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What is the long-run cost function for a fixed-proportions production function when it takes five units of labor and four uni

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Answer #1

Inputs are used in fixed proportions of five units of L and 4 units of K. So, the production function can be written as:
q = min{4L, 5K}

So, q = 4L = 5K
So, L = q/4 and K = q/5

Cost, C = wL + rK = [w(q/4)] + [r(q/5)] = 0.25wq + 0.2rq = (0.25w + 0.2r)q
So, C(q) = (0.25w + 0.2r)q

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