For the production function $Q = 20 \sqrt { K L }$, the equation for a typical isoquant is
A) $K = \frac { 20 L } { Q ^ { 2 } }$
B) $K = \frac { Q ^ { 2 } } { 20 L }$
C) $L = \frac { K } { 20 Q }$
D) $K = 20 ( Q L ) ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the equation for an isoquant, we set the production function equal to a constant level of output, say q. Therefore, for this production function, the isoquant equation is:

Q = 20sqrt(KL) = q

Squaring both sides, we get:

K * L = (q/20)^2

Dividing both sides by L, we get:

K = (q/20)^2 / L

Simplifying, we get:

K = Q^2 / (20L)

Therefore, the correct answer is (B). Starting with the production function $\boldsymbol{ Q=20\sqrt{KL} }$, we can isolate K to obtain $\boldsymbol{ K=\frac{Q^2}{20L}}$. This equation represents the relationship between K and L required to produce a given level of output Q, which is exactly what an isoquant represents. Therefore, the equation for a typical isoquant for this production function is $\boldsymbol{ K=\frac{Q^2}{20L}}$, or choice B.

For the Production Function Q=20KLQ = 20 \sqrt { K L }Q=20KL​

For the Production Function $Q = 20 \sqrt { K L }$