ch11-constrained-optimization

ch11-constrained-optimization - Constrained Optimization...

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Constrained Optimization Professor Erkut Ozbay Economics 300
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Constraints Limited budget Li it d Limited revenue Limited hours to work • …. Scarce resources create constraints
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Constrained optimization Includes an objective function and constraints Choose variables (x 1 ,x 2 ) to maximize (or minimize) bj ti f ti f( ) bj t t t i t an objective function f(x 1 ,x 2 ) subject to constraints
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Consumption problem You have $6.00 to spend on a lunch of soup and salad Restaurant sells both soup and salad by weight An ounce of soup (S) is $0 25 – An ounce of soup (S) is $0.25 – An ounce of salad (V) costs $0.50 • How many ounces of each will you purchase? How many ounces of each will you purchase?
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Budget constraint Budget = $6 Price of Soup (P S )= 0 25 ) 0.25 Price of Salad (P V )= 0.50 If you spend all on soup, then you can buy 6/.25 =24 ounces of soup If you spend all on salad, then you can buy 6/.5 = 12 ounces of salad
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Budget constraint Budget = P S S + P V V B d t 6 Budget = 6 Price of Soup (P S )= 0.25 Price of Salad (P V )= 0.50 6 = 0.25 S + 0.5 V
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Objective Utility you derive from consumption of soup and salad is 1 1 ( , ) ln( ) ln( ) 2 2 U S V S V
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