An isoquant depicts all the combination of Capital and Labor that allows the firm to produce a given quantity of output.


In the cookie factory, the production function is `q (K, L) = K L^2`.

Tomorrow, they have to make 100 cookies. The combinations of Capital (K) and Labor (L) required to make 100 cookies satisfies

$$ \begin{align*} q (K, L) &= 100 \\ K L^2 &= 100 \\ K &= \frac{100}{L^2} \end{align*} $$


The production function is now `q(K, L) = K^2L^2`.

What is the equation of the isoquant representing the production of 64 cookies? Draw that isoquant.

The isoquant satisfies `q(K, L) = K^2L^2 = 64`.

Solving for `K`.

$$ \begin{align*} Y^2&= \frac{64}{L^2}\\K &= \frac{64^{\frac{1}{2}}}{L^{\frac{2}{2}}}\\K &= \frac{8}{L^{\frac{2}{2}}}\\K &= \frac{8}{ L }\end{align*} $$