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03_haust_lausn - Hskli slands Hsklinn Akureyri 1(10 Strfri...

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Háskóli Íslands - Háskólinn á Akureyri Stærðfræði Haustpróf 2003 Kennitala: Síða 2 af 11 1.(10%) Markaði er lýst með eftirfarandi jöfnum: Framboðsfallið S Q P = Eftirspurnarfallið 600 - 2 D Q P = Þar sem Q er magn og P er verð. a) Teiknið ferlana upp í hnitakerfi og reiknið út jafnvægispunktinn 600 2 200; 200 600 2 S D Q P P P P Q Q P = = - = = = - b) Finnið verðteygni eftirspurnarinnar og verðteygni framboðs í jafnvæginu ( ) 200 ( ; ) 2 2 200 200 ( ; ) 1 1 200 D S P dQ E Q P Q dP P dQ E Q P Q dP = = ⋅ - = - = = = c) Finnið neytandaábata (hagsbót neytandans) (CS) í jafnvægispunktinum 200 200 2 0 0 300 0,5 200*200 300 0,25 200*200 10000 CS QdQ Q Q = - - = - - = (Hér má líka nota þríhyrninga) d) Ef lagður er skatturinn 50 á hverja einingu, finnið þá jafnvægispunktinn og breytinguna í neytandaábata 50 50 600 2 3 650 216,67; 166,67 600 2 S N D Q P P P P P P Q Q P = = - - = - = = = = - 166,67 166,67 2 0 0 300 0,5 216,67*166,67 300 0,25 216,67*166,67 6944,44 N CS QdQ Q Q = - - = - - = Breytingin er þá 10000 6944,44 3055,56 N CS CS - = - =
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Háskóli Íslands - Háskólinn á Akureyri Stærðfræði Haustpróf 2003 Kennitala: Síða 3 af 11 2.(10%) Finnið gildi x til að jöfnurnar standist. a) 5log 2 4 x = ( ) 5 4 ln32 4 5log 2 4 2 ln32 4ln 2,378414 x x x x e = = = = = b) 1 2 2 x dt t = [ ] 1 1 1 1 2 2 1 ln 1 ln ln1 1 ln 0 1 x x x dt t t dt t x x x e - = = = - = - = =
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Háskóli Íslands - Háskólinn á Akureyri Stærðfræði Haustpróf 2003 Kennitala: Síða 4 af 11 3.(15%) a) Þú semur um að greiða 500 000 kr. skuld á 10 árum með jöfnum greiðslum mánaðarlega, fyrstu greiðslu eftir mánuð. i) Hve mikið áttu að greiða á mánuði ef ársvextirnir eru 6% og reiknast mánaðarlega.
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