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) $1.5 m = L + K$.
B) $1.5 \mathrm {~m} = 5 \mathrm {~L} + 15 \mathrm {~K}$.
C) $1.5 \mathrm {~m} = ( 5 \mathrm {~L} ) ( 15 \mathrm {~K} )$.
D) $1.5 \mathrm {~m} = ( 5 \mathrm {~L} + 15 \mathrm {~K} ) Q$.

Question

Quizplus · Accepted Answer

The equation of an isocost line is given by:
Cost = wL + rK
Plugging in the given values, we get:
Cost = 5L + 15K
Since the cost is $1.5 million, we have:
$1.5 million = 5L + 15K
Dividing both sides by $1 million, we get:
1.5 = 5L/1000 + 15K/1000
Simplifying, we get:
1.5 = 0.005L + 0.015K
Multiplying both sides by 1000, we get:
1500 = 5L + 15K
Therefore, the equation of the $1.5 million isocost line is:
1.5 million = 5L + 15K or $1500 = 5L + 15K (in thousands of dollars). So the answer is B. The equation for the isocost line is given by: $wL + rK = C$, where C is the total cost. Substituting in the given values, we get: $5L + 15K = C$. To find the equation for the $1.5$ million isocost line, we can set $C$ equal to $1.5$ million: $5L + 15K = 1.5\text{m}$. Dividing both sides by $1\text{m}$, we get: $5L/1\text{m} + 15K/1\text{m} = 1.5$. Simplifying, we get: $5L + 15K = 1.5\text{m}$. Therefore, the correct answer is (B).

Let a Firm Use Labor (L)( L )(L) And Capital (K) as Its Only Inputs to Produce an (K)

Let a Firm Use Labor $( L )$ And Capital (K) as Its Only Inputs to Produce an (K)