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

A) [tex]1.5m = L + K[/tex]

B) [tex]1.5m = 5L + 15K[/tex]

C) [tex]1.5m = (5L)(15K)[/tex]

D) [tex]1.5m = (5L + 15K)Q[/tex]

Answer :

Final Answer:

The equation of the $1.5-million isocost line is b) 1.5m = 5L + 15K.

Explanation:

An isocost line represents all the combinations of labor (L) and capital (K) that a firm can purchase for a given total cost. In this case, the total cost is $1.5 million, which can be represented as 1.5m.

The cost of labor is $5 per labor hour (w), and the cost of capital is $15 per machine hour (r). To find the equation of the isocost line, you need to consider the total cost equation:

Total Cost (1.5m) = Cost of Labor (5L) + Cost of Capital (15K)

So, the equation is:

1.5m = 5L + 15K

This equation represents the $1.5-million isocost line, showing the various combinations of labor and capital that can be obtained for a total cost of $1.5 million.

Option B is answer.

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