How much capital versus labor should a firm buy? The Cobb-Douglas function answers it — the workhorse model of production and growth economics.
Cobb-Douglas ProductionLive
optimal input mix
Controls
Presets
The Cobb-Douglas function Q = A·Kᵅ·L¹⁻ᵅ describes how capital and labor combine to make output. Isoquants show input mixes yielding the same output; the budget line shows what you can afford. Production is maximized where the budget line just touches the highest isoquant — the cost-minimizing input mix, splitting spending by the exponents.
Reading this result: Cost-minimizing plan spends 50% of the budget on capital and 50% on labor — the exponents fix these shares no matter what r and w are; prices only change how many units of each that money buys.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
The Cobb-Douglas function Q = A·Kᵅ·L¹⁻ᵅ combines capital and labor into output, with the exponents setting each input's importance. Isoquants trace input mixes giving the same output, and the budget line shows affordability. Output is maximized where the budget line is tangent to the highest isoquant — spending split by the exponents. The same math describes consumer utility.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this Cobb-Douglas production function tool really free?▾
Yes. Cobb-Douglas Production runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.