Lerner index calculator
Gauge how much pricing power a firm has: a price of 100 with a marginal cost of 60 gives a Lerner index of 0.4, or 40%, a moderate level of market power. Zero means price equals marginal cost. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Price
- 100
- Marginal cost
- 60
- Price cost gap
- 40
- Lerner index
- 0.4
- Lerner percent
- 40
- Market power band
- moderate_market_power
The Lerner index is the standard single-number measure of firm-level market power in microeconomics and industrial organization: it expresses how far price sits above marginal cost as a fraction of price itself. When price equals marginal cost the index is zero, the competitive benchmark; when marginal cost is far below price the index approaches one, the extreme monopoly case. This Lerner index market power calculator accepts a positive market price and a non-negative marginal cost that does not exceed price, returns the price–cost gap, the index on the unit interval, a percent form for slides and reports, and a coarse band label for classroom display.
What the Lerner index measures and why it sits between zero and one
Under profit maximization with a smooth demand curve the index also equals the negative reciprocal of the firm’s residual demand elasticity, which is why a very elastic residual demand forces L near zero while inelastic residual demand permits a large gap. Perfect competition is the special case where residual demand is infinitely elastic, price equals marginal cost, and L is exactly zero.
As residual demand becomes less elastic, the firm can raise price further above cost and L rises toward one; L equals one would require marginal cost of zero at a positive price. This calculator enforces the textbook domain used in principles and intermediate courses: price must be strictly positive, marginal cost must be non-negative and no greater than price, so every successful result lies in the closed interval from zero to one.
The response also echoes a short formula string L equals (P minus MC) over P so learners can line up the algebraic identity with the numeric fields without consulting a separate reference sheet.
Where measuring market power helps
Principles and industrial-organization courses use a Lerner index market power calculator so students can convert any valid price and marginal-cost pair into the canonical [0, 1] measure without mixing markup-on-cost with the Lerner ratio. Exam generators and LMS plugins need a deterministic oracle that rejects zero or negative prices and cost above price instead of inventing a hollow zero that a buggy grader might treat as perfect competition. Failed validation does not consume balance.
Keep requests small, pin the rounded index and percent fields in tests, and you get reproducible market-power numbers for homework, LMS plugins, and edge workers without standing up a full industrial-organization simulation stack of your own.
What you can do with it
Classroom market-power checks
Let students enter price and marginal cost and verify L=(P−MC)/P on the unit interval against textbook worked examples.
LMS and exam auto-grading
Mark Lerner-index items with a deterministic oracle that rejects non-positive price or marginal cost above price.
Antitrust and IO notebooks
Batch-compute firm-level Lerner indices from price and cost proxies without spreadsheet formula drift.
FAQ
How is the Lerner index calculated?
L = (P − MC) / P. Send a positive price P and a marginal cost MC with 0 ≤ MC ≤ P.
Can the Lerner index be greater than one?
Not with this calculator. MC is required to be non-negative and at most equal to price, so L stays in [0, 1].
Is this the same as markup over cost?
No. Markup over cost is (P − MC) / MC. The Lerner index divides the same gap by price, so it is always between zero and one when P ≥ MC ≥ 0.
What does a Lerner index of zero mean?
It means price equals marginal cost, the benchmark of perfect competition. The further marginal cost sits below price, the closer the index gets to one, the extreme monopoly case.
How is the Lerner index related to demand elasticity?
When a firm maximizes profit, the index equals the negative reciprocal of the elasticity of the demand it faces. Very elastic demand keeps the index near zero; less elastic demand allows a larger gap.
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/lerner-index \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"price":100,"marginal_cost":60}'const res = await fetch("https://api.kit.forhosting.com/econ/lerner-index", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"price": 100,
"marginal_cost": 60
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/econ/lerner-index",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"price": 100,
"marginal_cost": 60
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/lerner-index", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"price":100,"marginal_cost":60}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"price":100,"marginal_cost":60}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/lerner-index", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"price": 100,
"marginal_cost": 60
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "econ.lerner_index",
"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
What the Lerner index measures and why it sits between zero and one
Abba Lerner’s classic definition writes market power as the relative markup of price over marginal cost: L equals price minus marginal cost, all divided by price. That ratio is dimensionless, so a firm charging one hundred with marginal cost sixty has the same index of zero point four as a firm charging ten with marginal cost six. Inputs that would produce a negative index (cost above price) or a non-finite ratio are rejected as invalid_input rather than returned as a silent negative that confuses graders.
Input contract, response fields, and validation rules
Optionally send decimals as an integer from zero through twelve (default six) to control half-up rounding on every computed field. Price must be strictly greater than zero because division by price is the defining step of the index. POST a JSON body with two required finite numbers: price (market price P) and marginal_cost (unit marginal cost MC). Marginal cost must be greater than or equal to zero and must not exceed price; a cost above price would push L below zero, outside the zero-to-one range this endpoint certifies. Missing fields, empty strings, non-finite values, and non-integer decimals outside the allowed range fail with invalid_input and are not billed. Common aliases are accepted: p or selling_price for price, and mc, cost, or unit_cost for marginal_cost. On success the body returns the echoed price and marginal_cost (rounded), price_cost_gap as P minus MC, lerner_index as the unit-interval ratio, lerner_percent as one hundred times the index for charts that want a percent axis, market_power_band as a coarse classroom label (perfect_competition, low_market_power, moderate_market_power, high_market_power, or near_monopoly), and formula. Example: price one hundred and marginal cost sixty yields gap forty, Lerner index zero point four, forty percent, and moderate_market_power. Pair the numbers with your own demand estimate if you need the elasticity interpretation L equals negative one over epsilon; this endpoint computes only the price–cost form of the index and does not estimate demand curves or multi-product cost functions.
Where a Lerner index API earns its keep
Consulting notebooks and antitrust worksheets often tabulate firm-level L values from accounting proxies for marginal cost; pinning the arithmetic in a tiny parse API keeps spreadsheet drift out of the comparison column.
Technical questions
What does a Lerner index of zero mean?
L = 0 when price equals marginal cost, the perfect-competition benchmark with no price–cost margin relative to price.
What does the Lerner index market power calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.