Exercises PT3 - Exer ci ses PT 3 [ Pl ease do not di st r i...

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Exer ci ses PT 3 [ Pl ease do not di st r i but e]
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Ch 12: Uncer t ai nt y I n t he next f ew weeks, t he gover nment i s goi ng t o deci de whet her or not t o devel op an expensi ve new weapons syst em. I f t he syst em i s appr oved, i t wi l l be ver y pr of i t abl e f or t he def ense cont r act or , Gener al Weapons . I ndeed, i f t he new syst em i s appr oved, t he val ue of st ock i n Gener al Weapons wi l l r i se f r om $10 per shar e t o $15 a shar e, and i f t he pr oj ect i s not appr oved, t he val ue of t he st ock wi l l f al l t o $5 a shar e. I n hi s capaci t y as a messenger f or t he gover nment , Somchai has di scover ed t hat t he weapons syst em i s much mor e l i kel y t o be appr oved t han i s gener al l y t hought . On t he basi s of what he knows, he has deci ded t hat t he pr obabi l i t y t hat t he syst em wi l l be appr oved i s 3/ 4 and t he pr obabi l i t y t hat i t wi l l not be appr oved i s 1/ 4. Let c A be Somchai ’ s consumpt i on i f t he syst em i s appr oved and c NA be hi s consumpt i on i f t he syst em i s not appr oved. Somchai ’ s von Neumann- Mor genst er n ut i l i t y f unct i on i s U ( c A , c NA ) = . 75 l n c A + . 25 l n c NA Somchai ’ s t ot al weal t h i s $50, 000, al l of whi ch i s i nvest ed i n per f ect l y saf e asset s. Somchai i s about buy st ock i n Gener al Weapons .
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( a) I f Somchai buys x shar es of st ock, and i f t he weapons syst em i s appr oved, he wi l l make a pr of i t of $5 per shar e. Thus t he amount he can consume, cont i ngent on t he syst em bei ng appr oved, i s c A = $50 , 000+5 x . I f Condor buys x shar es of st ock, and i f t he weapons syst em i s not appr oved, how much wi l l he l ose per shar e? So what i s t he amount he can consume cont i ngent on t he syst em not bei ng appr oved? ( b) You can sol ve f or Somchai ’ s budget const r ai nt on cont i ngent commodi t y bundl es ( c A , c NA ) by el i m i nat i ng x f r om t hese t wo equat i ons. What i s hi s budget const r ai nt ?
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( c) Somchai has no mor al qual ms about t r adi ng on i nsi de i nf or mat i on, nor does he have any concer n t hat he wi l l be caught and puni shed. To deci de how much st ock t o buy, he si mpl y maxi m i zes hi s von Neumann- Mor genst er n ut i l i t y f unct i on subj ect t o hi s budget . I f he set s hi s mar gi nal r at e of subst i t ut i on bet ween t he t wo cont i ngent commodi t i es equal t o t hei r r el at i ve pr i ces and si mpl i f i es t he equat i on, what i s c A / c NA ? ( Rem i nder : Wher e a i s any const ant , t he der i vat i ve of a l n x wi t h r espect t o x i s a/ x . ) ( d) Somchai f i nds t hat hi s opt i mal cont i ngent commodi t y bundl e i s ( c A , c NA ) = ( 75, 000, 25, 000) . To acqui r e t hi s cont i ngent commodi t y bundl e, how many shar es of st ock
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12. 2 W i l l y owns a smal l chocol at e f act or y, l ocat ed cl ose t o a r i ver t hat occasi onal l y f l oods i n t he spr i ng,
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This note was uploaded on 03/14/2010 for the course ECON microecono taught by Professor Yy during the Spring '10 term at Seoul National.

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Exercises PT3 - Exer ci ses PT 3 [ Pl ease do not di st r i...

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