Monopoly Deadweight Loss Calculator for a Linear Market
See how much welfare a monopoly loses by cutting output: with a demand intercept of 100, a slope of 2 and marginal cost of 20, output falls from 40 to 20, price rises to 60 and the deadweight loss is 400. Free in your browser.
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Worked example
- Demand intercept
- 100
- Demand slope
- 2
- Marginal cost
- 20
- Competitive quantity
- 40
- Monopoly quantity
- 20
- Monopoly price
- 60
- Quantity reduction
- 20
The monopoly deadweight loss calculator estimates how much total welfare is lost when a single profit-maximizing seller restricts output in a linear market. Enter the intercept and slope from inverse demand, plus constant marginal cost. The calculator finds the competitive quantity, monopoly quantity, monopoly price, output reduction, price-cost markup, and the welfare triangle between the two quantities. It is designed for economics coursework, policy analysis, market models, and quick checks of a standard linear-demand result.
Describe the linear market correctly
Start with inverse demand written as P = a - bQ. The demand intercept is a: the price at which quantity demanded would fall to zero. The demand slope is b, a positive number that describes how quickly willingness to pay falls as output rises.
Enter constant marginal cost as c, using the same currency per unit as price. The calculator assumes one market, a single-price monopolist, no price discrimination, and no taxes or externalities. It also assumes marginal cost is horizontal, so fixed cost does not change the profit-maximizing quantity or the welfare triangle.
The intercept must exceed marginal cost; otherwise the model has no positive competitive output. Pay close attention to units. If quantity is measured in thousands of items, the returned quantities use thousands of items and the deadweight-loss figure is in thousands of currency units.
Rescale the result if you need a total stated in individual items. Do not enter the slope from direct demand Q as a function of P without first rearranging it into inverse-demand form.
How monopoly output and the welfare triangle are calculated
Under competition, price equals marginal cost. Substituting P = c into inverse demand gives the competitive quantity Qc = (a - c) / b. A monopolist instead chooses output where marginal revenue equals marginal cost.
For linear inverse demand, marginal revenue has the same intercept and twice the slope, so MR = a - 2bQ. Solving MR = c gives monopoly quantity Qm = (a - c) / (2b). Substituting Qm into demand gives monopoly price.
The units between Qm and Qc are not produced even though buyers value them above marginal cost. Their lost gains from trade form a triangle. Its base is the quantity reduction, Qc - Qm, and its height is the monopoly price minus marginal cost.
Deadweight loss is one half times that base times that height. The result measures lost total surplus, not monopoly profit, consumer spending, or the transfer of surplus from consumers to the producer. The output includes each intermediate quantity so the calculation is transparent and easy to audit.
Interpret the estimate and know its limits
Treat the result as a model-based estimate whose quality depends on the demand and cost inputs. A larger gap between the demand intercept and marginal cost increases both the restricted quantity and the markup, so deadweight loss rises rapidly. A steeper inverse-demand slope reduces the quantity scale and therefore changes the triangle's area.
When comparing markets, keep currency, time period, and quantity units consistent. The standard calculation is useful for classroom exercises, merger screening scenarios, regulated-industry discussions, and sensitivity analysis, but it does not establish that a real firm is a monopolist. Real markets may have multiple products, nonlinear demand, increasing marginal cost, capacity limits, uncertainty, entry, strategic rivals, quality changes, or price discrimination.
Those features can move the profit-maximizing outcome away from this benchmark. The calculator also does not add distributional weights: a transfer from buyers to the monopolist changes who receives surplus but is not itself counted as deadweight loss. Use several plausible demand and cost estimates when inputs are uncertain, and explain the assumptions beside any reported figure.
What you can do with it
Check an economics exercise
Verify the competitive benchmark, monopoly price and quantity, and welfare loss for a linear inverse-demand problem.
Run policy sensitivities
Compare how alternative marginal-cost or demand estimates change the output restriction and deadweight-loss triangle.
Document a market model
Produce transparent intermediate values that can be reviewed alongside the assumptions in an internal economic analysis.
FAQ
What demand equation does the calculator use?
It uses linear inverse demand P = a - bQ, where a is the demand intercept and b is a strictly positive slope coefficient.
Why must the demand intercept exceed marginal cost?
That condition creates a positive competitive quantity. If marginal cost equals or exceeds the maximum willingness to pay, this positive-output monopoly model does not apply.
Is monopoly profit the same as deadweight loss?
No. Profit includes surplus transferred from consumers to the monopolist. Deadweight loss counts gains from trade that disappear because output is restricted.
Does fixed cost affect this result?
Not in this standard model. A fixed cost changes profit but not the output choice or welfare triangle when marginal cost remains constant.
What units does deadweight loss use?
It uses price units multiplied by quantity units. If quantity is entered in thousands, the welfare result is also scaled in thousands of currency units.
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
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/econ/monopoly-deadweight-loss \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"demand_intercept":100,"demand_slope":2,"marginal_cost":20}'const res = await fetch("https://api.kit.forhosting.com/econ/monopoly-deadweight-loss", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"demand_intercept": 100,
"demand_slope": 2,
"marginal_cost": 20
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/econ/monopoly-deadweight-loss",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"demand_intercept": 100,
"demand_slope": 2,
"marginal_cost": 20
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/monopoly-deadweight-loss", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"demand_intercept":100,"demand_slope":2,"marginal_cost":20}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"demand_intercept":100,"demand_slope":2,"marginal_cost":20}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/monopoly-deadweight-loss", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"demand_intercept": 100,
"demand_slope": 2,
"marginal_cost": 20
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "econ.monopoly_deadweight_loss",
"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
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
Interpret the estimate and know its limits
Browser calculations are free; automated API requests cost $0.002 each.
Technical questions
What does the API request cost?
Each API request costs $0.002. You can also run the same deterministic calculation free in your browser.