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^0.5K^0.5, where MPL = 2K^0.5L^-0.5 and MPK = 2L^0.5K^-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?