8}'

const res = await fetch("https://api.kit.forhosting.com/fin/spending-multiplier", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "spending": 100,
    "mpc": 0.8
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/fin/spending-multiplier",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "spending": 100,
    "mpc": 0.8
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/fin/spending-multiplier", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"spending":100,"mpc":0.8}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"spending":100,"mpc":0.8}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/fin/spending-multiplier", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "spending": 100,
  "mpc": 0.8
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "fin.spending_multiplier",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Technical notes

Successful API calls use prepaid balance at $0.002 per item; invalid input is not billed.

Inputs, outputs, validation, and how to call the calculator

Numeric strings that parse to finite numbers are accepted so form posts and spreadsheet exports work without an extra cast. The MPC must lie between zero and one, including zero and excluding one: values below zero or at or above one are rejected because they are not valid spending shares in this model and because MPC equal to one would make the denominator zero. Spending may be positive (a stimulus or investment impulse), zero, or negative (a spending cut); a negative injection produces a negative output change of the same multiplier magnitude. Values are rounded to twelve decimal places for stable goldens across runtimes. POST a JSON body with two required finite numbers: spending, the initial autonomous spending injection in any consistent currency units, and mpc, the marginal propensity to consume expressed as a fraction of extra income. Aliases are accepted: injection, initial_spending, delta_g, government_spending, and amount for spending; marginal_propensity_to_consume for mpc. Missing fields, empty strings, non-numeric text, Infinity, and NaN fail with invalid_input naming the field. On success the response echoes spending and mpc, reports mps as one minus mpc, reports multiplier as one over one minus mpc, reports output_change as spending times the multiplier, and includes a formula string restating Delta Y equals spending times one over one minus MPC. Example: spending one hundred and mpc zero point eight yields mps zero point two, multiplier five, and output_change five hundred. The browser tool is free for interactive checks; successful API calls use prepaid balance at $0.002 per item, and failed validation is not billed.

Where a spending-multiplier calculator earns its keep

Introductory macroeconomics courses assign spending-multiplier problems because the geometric re-spending story is the first link between a fiscal impulse and GDP. Tutoring sites and LMS plugins need a deterministic oracle that rejects an MPC of one point two or minus zero point one instead of silently returning a negative or infinite multiplier that a buggy grader might accept. Policy and forecasting notebooks that start from a published household MPC often convert an announced spending package into a first-pass output effect before layering taxes, imports, or crowding-out; a single validated call avoids off-by-one errors when analysts flip between percent and fraction notation. Pair those intents with their own calculators; keep this surface focused on Delta Y from a spending injection and an MPC. Because every successful call stays cheap at $0.002 with no language model in the path, you can wire the endpoint into bulk homework generators without token budgets. This page is not an MPC-from-MPS complement, which answers a different search (given the saving rate, return one minus that rate). It is also not a money multiplier, which uses the reserve ratio in banking, and not a tax-multiplier or balanced-budget-multiplier tool.

Integration use cases

LMS and tutoring auto-grading

Score fiscal-impulse items with a deterministic oracle that rejects MPC outside [0, 1) as invalid_input instead of an infinite multiplier.

Technical questions

What does the spending multiplier calculator cost?

The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.

Read the full KIT documentation →

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