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Wiskunde week 12, antw - Opgavencollege Wiskunde 1 10...

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Opgavencollege Wiskunde 1, 10 December 2010 Les 12 Uitwerkingen Opgavencollege Wiskunde 1 Les 12 Uitwerkingen Pag. 1/4 Opgave 1 a) 3 2 1 2 1 2 1 1 2 2 ( , ) 320 20 725 10 100 200 w q q q q q q q q 3 2 1 1 2 2 300 10 220 925 q q q q   b)   1 1 2 2 1 2 1 ( , ) 3 300 (6,10) 3 6 300 192 q q w q q q w     2 2 1 2 2 ( , ) 20 220 (6,10) 20 10 220 20. q q w q q q w     1 1 1 1 2 1 1 2 1 1 2 ( , ) 6 1152 ( , ) (6,10) (6,10) 0,6197 ( , ) 1859 1859 w w q q q w q q q E q q E w q w q q 2 2 2 1 2 2 1 2 2 1 2 ( , ) 10 200 ( , ) (6,10) (6,10) 0,1076 ( , ) 1859 1859 w w q q q w q q q E q q E w q w q q 1) 1 1 0,025 q q en 2 2 0,015 q q   . 1 2 1 2 1 2 1152 200 (6,10) (6,10) 0,025 0,015 0,01388. 1859 1859 w w q q q q w E E w q q   De winst zal met ongeveer 1,4% stijgen. N.B.: Er geldt: (6,15;9,85) 1884,166625 1,0135 1859 w Opgave 2 a) 1 1 1,5 1 1 2 1 2 1 1 2,5 1,5 2,5 1 1 1 2 1 2 1 150 150 1,5 100 100 Q p Q p I p p I p p p E p Q p I p p I p p     b) 1 2 1,5 1 1,5 1 2 2 1 1,5 1,5 1 1 2 1 2 50 50 0,5 100 100 Q I p p Q I p I p Ip E I Q I p I p I p I p De functie kan geschreven worden als: 1 2 1.5 1 1 1 2 100 Q p p - = I De elasticiteiten zijn precies die exponenten! De directe prijselasticiteit: 1,5 De indirecte (kruis) elasticeit: 1 De inkomenselasticiteit: 0,5 Algemeen: de functie waarbij constanten zijn heeft als elasticiteiten: El ( , , ) f x y z C x y z a b g = , El e x y a b = = , , en C a b g . z g = n El Dit kan men gemakkelijk nagaan. c) Gebruik makend van de stelling van Euler (en onderdeel b)): , n E E E Q I Q p Q p 1 1 2 1 1 waarbij n de graad van homogeniteit is. Hier . 0
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