1 A firm has the production function Q 4LK The marginal products are given by MPL 4K and MPK 4L a)Suppose that the prices of labour and capital are given by w and r Solve for the quantities of L and K that minimize the cost of producing Q units of output Provide an expression for the long run total cost function b)What returns to scale are exhibited by this production function What economies of scale are exhibited Show the algebraic work for both c)Now suppose Q 4L 0 5 K 0 5 , where MPL 2K 0 5 L 0 5 and MPK 2L 0 5 K 0 5 Repeat (a) d)With the production function in (c), repeat (b) Based on your findings in (b) and (c), what can you conclude

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1 A firm has the production function Q  4LK  The marginal products are given by MPL   4K and MPK  4L  a)Suppose that the prices of labour and capital are given by w and r  Solve for the quantities of L and K that minimize the cost of producing Q units of output  Provide an expression for the long run total cost function  b)What returns to scale are exhibited by this production function  What economies of scale are exhibited  Show the algebraic work for both  c)Now suppose Q   4L 0 5 K 0 5 , where MPL   2K 0 5 L  0 5 and MPK   2L 0 5 K  0 5   Repeat (a)  d)With the production function in (c), repeat (b)  Based on your findings in (b) and (c), what can you conclude

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1.A firm has the production function Q= 4LK. The marginal products are given by MPL = 4K and MPK= 4L. a)Suppose that the prices of

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