Example
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
$$ \begin{align*} q (K, L) &= 100 \\ K L^2 &= 100 \\ K &= \frac{100}{L^2} \end{align*} $$Question
The production function is now `q(K, L) = K^2L`.
What is the equation of the isoquant representing the production of 81 cookies? Draw that isoquant.
The isoquant satisfies `q(K, L) = K^2L = 81`.
Solving for `K`.
$$ \begin{align*} Y^2&= \frac{81}{L}\\K &= \frac{81^{\frac{1}{2}}}{L^{\frac{1}{2}}}\\K &= \frac{9}{L^{\frac{1}{2}}}\end{align*} $$