# UCLA PSYCH 10 - PS1 (2 pages)

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## PS1

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## PS1

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Pages:
2
School:
University of California, Los Angeles
Course:
Psych 10 - Introductory Psychology
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ECON 11 Problem Set 1 Due Thursday October 6 before 9 30am in class 1 Unconstrained optimization in one variable Consider the following function f x 3x3 5x2 x where x 0 2 1 Find the x s that are critical value points of f x values of x that are a potential minimum or maximum Are those critical values maxima or minima Hint Check the second order derivative Check also the value of the function at the endpoints 0 and 2 to make sure you have the correct answer 2 Unconstrained optimization in two variables Consider the function f x1 x2 x13 3x23 9x1 x2 1 Find a minimum given that x1 x2 1 3 Constrained optimization Julia maximizes the following utility function 2 7 5 7 u x1 x2 x1 x2 subject to the budget constraint p1 x1 p2 x2 I 1 where p1 p2 x1 x2 I 0 1 Find the x1 x2 that maximizes u x1 x2 2 Show that the maximizer x2 p1 p2 I is decreasing in p2 and increasing in I Hint Use the partial derivatives 3 Does x2 p1 p2 I change if p1 changes Hint partial derivatives 2

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