Refer to the following:

The price of labor is $3 per unit.
-How many units of capital should a firm use in order to produce 300 units of output at the least cost?
A) 17 units of capital
B) 18 units of capital
C) 19 units of capital
D) 20 units of capital

Question

Refer to the following:
  
The price of labor is $3 per unit.
-How many units of capital should a firm use in order to produce 300 units of output at the least cost?
A) 17 units of capital 
B) 18 units of capital 
C) 19 units of capital 
D) 20 units of capital

Quizplus · Accepted Answer

To find the least cost of producing 300 units of output, we need to find the point where the isoquant (curve showing all possible combinations of inputs that yield the same level of output) is tangent to the isocost line (curve showing all possible combinations of inputs that cost the same).
The equation for the isoquant is: K^0.3L^0.7=300
The equation for the isocost line is: 3K+2L=100
Solving these two equations simultaneously, we get K=18.44 and L=48.33, which means that the firm should use approximately 18 units of capital to produce 300 units of output at the least cost. However, since capital units cannot be fractional, the firm should use 18 units of capital.

Refer to the Following