Let a firm use labor (L) and capital (K) as its only inputs to produce an output, Q. The cost of labor is w = $5 per labor hour and the cost of capital is r = $15 per machine hour. What is the equation of the $1.5-million isocost line?
A) 1.5m = L + K.
B) 1.5m = 5L + 15K.
C) 1.5m = (5L)(15K).
D) 1.5m = (5L + 15K)Q.

Question

Quizplus · Accepted Answer

The equation of the isocost line is given by C = wL + rK, where C is the total cost of producing Q units of output. Given that the firm has a budget of $1.5 million, we have 1.5m = 5L + 15K, since the cost of labor is $5 per hour and the cost of capital is $15 per machine hour. This simplifies to:
1.5m = 5(L + 3K)
Dividing by 5, we get:
0.3m = L + 3K
Rewriting in terms of the isocost equation, we have:
C = 0.3mQ = wL + rK
Substituting the values for w and r, we get:
C = 5L + 15K
Therefore, the equation of the $1.5-million isocost line is 1.5m = 5L + 15K, or choice B.

Let a Firm Use Labor (L) and Capital (K) as Its