ForHosting KIT · Developer Utilities

Total product from production function

Total product is the output a firm can produce from a chosen quantity of one variable input when every other factor stays fixed.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Intermediate microeconomics writes that short-run map as a cubic polynomial, TP of L equals a times L plus b times L squared plus c times L cubed, because the cubic is the simplest closed form that can rise, flatten, and then fall — the shape that creates the three classical stages of production. This calculator evaluates total product at your labor (or other variable input), differentiates the same polynomial for marginal product, forms average product when L is positive, and labels the stage from the MP versus AP comparison. Students use it to check homework tables; instructors and LMS plugins use it as a deterministic oracle; analysts use it when a fitted cubic must become a single TP, MP, and stage at a planned staffing level. The same analytic path powers the free browser widget and the API, so homework keys and production notebooks never disagree on a derivative that is only a few multiplications.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

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/econ/total-product-from-function

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/total-product-from-function \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"linear_coef":10,"quadratic_coef":5,"cubic_coef":-0.5,"labor":4}'

const res = await fetch("https://api.kit.forhosting.com/econ/total-product-from-function", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "linear_coef": 10,
    "quadratic_coef": 5,
    "cubic_coef": -0.5,
    "labor": 4
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/econ/total-product-from-function",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "linear_coef": 10,
    "quadratic_coef": 5,
    "cubic_coef": -0.5,
    "labor": 4
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/total-product-from-function", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"linear_coef":10,"quadratic_coef":5,"cubic_coef":-0.5,"labor":4}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"linear_coef":10,"quadratic_coef":5,"cubic_coef":-0.5,"labor":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/total-product-from-function", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "linear_coef": 10,
  "quadratic_coef": 5,
  "cubic_coef": -0.5,
  "labor": 4
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "econ.total_product_from_function",
  "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.

Read the full KIT documentation →