A firm uses labor and machines to produce output according to the production function f(L,M) = 4L 1/2M1/2 , where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. a) On a graph, draw an isocost line for this firm, showing com- binations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. What is the slope of these isocost lines? b) 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.) c) On the graph, sketch the production isoquant corresponding to an output of 40. Calculate the amount of labor and the number of machines that are used to produce 40 units of output in the cheapest possible way, given the above factor prices. Calculate the cost of producing 40 units at these factor prices.
1) A firm uses labor and machines to produce output according to the production function f(L,M) = 4L 1/2M1/2 , where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10.
a) On a graph, draw an isocost line for this firm, showing com- binations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. What is the slope of these isocost lines?
b) 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.)
c) On the graph, sketch the production isoquant corresponding to an output of 40. Calculate the amount of labor and the number of machines that are used to produce 40 units of output in the cheapest possible way, given the above factor prices. Calculate the cost of producing 40 units at these factor prices.
d) How many units of labor and how many machines would the firm use to produce y units in the cheapest possible way? How much would this cost? (Hint: Notice that there are constant returns to scale.)
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