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

The total cost of using labor and capital for a given period can be expressed as:

$10L + $50K = Total Cost

To find the combinations of labor and capital that represent points on the firm's $100,000 isocost line, we can set the total cost equation equal to $100,000 and solve for either L or K.

$10L + $50K = $100,000

Dividing both sides by $10:

L + 5K = 10,000

Now we can test the given combinations of labor and capital hours to see if they satisfy this equation:

A) (10,000, 2000) 
10,000 + 5(2000) = 20,000 
This combination produces a total cost of $20,000, which is not on the $100,000 isocost line.

B) (2000, 10,000) 
2000 + 5(10,000) = 52,000 
This combination produces a total cost of $52,000, which is not on the $100,000 isocost line.

C) (1000, 1800) 
1000 + 5(1800) = 10,000 
This combination produces a total cost of $10,000, which is on the $100,000 isocost line.

D) (1000, 1000) 
1000 + 5(1000) = 6000 
This combination produces a total cost of $6,000, which is not on the $100,000 isocost line.

Therefore, the best choice that represents a point on the firm's $100,000 isocost line is (1000, 1800), and the answer is C.

A Firm Uses Labor and Capital (L,K)( L , K )(L,K)

A Firm Uses Labor and Capital $( L , K )$