A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L^1/2M^1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10. 1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. 2. Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.)
A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L^1/2M^1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.
1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400
and another isocost line showing combinations that cost $200.
2. Suppose that the firm wants to produce its output in the cheapest possible way. Find the
number of machines it would use per worker. (Hint: The firm will produce at a point where
the slope of the production isoquant equals the slope of the isocost line.)
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