Tariff-quota equivalence calculator
With a world price of 8, a tariff of 2 lifts the domestic price to 10 and cuts imports to 2, so a quota of 2 has the same effect, an ad valorem equivalent of 25%. Free in your browser.
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Worked example
- Demand intercept
- 20
- Demand slope
- 1
- Supply intercept
- 2
- Supply slope
- 1
- World price
- 8
- Calculate
- Quota from tariff
- Autarky price
- 11
- Autarky quantity
- 9
- Free trade demand
- 12
- Free trade supply
- 6
In a small open economy the world price is given, so a specific tariff and a binding import quota can be set to produce the same domestic price, the same production, and the same consumption. That is the Lerner equivalence result for competitive markets: the quota that replicates a tariff is simply the import volume that occurs under the tariff, and the tariff equivalent of a quota is the wedge between the quota-ridden domestic price and the world price. This tariff-quota equivalence calculator accepts linear inverse demand and inverse supply, the world price, and either a specific tariff or an import quota. It returns the matching instrument, the ad valorem equivalent, free-trade and protected quantities, the rent rectangle, surplus changes, and deadweight loss.
What tariff–quota equivalence means in a small open economy
Two instruments are equivalent in a small open economy when they produce the same domestic price. Linear inverse demand is written P equals a minus b Q, so quantity demanded at a price P is a minus P, divided by b. Linear inverse supply is written P equals c plus d Q, so quantity supplied is P minus c, divided by d.
The world price is exogenous: the country is too small to move it. At that world price the country must be a competitive importer, which means free-trade demand exceeds free-trade supply and the gap is free-trade imports. Autarky is the opposite corner, where the two domestic curves cross and imports are zero.
A specific tariff t raises the internal price to the world price plus t, provided that wedge does not overshoot autarky. Imports then fall to demand minus supply at the new price, and that residual import volume is exactly the quota that replicates the tariff. Conversely, a binding quota of M units clears when excess demand equals M.
Solving the linear excess-demand schedule for price yields the quota-ridden domestic price, and the tariff equivalent is that price minus the world price. The ad valorem equivalent is the same wedge divided by the world price. Under competition the two instruments then share production, consumption, and the two Harberger triangles; they differ only in who receives the rectangle between the domestic price and the world price — the treasury under a tariff, licence holders under a quota.
A wedge large enough to reach autarky is prohibitive: the equivalent quota is zero. A quota at or above free-trade imports is not binding: the tariff equivalent is zero and the domestic price stays at the world price.
Where a tariff–quota equivalence calculator earns its keep
International-trade and intermediate-micro courses use a tariff quota equivalence calculator so students can convert any specific tariff into the quota that holds the same domestic price, or invert a quota into the specific and ad valorem equivalents, without mixing up the rent rectangle with the two deadweight-loss triangles or forgetting that a small country cannot push the world price.
Exam generators and LMS plugins need a deterministic oracle that rejects a world price at or above autarky, a negative instrument, or a downward-sloping supply, instead of inventing a hollow zero-import success that a buggy grader might treat as a correct prohibitive case. Failed validation does not consume balance.
Keep requests small, pin the rounded domestic price, equivalent quota, ad valorem rate, rent and deadweight loss in tests, and you get reproducible two-instrument identities for homework, LMS plugins, and edge workers without standing up a full computable general-equilibrium stack of your own.
What you can do with it
Classroom and problem-set checks
Convert a textbook specific tariff into the quota that holds the same domestic price, or invert a quota into the specific and ad valorem equivalents, and check the rent rectangle against the two Harberger triangles.
Exam and LMS auto-grading
Mark tariff–quota equivalence items with a deterministic oracle that rejects a non-importing world price and never invents a wedge when the quota is not binding.
Policy notebooks and licence-versus-levy briefs
Tabulate equivalent instruments for a small importer when comparing a levy that raises revenue with a quota that assigns the same rent to licence holders.
FAQ
How do I find the import quota that replicates a tariff?
The equivalent quota is demand minus supply at the protected domestic price Pw plus t, capped at autarky.
How do I find the tariff equivalent of a quota?
The specific equivalent is the quota-ridden domestic price minus the world price; the ad valorem equivalent is that wedge divided by the world price.
Are a tariff and a quota really equivalent?
In a small competitive economy they produce the same price, production, consumption and deadweight loss when they admit the same imports. They differ in who receives the rent rectangle: the treasury under a tariff, licence holders under a quota.
What if the tariff is prohibitive or the quota is not binding?
A tariff at least as large as autarky minus the world price yields equivalent quota zero and prohibitive true. A quota at or above free-trade imports yields tariff equivalent zero and binding false.
Who receives the rent under each instrument?
Under a tariff the rectangle between the domestic and world price goes to the treasury; under a quota it goes to licence holders. In the example both create a rent of 4 and the same deadweight loss of 4.
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/tariff-vs-quota-equivalent \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"demand_intercept":20,"demand_slope":1,"supply_intercept":2,"supply_slope":1,"world_price":8,"tariff":2}'const res = await fetch("https://api.kit.forhosting.com/econ/tariff-vs-quota-equivalent", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"demand_intercept": 20,
"demand_slope": 1,
"supply_intercept": 2,
"supply_slope": 1,
"world_price": 8,
"tariff": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/econ/tariff-vs-quota-equivalent",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"demand_intercept": 20,
"demand_slope": 1,
"supply_intercept": 2,
"supply_slope": 1,
"world_price": 8,
"tariff": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/tariff-vs-quota-equivalent", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"demand_intercept":20,"demand_slope":1,"supply_intercept":2,"supply_slope":1,"world_price":8,"tariff":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"demand_intercept":20,"demand_slope":1,"supply_intercept":2,"supply_slope":1,"world_price":8,"tariff":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/tariff-vs-quota-equivalent", 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": 20,
"demand_slope": 1,
"supply_intercept": 2,
"supply_slope": 1,
"world_price": 8,
"tariff": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "econ.tariff_vs_quota_equivalent",
"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
Input contract, closed-form identities, and validation
Optional decimals is an integer from zero through twelve and defaults to six. Example: a equals twenty, b equals one, c equals two, d equals one, world price eight and tariff two yields domestic price ten, imports two, an ad valorem equivalent of twenty-five percent, rent of four and deadweight loss of four. The same market with quota two inverts to the same wedge. POST a JSON body with five required finite numbers that describe the market: demand_intercept a and demand_slope b of inverse demand P equals a minus b Q; supply_intercept c and supply_slope d of inverse supply P equals c plus d Q; and world_price, the exogenous Pw. Slopes must be strictly positive, a must exceed c so the curves cross, and Pw must lie strictly between c and the autarky price so free-trade supply is positive and the country is a net importer. solve_for is an enum: quota_from_tariff, the default, recovers the equivalent import quota from a specific tariff; tariff_from_quota recovers the specific and ad valorem tariff equivalents from a quota. Send tariff (aliases t, specific_tariff) or quota (aliases import_quota, q); at least one is required. Missing fields, empty strings, non-finite values, a non-positive slope or world price, a negative tariff or quota, a world price that does not make the country an importer, and an unknown solve_for all fail with invalid_input and are not billed. On success the body echoes the curves and world price, returns autarky_price and autarky_quantity, free_trade_demand, free_trade_supply and free_trade_imports, then the protected domestic_price, domestic_demand, domestic_supply and imports. specific_tariff is the effective wedge, ad_valorem_tariff is that wedge over Pw, ad_valorem_percent is one hundred times the fraction, and equivalent_quota equals protected imports. rent is the rectangle t times M (tariff revenue or quota rent). consumer_surplus_change and producer_surplus_change are the usual linear triangles relative to free trade; deadweight_loss equals one half times t times the fall in imports. binding is true when imports sit below free-trade imports; prohibitive is true when imports are zero.
Where a tariff–quota equivalence calculator earns its keep
Policy notebooks and consulting workbooks often tabulate “tariff-rate quota” and “licence versus levy” scenarios for briefings; pinning the arithmetic in a tiny parse API keeps spreadsheet drift out of the comparison column when someone later changes only the slope of demand.
Technical questions
What does the tariff-quota equivalence calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.