191hw3-09 - How do you interpret these results(3 Suppose...

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1 Econ 191 Spring 2009 Francis Lui Problem Set 3 Due Date: March 24, 1:20pm sharp. (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.
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Unformatted text preview: 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 MC = 3Q 2 – 2Q +1. (i) Express algebraically the average cost function for each firm. (ii) Find the long-run supply curve of this industry. (iii) Suppose that the market demand for the product of this industry is given by Q = -4P + 103. At equilibrium, how many firms will operate in this industry? (4) Pindyck, Rubinfeld and Koh, p. 385, #14. (5) Pindyck, Rubinfeld and Koh, p. 385, #15....
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This note was uploaded on 10/11/2009 for the course ECON 191 taught by Professor Chen during the Spring '08 term at HKUST.

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