A firm uses labor and machines to produce output according to the production function f(L,M) = 4L1/2M1/2, 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 the graph below, 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. 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.
(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? ____.