Econ 299 Chapter2d - 2.A Optimization It can be argued that...

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1 2.A Optimization It can be argued that economists are involved in three practical areas: 1) Analyze what has happened 2) Specify where an economy is now 3) Advise on future decisions To achieve the third goal, often an economist must know what the best result is in order to achieve it.
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2 2.A Optimization Optimization falls into two categories: 1) Maximization (ie: production, profits, utility, happiness, grades, health, employment, etc.) 2) Minimization (ie: costs, pollution, disutility, unemployment, sickness, homework, etc.)
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3 2.A Optimizing There are three steps for optimization: 1) Find where f’(x)=0. This is your FIRST ORDER CONDITION (FOC) and gives potential maxima/minima. 2) Evaluate f’’(x) at your potential maxima/minima. This is your SECOND ORDER CONDITION (SOC) and determines maxima/minima/inflection point status 3) Obtain the co-ordinates of your maxima/minima
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4 2.A Optimizing Example Cooking quality oatmeal is an tricky business – too long spent cooking, and it burns, too little time spent cooking – and some of it is raw and inedible. Production of oatmeal is expressed as: Let x=15+10t-t 2 x=bowls of oatmeal t=5 minute intervals of time Maximize Oatmeal Production
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5 2.A Optimous Oatmeal Let x=15+10t-t 2 FOC: x’ = 10-2t = 0 10 = 2t 1 = t SOC: x’’ = -2 x’’ < 0, concave, maximum
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6 2.A Optimous Oatmeal Let x=15+10t-t 2 Co-ordinates : x(5) = 15+10(5)-5 2 x(5) = 15+50-25 = 40 Gourmet oatmeal production is maximized at 40 bowls when 25 minutes (5X5) is spent cooking it (All else held equal).
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7 2.A – Oatmeal for everyone Production is maximized at (5,40).
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