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StA_verkefni_06

# StA_verkefni_06 - Hskli slands Viskipta og hagfrideild...

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Háskóli Íslands Viðskiptaskor haustið 2009 Viðskipta- og hagfræðideild Stærðfræði A fyrir viðskiptafræðinga. Heimadæmi 1. Gefin eru föll. Finnið afleiður: a) 5 , 0 6 , 0 10 L X U = Finnið afleiðurnar: XL LL XX L X U U U U U , , , , b) 2 1 ln 2 ln 5 x x U + = Finnið: 21 12 22 11 2 1 , , , , , U U U U U U c) 2 1 1 2 2 2 1 5 8 5 20 90 q q q q q - - + + - = Π Finnið: 21 12 22 11 2 1 , , , , , Π Π Π Π Π Π 2. Fyrirtæki framleiðir tvær vörur í magninu x og y og býr við kostnaðarfallið xy y x y x TC 5 , 0 2 , 0 05 , 0 10 2 2 + + + + + = Eftirspurn eftir þessum vörum er lýst með andhverfu föllunum: y p x p y x 3 , 0 17 45 , 0 15 - = - = Finnið tekjufall og hagnaðarfall. Finnið síðan hámark hagnaðarins með því að nota annarstigs skilyrði (Hessian). 3. Fyrirtæki selur vöru sína á tveim aðskildum mörkuðum og eru (andhverfu) eftirspurnarföllin sem hér segir:
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