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Unformatted text preview: Econ 101A Problem Set 1 Due in class on Th 5 February. No late Problem Sets accepted, sorry! This Problem set tests the knowledge that you accumulated in the f rst 4 lectures. It is mostly on the mathematical techniques that we developed, but there is also some application to consumer decisions, as introduced in Lecture 4. General rules for problem sets: show your work, write down the steps that you use to get a solution (no credit for right solutions without explanation), write legibly. If you cannot solve a problem fully, write down a partial solution. We give partial credit for partial solutions that are correct. Do not forget to write your name on the problem set! Problem 1. Univariate unconstrained maximization. (10 points) Consider the following maxi- mization problem: max x f ( x ; x ) = exp( ( x x ) 2 ) 1. Write down the f rst order conditions for this problem with respect to x (notice that x is a parameter, you should not maximize with respect to it). (1 point) 2. Solve explicitely for x that satis f es the f rst order conditions. (1 point) 3. Compute the second order conditions. Is the stationary point that you found in point 2 a maxi- mum? Why (or why not)? (2 points) 4. As a comparative statics exercise, compute the change in x as x varies. In other words, compute dx /dx . (2 points) 5. We are interested in how the value function f ( x ( x ); x ) varies as x varies. We do it two ways....
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- Spring '08