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Homework5

# Homework5 - i is not built then factory i cannot produce...

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W3211 Spring 2009 Professor Vogel Homework #5: Due Tuesday 04/14/09 Please write your name on the top of every page of your homework (in case they get separated) and please staple all pages together . Where appropriate, you must show all work. If you just give an answer without work, A.1 Suppose that demand for widgets is given by q = 100 ± 2 p , where the price of widgets is p and where q is the total amount of widgets produced. A.2 Suppose that only one ±rm produces widgets: ColumbiaTech. ColumbiaTech can choose to produce widgets either in one factory or two factories, or ColumbiaTech can choose not to produce widgets at all. The cost of building its ±rst factory is K 1 > 0 and the cost of building its second factory is K 2 > 0 . A.3 If factory one is built, then the total cost of producing q 1 units of output in factory 1 is C 1 ( q 1 ) = K 1 + 6 q 1 . If factory two is built, then then the total cost of producing q 2 units of output in factory 2 is C 2 ( q 2 ) = K 2 + 12 q 2 . A.4 Of course, if factory
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Unformatted text preview: i is not built, then factory i cannot produce any output, but ColumbiaTech does not incur any cost in factory i . Answer questions 1-6 using information from A.1-A.4 1. Suppose that ColumbiaTech chooses to build both factories. Determine ColumbiaT-ech&s output in factory 1 , q 1 ; its output in factory 2 , q 2 ; and its total pro±t. 2. Suppose that ColumbiaTech only chooses to build factory 1 . Determine ColumbiaT-ech&s output in factory 1 , q 1 , and its total pro±t. 3. Suppose that ColumbiaTech only chooses to build factory 2 . Determine ColumbiaT-ech&s output in factory 2 , q 2 , and its total pro±t. 4. What are the weakest conditions under which ColumbiaTech should build both factories 1 and 2 ? 5. What are the weakest conditions under which ColumbiaTech should build only factory 1 ? 6. What are the weakest conditions under which ColumbiaTech should build only factory 2 ?...
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