Econ100B PS3

Econ100B PS3 - Q D = 3 & P . Find the...

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ECO 100B Problem Set 3 Answers will be posted on May 9, 2008 C ( q ) = 4 + q 2 , and faces a market demand of Q D = 10 P . (a) What is the long-run equilibrium price? (c) How much does the industry as a whole produce? 2. Consider the same question as above, but suppose that C ( q ) = 4 q . Can you still determine 3. Consider two &rms operating in the short-run; Firm 1 has cost function C 1 ( q ) = 4 q + q 2 . C 2 ( q ) = q 2 . (a) For a given market price p , how much does Firm 1 supply? How much does Firm 2 supply? (Hint: Use the FOC for each &rm; remember to verify that the SOC holds, and (b) For a given market price p , what is the total supply for the industry as a whole? Draw each individual supply curve and the industry supply curve. (c) Suppose that the market demand is
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Unformatted text preview: Q D = 3 & P . Find the equilibrium price and quantity sold. Do both &rms produce or does only one of the two &rms produce? (d) Now suppose that there is an increase in demand and after the increases, Q D = 10 & P . Find the new equilibrium price and quantity sold. Do both &rms produce now? 4. Consider a &rm making long-run choices of capital and labor, f ( L;K ) = L 1 5 K 2 5 , and w = 1 , r = 1 . (a) What is the MRTS? Does the production function have diminishing MRTS? (b) Given a &xed level of production & q , what relationship is there between L and K ? (c) To produce & q units of output, how many units of L and K are used? (d) Can you derive the total cost, C ( q ) of producing q units of output? (e) At a price level of p , how much does the &rm produce? (f) At what quantity and price does the &rm make zero pro&ts? Additional questions from book that would be good practice: Q. 32 and 33. 1...
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