ࡱ> GIWXHU( / 0LDTimes New RomanLL`Ԗ0Ԗ@ .  @n?" dd@  @@`` 0%n        0AA@ʚ;ʚ;g4xdxd0Fppp@ <4!d!dA10L<<4ddddA10L<<4BdBdA10L< 0___PPT10___PPT92( x, @? ,O =M6Why Do We Procrastinate?: An Evolutionary Perspective 77$based on Uncertainty and Hyperbolic Discounting P. Dasgupta (Cambridge)E. Maskin (I.A.S.)@ U4+ Suppose in February, we confront choice betweenpainful 5-hour task on April 1painful 8-hour task on April 15 (tax deadline in U.S.) (last minute hitches in finding all the receipts, long lines at the post office, etc.)Most of us will choose April 10V Y!   $$$V X   $  But as April 1 approaches, we are apt to postpone the task until April 15 after all - - we procrastinatePut differently, we discount the future pain of April 15 more heavily as April 1 approaches (the fact that task will take 8 hours on April 15 doesn t matter so much as time grows short)To clarify: The more heavily we discount, the less weight we put on the future compared with the present@[ Another example:A lot of people resolve early in the year to set aside money for ChristmasBut often they find themselves spending the money on intervening opportunities summer vacations, back-to-school clothesAgain, as the year progresses, they discount the future (buying Christmas presents) more heavily - - i.e., they become more impatientPI" ?   Many people realize they are vulnerable to this tendencysave by putting money in  Christmas account accounts pay no interestdistinguishing feature is that accounts are illiquidpeople can t get their money out until NovemberZ9{" 0 9r 0  So, in both the tax and Christmas examples, people discount the future more and more heavily as time goes on (hyperbolic discounting)Why are economists interested in this phenomenon?because it gets in the way of saving and other long-term planning:B  We know that we should be saving for retirementbut taking the trouble to actually do so is something we often postponeas a result, most people do not save enough&0t0t  Jgreat virtue of government social security plans:they force us to do what procrastination (hyperbolic discounting) prevents us from doing on our ownthis is best economic rationale for such social security schemesif we weren t subject to hyperbolic discounting, wouldn t need social security<2d 2d,2 ZInterestingly, we re not only species that discounts hyperbolicallybirds (more specifically, pigeons and starlings) do it toolarge experimental literature documenting thisDj  In typical experiment, bird is offered choice betweena big but distant reward ( Christmas ), say 10 seeds after 30-minute waitanda small but more immediate reward ( summer vacation ), say 3 seeds after 10-minute waitbird makes choice by pecking corresponding key (need preparation)many birds opt for later rewardbut after say 8 minutes, switch to earlier option (have become more  impatient )6ZJZZXZZZ6NX  <Notable additional feature:sometimes a third key is introduced disables early-option keymany birds that switch from late to early option eventually peck this keycommits them to later option (just as savers commit to having money for Christmas by creating an illiquid bank account)$"  g" \" $  Why do we (and birds) discount hyperbolically ?most likely, we re acting on the basis of  urges or  inclinations (rather than rational calculation)this is even clearer for the bird subjectsbut these urges come from somewhere(0   \Hypothesis: urges are genetic, i.e., they are shaped by evolutionary forcesWith human behavior, always difficult to separate nature from nurtureThat s why bird evidence so intriguingbirds behavior has a high genetic componentso, things we see them do were likely selected to enhance their survival8vv Will argue that there is a simple evolutionary explanationfor why bird has urge to switch from late (bigger-payoff) option to early (smaller-payoff) option or for why a person might feel inclined to put off doing his taxes from April 1 to April 15 as April 1 approachesThat is, tendency of an individual to discount the future more as time passes (to discount hyperbolically) has survival valuez;co;hoo       But first a simpler question: Why should we be inclined to discount the future at all?Two straightforward and conventional answers: FThe future is uncertain (a bird in the hand is worth two in the bush) a bird may opt for 1 seed now rather than 2 seeds in 5 minutes because the 2 seeds might not be there when 5 minutes elapse (perhaps just one will be left, or even none)It is costly to waitWaiting entails using up energy (physiological cost) bird may go for 1 seed now because because burns up too many calories waiting for bigger rewardWaiting entails passing up other prospects (opportunity cost) by hanging around the raspberry bush waiting for berries to ripen, blackbird may lose out on other goodiesF" Z" Z" Z5" Za Z>" Zl!Z" ZF5  a >k But in comparing 2 future prospects, why is it good idea to discount later prospect more and more relative to earlier prospect as time goes on (as hyperbolic discounting entails)?&TS 6Answer: There is typically uncertainty about not only whether a future prospect will be realized, but when it will be realized.Imagine blackbird is waiting for fruit on a raspberry bush to ripenmay be pretty sure raspberries will ripen by tomorrow morningbut some chance they will ripen earlier (or later)dZqZZ6)[q Expected (average) values If I face an uncertain prospect in which 20% chance of $5 30% chance of $10 50% chance of  $6,expected (average) value = .2 5 + .3 10 + .5 ( 6) = 1so, on average, this prospect will make me richer by $1prospects with higher expected values are on average better than prospects with lower expected valuesD): \Two prospects: raspberries and blackberries waiting cost: 1 calorie per hourraspberry payoff: 4 calories, bird must wait up to 2 hours for berries to ripenblackberry payoff: 5.2 calories, bird must wait up to 4 hours for ripeningFor either prospect, for each hour that goes by, 20% chance that berries will ripen thenAverage Net payoff from (1) = 4  .2 1  .8 2 = 2.2Average Net payoff from (2) = 5.2  .2 (1 + 2 + 3)  .4 4 = 2.4 so best to choose blackberries initiallySuppose 1 hour elapses and neither bush has ripened yetAv net payoff from (1) = 4  1 = 3Av net payoff from (2) = 5.2  .2 (1 + 2)  .6 3 = 2.8 so best to switch to raspberries after 1 hourPZ" Z" ZZP{)8]- ~Idea:bird compares raspberries and blackberriesinitially chooses blackberries, partly because of higher calories, partly because fruit might be ripe earlyafter hour passes, chance of early realization is lowerthis is true of raspberries too, but reduced chance of early ripening doesn t matter much because they will ripen in another hour anywayso bird will switch to raspberriesbasic principle is very general (established in theorem paper)r" a lUncertainty about when berries will ripen means that bird should behave as though it discounts hyperbolicallyoriginally, it is  patient and chooses later,  bigger option: blackberriesafter some time, it becomes  impatient and switches to the earlier,  smaller option: raspberriesBecause urge to switch helps bird get more calories (and therefore improve its survival chances), we should expect urge to result from natural selectionFnZZZn 2But I m not quite done yetalthough have given evolutionary account of hyperbolic discounting, still haven t explainedChristmas accountswhy pigeons peck the third key (which prevents them from later switching from the later 10-seed to the early 3-seed option)if switching is a good calorie-maximizing (survival-maximizing) strategy, why do people and pigeons take pains to commit themselves not to switch?\" 2 ^!" \2^   There is straightforward answerurge to switch was  designed to handle choices in which there is significant uncertainty about when payoffs will be realizedbut in the case of saving for Christmas, there is no such uncertainty- - Christmas is not going to arrive early one year similarly, in the pigeon experiments, the various options are usually programmed to arrive at fixed times. " 2" k"  ` Thus the rationale for switching is lost in those scenariosThis means urge to switch is not well adapted to the different (artificial?) circumstancesBut the poor pigeons and people are stuck with their urges$$ FSo what can they do?can t turn off the urgesbut after learning from experience that urges are ill-adapted, can take steps to stop themselves from acting on themthis is where the commitment devices (Christmas accounts and third keys) come in - - they are solutions to  nonstandard problem6" $  @fact that people and pigeons are learning is important piece of evidencecommitment devices are not used right awaypeople typically struggle unsuccessfully for years with trying to save before resorting to Christmas accountspigeons switch many times before start pecking the third key (which disables option to switch)8t!K  This learning suggests that these scenarios fall outside the norm of  evolutionary experience Also suggests a test of theory: introduce uncertainty about when seeds are realized in pigeon experiments now, switching makes sense again so, pigeons should no longer commit themselves not to switch to the early option& 0` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> f(    6 Ў P T Click to edit Master title style! !  0Ҏ  RClick to edit Master text stylesSecond levelThird levelFourth levelFifth level!   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̙33___PPT10p+qZDT' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*<@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*<@Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<@\%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*<@\D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*<@\Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<\%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*<\D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*<\Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*<Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*<+J0 F>@(  @ @ S h+# @<$D 0 #  H @ 0޽h ? ̙33___PPT10+qZDh' =@B D#' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*@0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*@0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*@Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*@+0 F>D(  D D S <8# <$D 0 #  H D 0޽h ? ̙33"___PPT10+qZD' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*DL%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*DLD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*DLDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*DD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*DDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*DD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*DDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D/%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*D/D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*D/+0 F> H(  H H S E# <$@ 0 #  H H 0޽h ? ̙33rj___PPT10J+1;[D.' =@B D' =@BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H;%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*H;D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*H;D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*HD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*HDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*HD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*HDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*HD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*H+ 0 F>0L(  L L S |Z# <$D 0 #  H L 0޽h ? ̙336 . ___PPT10 +qZD ' =@B D ' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*LY%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*LYD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*LYDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*LZ%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*LZD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*LZ+0 \T@P(  P P S |l#  `<$D 0 # "p`PpH P 0޽h ? ̙33^V___PPT106+qZD' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*PF%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*PFD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*PFDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*PD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*PD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P;%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*P;D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*P;D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P;%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*P;D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*P;Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*PD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*PDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*PF%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*PFD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*PF+0 PT(  Tr T S <#  #  H T 0޽h ? ̙33y___PPT10Y+D=' {=@B +J0 F>`X(  X X S ! <$D 0 #  H X 0޽h ? ̙33___PPT10+qZDh' =@B D#' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*XD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*XDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*XD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*XDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X6%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*X6D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*X6+""0 F> \(  \ \ S H# p<$D 0 #  H \ 0޽h ? ̙33 | ___PPT10\ +qZD@ ' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\DD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\DDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\DW%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\DWD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\DWDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\Wk%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\WkD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\WkDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\k%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\kD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\kDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\Z%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*\ZD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*\Z+/0 \Tp`(  ` ` S # P<$D 0 # "p`PpH ` 0޽h ? ̙33--___PPT10-+qZD-' =@B D]-' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`P%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`PD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`PDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`E%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`ED' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`EDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`E}%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`E}D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`E}Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`}%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`}D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`}Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`$%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`$D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`$Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`$G%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`$GD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`$GDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`G%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`GD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`GDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*`D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*`+0 F>d(  d d S # <$D 0 #  H d 0޽h ? ̙33___PPT10+qZD' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d1%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*d1D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*d1Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d1%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*d1D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*d1Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*dDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d^%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*d^D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*d^Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d^%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*d^D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*d^Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*d+J0 F>h(  h h S X# <$D 0 #  H h 0޽h ? ̙33___PPT10+qZDh' =@B D#' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*hn%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*hnD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*hnDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*hD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*hDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*hD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*h+60 F>l(  l l S @# <$D 0 #  H l 0޽h ? ̙33___PPT10p+qZDT' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*lw%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*lwD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*lwDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*lw%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*lwD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*lwDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*lD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*lDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*lD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*lDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*lD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*l+0 F>p(  p p S # <$D 0 #  H p 0޽h ? ̙33"___PPT10+qZD' =@B D' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*p D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*p Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*pD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*pDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*pD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*pDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*pD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*p+ 0 F>x(  x x S 4 <$D 0 4  H x 0޽h ? ̙336 . ___PPT10 +qZD ' =@B D ' =@BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x<%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*x<D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*x<Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>Bppt_x<*xD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>Bppt_y<*x+J0 F>|(  | | S X <$D 0   H | 0޽h ? 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