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For K-12 Students · Cobb-Douglas

Cobb-Douglas for a game-theory standoff

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a game-theory standoff live below — adjust the inputs and watch it respond, right in your browser.

Cobb-Douglas ProductionLive

optimal input mix

Controls

Presets

Capital share α

Budget

Capital rental r

Wage w

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.

▶ Run in Python

Data Inspector

Optimal capital K12.5

Optimal labor L16.7

Output Q14.4

Governing equation

Q = A K^{0.50} L^{0.50} = 14.4, K^{*} = \frac{α B}{r} = 12.5, L^{*} = \frac{( 1 - α ) B}{w} = 16.7

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.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Cobb-Douglas for a game-theory standoff" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.