A firm uses labor and capital, $ (L, K) $ , to produce an output. The hourly cost of labor is $10, and the hourly cost of capital is $50. Which of the following combinations of labor and capital hours of use represent points on the firm's $100,000 isocost line?
A) (10000, 2000)
B) (2000, 10000)
C) (1000, 1800)
D) (1000, 1000)

Question

Quizplus · Accepted Answer

An isocost line represents all possible combinations of labor and capital that can be used to produce a specific cost. Let C be the cost of production, L be the labor hours, and K be the capital hours. Then, we can represent the isocost line with the equation:

C = 10L + 50K

To find the points on the $100,000 isocost line, we can set C = $100,000 and solve for L and K:

$100,000 = 10L + 50K

Dividing both sides by 10, we get:

$10,000 = L + 5K

Now we can check which of the given options satisfy the above equation:

A) (10000, 2000): 10000 + 5(2000) = 20,000 ≠ $10,000. Not on the isocost line.
B) (2000, 10000): 2000 + 5(10000) = 52,000 ≠ $10,000. Not on the isocost line.
C) (1000, 1800): 1000 + 5(1800) = 10,000. On the isocost line.
D) (1000, 1000): 1000 + 5(1000) = 6,000 ≠ $10,000. Not on the isocost line.

Therefore, choice C is the only option that represents a point on the $100,000 isocost line.

A Firm Uses Labor and Capital (L,K) (L, K) (L,K) , to Produce an Output

A Firm Uses Labor and Capital $(L, K)$ , to Produce an Output