1. Suppose thatarisk-averse individual hasawealth levelWo . This indi- vidual hastheoption ofinvesting intherisk-freeassetwithareturnof
There isanotherassetthatisriskywithareturnof(1+rh )inagoodstate withprobability1 and(1+rl )inabadstate withprobability1.Theexpected
2 (1+rh ) (2)
2 (1+rl )+
2 (1+rh ) > (1+rf) (3)
2 rl+2 rh > rf (4)
(a) Showthatarisk-averse person willalways invest someamount inthe riskyasset.
(b)What willbetheamountinvested intheriskyassetif1rl+1rh=rf?
2. Consider thefollowingPrisoner’s dilemma gameplayed simultaneously:
Thefirstpayoffisthatofplayer 1andthesecondthatofplayer 2. Ifplayer 1movesfirstorweareinasequential gamenow.
(a)What isnormal formofthegameinthesequentialversion? (b)What aretheNashEquilibriainthesequential version?
(c)Drawtheextensive forminthesequential version.
(d)What isthesubgame perfectNashEquilibriuminthesequential ver- sion?
(e)Explain whyitisthesubgameperfectNashEquilibriuminthesequen- tialversion?
3.Consider thecostfunction ofafirmforLRis:
andthedemand curveofthemarket is:
(a)What istheLRequilibrium PandQ? (b)Howmany firmswillexistintheLR?
4.Consider twoindividuals aandbwiththeutility functions:
Ua = (xc).5(yc).5 (7)
Ub = (xc).25(yc).75 (8)
(xc,yc )aretheamountthatconsumersconsume. Inordertopurchase these
bundles, theymustalsohavesomething tosell.Inthiseconomy,theproduction
of goodshasalready taken place. Eachconsumerhasthefollowingendowments ofgoods:
Ea : (xe,ye)=(500,500) (9)
Eb : (xe,ye)=(200,800) (10)
Theseendowmentscanbesoldinthe market.The total amountofendow- mentsintheeconomycanbeexpressed as:
X = xe +xe =700 (11)
Y = ye+ye =1300 (12)
(a)Find theequilibrium demand forgoodX. (b)What istheequilibrium Px ?
[Hint: Ifpricesofgoodsare: Px ,Py,thebudget constraintscanbewritten
Ia = Px xe +Pyye
Ib = Px xe +Pyye
5.Consider themarketdemand curvetobe:
P=1000−Q (15) Thecostfunctionofafirmtobe:
(b)What istheoutputforperfectly discriminatingmonopolist? (b)What istheCournotoutputifthere are2firms?
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