15.For any given output level, a firm's long-run costs Select one:
a. are always greater than or equal to its short-run costs.
b. are usually greater than or equal to its short-run costs except in the case of diminishing returns to scale.
c. are always less than or equal to its short-run costs.
d. are usually less than or equal to its short-run costs except in the case of diminishing returns to scale.
Cost- minimization problem:--
min wL + rk s.t Q = f(K,L)
This gives the first-order condition:
Long-run cost implies that all the factors are variable & hence the cost is minimized cost. This is because in the long-run cost minimization problem the first-order condition is that the isoquant and isocost should tangent. => MRTS = w/r
In short-run, factors like capital are fixed & hence the cost is not the cost minimized. This is because in the short-run MRTS = w/r not always possible. This is possible only when the short-run amount of fixed factor matches the long-run cost minimization fixed factor. Hence it will always greater than or equal to the long-run cost.
Hence the long-run cost is the lower envelope of the short-run cost.
Hence the correct answer is C
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