Suppose the production function can be expressed as $Q = 2 \sqrt { K L }$ . Which of the following combinations of capital and labor $( K , L )$ 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

To determine which combinations of capital and labor lie on the same isoquant, we need to find the level of output (Q) produced by each combination and see if they are equal. Using the given production function, we have:

Q(5,6) = 2√(5*6) = 2√30
Q(4,5) = 2√(4*5) = 2√20

Q(3,2) = 2√(3*2) = 2√6
Q(7,1) = 2√(7*1) = 2√7

Q(4,3) = 2√(4*3) = 2√12
Q(2,6) = 2√(2*6) = 2√12

Q(10,3) = 2√(10*3) = 2√30
Q(15,4) = 2√(15*4) = 2√120

We can see that only combinations (4,3) and (2,6) produce the same level of output (2√12), so they are on the same isoquant. Therefore, the answer is C.

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

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