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DiagnosticTest10-1

DiagnosticTest10-1 - JohnRiley Fall2010(revised Econ 200...

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John Riley Fall 2010 (revised) Econ 200 Diagnostic Quiz Attempt all three questions. Time allowed: 10 minutes reading and 100 minutes writing. To test out you need to show some progress on all three questions so manage your time carefully. As long as you are enrolled in the class I will let you know via email whether or not you must continue in Econ 200 or have completed the requirements of the course. Please keep this email as your official record as your grade will not be posted till the end of the Fall quarter. 1. Consumer Choice (a) Solve the following consumer problem. You should assume that income and prices are all strictly positive. 3 1 { ( ) ln | } j x j Max U x x p x I = = . State any theorems that you use to obtain your answer. (b) Suppose instead that 1 2 3 ( ) ln( ) ln U x x x x = + + , (1,2,3) p = and 100 I = . Solve for the utility maximizing consumption bundle. 2. Supporting Hyperplanes (a) A firm has a production function 1/2 , 0 q z z = where z is the single input and q the single output. What is the production set of the firm? Is it convex?
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