Question

Use calculus to derive the cost-minimizing combination of capital and labor for a firm that has production process described by a Cobb-Douglas isoquant, q = 10 · L^.5 K^.5, where q = 100. Assume that the price of labor, w, is 10 and the price of capital, r, is 40. That is, find the exact number of units of L and K that will minimize the cost of producing 100 units of output in the long run. When you are done, please draw a diagram (isoquant, isocost line, cost-minimizing point) that illustrates the solution you just found.

          Use calculus to derive the cost-minimizing combination of capital and labor for a firm that has production process described by a Cobb-Douglas isoquant, q = 10 · L^.5 K^.5, where q = 100. Assume that the price of labor, w, is 10 and the price of capital, r, is 40. That is, find the exact number of units of L and K that will minimize the cost of producing 100 units of output in the long run.

When you are done, please draw a diagram (isoquant, isocost line, cost-minimizing point) that illustrates the solution you just found.

Use calculus to derive the cost-minimizing combination of capital and labor for a firm that has production process described by a Cobb-Douglas isoquant, q = 10 · L^.5 K^.5, where q = 100. Assume that the price of labor, w, is 10 and the price of capital, r, is 40. That is, find the exact number of units of L and K that will minimize the cost of producing 100 units of output in the long run.

When you are done, please draw a diagram (isoquant, isocost line, cost-minimizing point) that illustrates the solution you just found.

Added by Allan H.

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