A firm that employs labor and capital has production function q = LK. Throughout this problem,...

 

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A firm that employs labor and capital has production function q = LK. Throughout this problem, the cost of capital is r = 1 and the cost of labor is w = 9. 1. What returns to scale does the production function exhibit? Demon- strate your answer. [3 marks] 2. Find the short-run cost function when capital is fixed at K = 3. Your answer should depend only on q. [3 marks] 3. Using the technique of Lagrange multipliers, find the long-run cost function. Your answer should depend only on q. [6 marks] 4. What economies of scale does the long-run cost function exhibit? Demonstrate your answer. [3 marks] A firm that employs labor and capital has production function q = LK. Throughout this problem, the cost of capital is r = 1 and the cost of labor is w = 9. 1. What returns to scale does the production function exhibit? Demon- strate your answer. [3 marks] 2. Find the short-run cost function when capital is fixed at K = 3. Your answer should depend only on q. [3 marks] 3. Using the technique of Lagrange multipliers, find the long-run cost function. Your answer should depend only on q. [6 marks] 4. What economies of scale does the long-run cost function exhibit? Demonstrate your answer. [3 marks]