Discussion
For the production function Q = 20K0.5L0.5 derive K = f(L) when the isoquant Q = 100.
Answer: B
The isoquant is \(K = 25L^{-1}\).
Set output at 100 and solve for \(K\):
\[ \begin{aligned} 20K^{0.5}L^{0.5} &= 100 \\ (KL)^{0.5} &= 5 \\ KL &= 25 \\ K &= \frac{25}{L} = 25L^{-1} \end{aligned} \]
This rectangular hyperbola is the Q = 100 isoquant. The option \(25K^{-1}\) gives \(K\) in terms of itself, and \(25L\) would make the isoquant slope upward, which an isoquant cannot do when both inputs are productive.
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