1. Consider the following production function
With w = $20 and r = $40, find the cost minimizing input combination to produce 100 units of output.
Assume w = $20 and r = $40 as in part (a) but now treat q as a variable. Derive the firm’s demand for labor and capital and use them to find the long run total cost, long run average cost, and long run marginal cost as functions of output q.
Again let w = $20 and r = $40, but now assume K = 5 in the short run. Derive the short run total cost, short run average cost, and short run marginal cost as functions of output q.
In the same diagram, draw the graph of short run and long run total cost functions you found in parts (b) and (c). For what level of output are the two costs the same? Verify your answer and show this level of output on the diagram.
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