191hw3-10 - Econ 191 Spring 2010 Francis Lui Problem Set 3...

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1 Econ 191 Spring 2010 Francis Lui Problem Set 3 Due Date: March 22, 4:00 pm sharp. Please submit your PS to the HW collection cabinet outside the ECON department (Lift 17-19) (1) Suppose that a production function is given by Y = 4K 0.25 L 0.75 . It can be shown that MPL = 3(K/L) 0.25 and MPK = (L/K) 0.75 . It is given that the price of K, P K , is $1/unit, and the price of L, P L , is $3 /unit. Assuming that the total cost of production (which is given by P K K + P L L) cannot exceed $8, what is the highest attainable level of production? How many units of K and L will be used? (2) Suppose that the production function of a firm is the same as that in Question 1. Show that (a) Y = (MPL)L + (MPK)K (b) (MPL)L/Y = 0.75 (c) (MPK)K/Y = 0.25. How do you interpret these results? (3) Suppose that all the firms in a perfectly competitive industry have the following identical cost function: C = Q 3 - Q 2 + Q. Show that their marginal cost function is given by
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191hw3-10 - Econ 191 Spring 2010 Francis Lui Problem Set 3...

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