Production Function

The production function tells us 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 (L) to make cookies. 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: $$ q \left( 3, 2 \right) = 100 \times 3 \times 2^2 = 1200 $$

Question

The cookie factory has the following production function `KL^3`

What is quantity of cookies produced with 3 ovens (K) and 2 grandmas (L)?

With 3 ovens (K) and 2 grandmas (L), the factory can produce $$ q (3, 2) = 3\times2^3 = 24 $$