A firm produces a product with labor and capital as inputs. Its production function is described...

A firm produces a product with labor and capital as inputs. Its production function is described by Q(L,K) = L^1/2 K^1/2. Let w and r be the prices of labor and capital, respectively.

a. Derive the firm’s long-run total cost and long-run marginal cost functions.

b. Assume capital is fixed at 4 units in the short-run and derive the firm’s short-run total cost and short-run average variable cost functions.

c. Rewrite your short-run and long-run total cost functions (for the grader) and then graphically depict both on the same graph.

d. In general, how do the long-run total cost and short-run total cost of producing each level of output compare? Explain when and why the short-run total cost would equal the long-run total cost.

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Expert Solution

Rahul Sunny answered 1 year ago

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