Suppose capital and labor are perfect substitutes resulting in a production function of q = K + L. That is, the isoquants are straight lines with a slope of -1
Derive the long-run total cost function TC = C(q) when the wage rate is w and the rental rate on capital is r.
The firm will always hire the input that is cheapest. So the function is
If w < r, TC = wq.
If w > r, TC = rq.
If w = r, either equation works.
Economics
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