Production Function

The production function tells the quantity that the firm produces given its level of Capital (K) and Labor (L).

Example

Ziggy runs a cookie factory. He has some ovens (K) and calls his grandma and his grandma's friends to make cookies (L). Assume that the production function is

$$ q \left( K, L \right) = 100 K L^2 $$

With `3` ovens and `2` grandmas, the factory produces 1,200 cookies:

$$ q \left( 3, 2 \right) = 100 \times 3 \times 2^2 = 1,200 $$

Question

The cookie factory has the following production function `K^3L^3`

What is quantity of cookies produced with 3 ovens (K) and 3 grandmas (L)?

With 3 ovens (K) and 3 grandmas (L), the factory can produce

$$ q (3, 3) = 3^3\times3^3 = 729 $$
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