ajaz_eco204_2009_chapter_1.1

ajaz_eco204_2009_chapter_1.1 - University of Toronto,...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Theorem Please help improve the course by sending me an e mail about typos or suggestions for improvements 1: About Optimization Problems In ECO 204 and upper level economics and finance courses, you will frequently solve optimization problems. There are two categories of optimization problems in economics and finance: static and dynamic. Static optimization is at a point in time whereas dynamic optimization is over time. Here are some examples of each: Static Optimization Examples: A firm chooses output(s) to maximize revenues (or profits) over a period. A firm chooses output(s) to maximize revenues (or profits) subject to capacity constraints over a period. A consumer chooses how much to consume to maximize utility subject to expenditure equal to income over a period. An investor chooses fraction of portfolio in risky and risk free assets to maximize expected returns subject to a risk tolerance constraint for a period. Dynamic Optimization Examples: A firm chooses output(s) in each of T periods to maximize present value of revenues (or profits). A firm chooses output(s) and inventory quantities in each of T periods to maximize the present value of revenues (or profits) subject to period specific capacity and inventory related constraints An investor chooses fraction of portfolio in risky and risk free assets in each of T periods to maximize present value of expected returns subject to a period specific risk tolerance constraint 1 ECO 204 (Draft) Chapter 1.1

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain An investor chooses the number of periods (T) to invest in risky and risk free assets. Next, investor chooses fraction of portfolio in risky and risk free assets in each period to maximize present value of expected returns subject to a period specific risk tolerance constraint. 2: About Static Optimization Problems In micro, you will primarily see static optimization problems. We’re going to examine 3 classes of static optimization problems. Let’s first look at the general definition followed by a discussion Unconstrained optimization problems : We choose ݔ to maximize (or minimize) the function ݂ሺݔሻ . That is either: max ݂ሺݔሻ or: min ݂ሺݔሻ Note that any minimization problem can be transformed into a maximization problem (and vice versa) since minimizing a function is the same as maximizing its negative: min ݃ሺݔሻ ൌ െ max ݃ሺݔሻ. In the graph below, observe how the ݔ which minimizes ݂ሺݔሻ also maximizes െ ݂ሺݔሻ . x
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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ajaz_eco204_2009_chapter_1.1 - University of Toronto,...

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