Suppose the production function can be expressed as $$Q = 2 \sqrt { K L }$$ Which of the following combinations of capital and labor lie on the same isoquant?
A)(5, 6)and (4, 5)
B)(3, 2)and (7, 1)
C)(4, 3)and (2, 6)
D)(10, 3)and (15, 4)

Question

Quizplus · Accepted Answer

For a combination of capital (K) and labor (L) to lie on the same isoquant, they must produce the same level of output (Q). Using the production function $Q = 2 \sqrt { K L }$, we can check each pair of combinations:A) $Q_1 = 2 \sqrt{5 \times 6} = 2 \sqrt{30}$ and $Q_2 = 2 \sqrt{4 \times 5} = 2 \sqrt{20}$. These do not produce the same output.B) $Q_1 = 2 \sqrt{3 \times 2} = 2 \sqrt{6}$ and $Q_2 = 2 \sqrt{7 \times 1} = 2 \sqrt{7}$. These do not produce the same output.C) $Q_1 = 2 \sqrt{4 \times 3} = 2 \sqrt{12}$ and $Q_2 = 2 \sqrt{2 \times 6} = 2 \sqrt{12}$. These produce the same output.D) $Q_1 = 2 \sqrt{10 \times 3} = 2 \sqrt{30}$ and $Q_2 = 2 \sqrt{15 \times 4} = 2 \sqrt{60}$. These do not produce the same output.Therefore, only option C has combinations of capital and labor that lie on the same isoquant.

Suppose the Production Function Can Be Expressed As Q=2KLQ = 2 \sqrt { K L }Q=2KL​

Suppose the Production Function Can Be Expressed As $Q = 2 \sqrt { K L }$