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1.  Suppose  thatarisk-averse  individual  hasawealth  levelWo .  This  indi- vidual  hastheoption  ofinvesting  intherisk-freeassetwithareturnof


(1+rf)                                                        (1)



There  isanotherassetthatisriskywithareturnof(1+rh )inagoodstate withprobability1  and(1+rl )inabadstate  withprobability1.Theexpected










(1+rl )+





2 (1+rh )                                             (2)



Weassumethattheexpected  returnontheriskyassetishigher:




2 (1+rl )+



2 (1+rh )    >  (1+rf)                                (3)

1        1


2 rl+2 rh    >  rf                                            (4)


(a)  Showthatarisk-averse  person  willalways  invest  someamount  inthe riskyasset.

(b)What  willbetheamountinvested  intheriskyassetif1rl+1rh=rf?

2            2

2.   Consider  thefollowingPrisoner’s  dilemma  gameplayed  simultaneously:




  NC(2) C(2)
NC(1) -2,-2 -10,-1
C(1) -1,-10 -5,-5


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:


C(q)=q3−20q2+110q                                     (5)


andthedemand  curveofthemarket  is:



QD=3,000−3P                                           (6)







(a)What  istheLRequilibrium  PandQ? (b)Howmany  firmswillexistintheLR?

4.Consider  twoindividuals  aandbwiththeutility  functions:


Ua      =   (xc).5(yc).5                                                    (7)

a        a

Ub     =   (xc).25(yc).75                                                 (8)

b             b


(xc,yc )aretheamountthatconsumersconsume.  Inordertopurchase  these

i     i

bundles,  theymustalsohavesomething  tosell.Inthiseconomy,theproduction

of goodshasalready  taken  place.  Eachconsumerhasthefollowingendowments ofgoods:


Ea    :   (xe,ye)=(500,500)                                       (9)

a     a

Eb      :     (xe,ye)=(200,800)                                    (10)

b       b


Theseendowmentscanbesoldinthe  market.The  total  amountofendow- mentsintheeconomycanbeexpressed  as:


X    =  xe  +xe  =700                                          (11)

a       b

Y      =  ye+ye  =1300                                         (12)

a       b








(a)Find  theequilibrium  demand  forgoodX. (b)What  istheequilibrium   Px ?



[Hint:  Ifpricesofgoodsare:  Px ,Py,thebudget  constraintscanbewritten




Ia    =  Px xe  +Pyye



a            a


Ib    =   Px xe  +Pyye



b                  b



5.Consider  themarketdemand  curvetobe:


P=1000−Q                                                 (15) Thecostfunctionofafirmtobe:

C(q)=10q+q2                                                                    (16)


(a)What  isthemonopolyoutput?

(b)What  istheoutputforperfectly  discriminatingmonopolist? (b)What  istheCournotoutputifthere  are2firms?


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