A Practicum in Behavioral Economics 3 The Rationality of Homo economicus

CHAPTER . THE RATIONALITY OF HOMO PRINCIPAL RATIONALITY AXIOM Suppose Homo faces two lotteries , which we will denote as lotteries and , where both lotteries are taken from what is known as the space of available lotteries Then , it must be the case that either , or . What the previous sentence says is that Homo either likes lottery at least as much as lottery ( likes lottery at least as much as lottery ( or is indifferent between the two lotteries ( This is known as the Completeness Axiom . For future reference , we will use the equivalent terminology weakly preferred to rather than likes at least as much when referring to the preference relation TRANSITIVITY AXIOM Given any third lottery taken from the space of available lotteries if , and , then BEHAVIORAL ECONOMICS

i . In other words , Homo would never fall victim to a preference reversal , whereby she makes choices that contradict her stated preference ranking . This is known as the Transitivity Axiom . So that we are clear on what a lottery is , here is an example of three possible lotteries , and . Lu 60 chance to win 200 50 chance to 100 55 chance to win 20 40 chance to lose 100 50 Chance lose 70 45 chance to lose 20 As a final note , it is worth pointing out that the Principal Rationality Axioms imply the existence of whats known as a utility function representing an individual preferences over lottery space , specifically , such that ( ZU ( Let unpack this mathematical statement . The first part of the statement ( says that utility function magically translates an individual preferences for the different lotteries that make up lottery space into real numbers . The real numbers , by the way , are measured in what known as , or units of happiness . For example , if ( then the individual facing lottery gets units of happiness just from the opportunity of being able to play the lottery . The second part of the statement ( says that the statement lottery is weakly preferred to lottery ( is equivalent to the statement the utility level obtained from lottery is no less than the utility level obtained from lottery ' 82 ARTHUR

ADDITIONAL RATIONALITY DOMINANCE AXIOM If in all respects ( expected win outcomes are larger than , and Us expected loss outcomes are lower ) then i . To see what we mean by expected win and expected loss outcomes , refer to the example lotteries above in the discussion of the Transitivity Axiom . Lottery expected win and expected loss outcomes , respectively , are 120 ( 200 ) and 40 ( 100 ) while lottery are 50 ( 100 ) and 35 ( 70 ) The final part of this axiom statement , states that lottery is strictly preferred to lottery . An equivalent way to say strictly preferred to is to say likes more This is known as the Dominance Axiom . Again referring to the example above , is by the Dominance Axiom ?

The answer is Although lottery expected win of 120 is larger than lottery expected win of 50 , expected loss of 40 is also larger than expected loss of 35 . If lottery expected loss had instead been some amount less than 35 , we could have concluded that by the Dominance Axiom . INVARIANCE AXIOM If an individual preference ordering of different lotteries does not depend on how the lotteries are described , then the individuals preferences satisfies the Invariance Axiom . We do not have a mathematical expression for this axiom . But there will be plenty of examples as we explore the seminal experiments BEHAVIORAL ECONOMICS PRACTICUM 83

conducted by and , experiments that motivated their famous theories in behavioral economics . We will be learning about these theories later in this section of the textbook . PRINCIPLE If in any possible known state of the world , then even when the state of the world is unknown . This is known as the Principle . Similar to the Invariance Axiom , we do not have a mathematical expression to contend with . We will soon see an example . The Principle implies that an individual does not need to consider uncertainties when making a decision if the individual deems the uncertainties to be irrelevant . For example , if an investor has decided to purchase a company stock regardless of its upcoming earnings report , then it makes no sense for the investor to worry about whether the company will ultimately report a profit or a loss . His preference for the stock is unaffected by the uncertainty surrounding its reported profit level . INDEPENDENCE AXIOM An individual preferences defined over lottery space satisfies the Independence Axiom if for any three lotteries , and , and some constant oz that lies between and ( of and ) we have , This last part of the axiom is a bit ugly . So let look at an example . 84 ARTHUR

Let or and recall , and from the previous example I , 60 chance to win 200 50 chance to 100 55 chance to win 520 40 chance to less 510 50 chance to 70 45 chance to 20 aL ( a ) oz ) 35 chance to 200 30 chance to 3100 22 chance to 20 22 chance to 20 24 chance to lose 100 30 chance to lose 70 12 chance to lose 20 13 chance to lose 520 Thus , in adherence to the Independence Axiom , if , say , an individual weakly prefers lottery to lottery , then that individual will also weakly prefer lottery ( to lottery ( 01 ) By the looks of our example , the comparison between lottery ( oz ) and lottery ( 05 ) is likely to be difficult for Homo sapiens , who would thus be prone to violate this axiom . Hats off to Homo for not violating the Independence Axiom . SUBSTITUTION AXIOM An individual preferences defined over lottery space , satisfies the Substitution Axiom if , for any two lotteries and , and again some constant 02 that lies between and ( of and ) we have , i id . This is a simpler axiom than the Independence Axiom , but lets look at an example anyway . BEHAVIORAL ECONOMICS PRACTICUM 85

Let and recall earlier and from the previous examples , 60 chance to win 200 50 Chance 10 Wit 3100 40 chance to lose 100 50 chance to Then , 36 chance to win 200 30 chance to win 100 24 chance to lose 100 chance to lose 70 In adherence to the Substitution Axiom , if , say , an individual weakly prefers lottery to lottery , then that individual will also weakly prefer lottery to lottery aL ' By the looks of our example , Homo sapiens should at least be able to make the necessary comparisons between each of these lotteries and thus potentially satisfy this axiom . HOMO AND THE EXPECTED UTILITY FORM One of the key assumptions of rational choice theory is that Homo maximizes expected utility based upon his or her total wealth associated with the different outcomes of a lottery . It turns out that because Homo satisfies the Independence Axiom , his or her expected utility is expressed in what is known as the expected utility form ( Mathematically , we say that utility function I , has the if there is an assignment of utility and probability Values ( and my respectively ) defined over a given lottery outcomes i 17 . such that ( 115 ) where , represents the individuals total wealth associated with outcome ' 86 ARTHUR

the sum of his or her initial wealth level plus ( or minus ) the winnings ( or losses ) associated with outcome Ouch . We had better jump to an example where , for simplicity , We set ( we consider lotteries with only two possible win and a loss ) like the lotteries , and presented in the previous examples . Thus , in this case expected utility ( can be Written as ( Suppose an individual has initial wealth of and his or her utility function ( Then , using the values from the previous examples , Thus , You are probably wondering where all of the numbers in the example are coming from . Let first take a look at the value for ( the expected utility associated with lottery Starting with the values and , note that according to lottery , if the individual wins , then he wins 200 , which , added to his initial wealth of 100 , results in 300 . Similarly , if the individual loses , then he loses 100 , which , subtracted from his initial wealth of 100 , results in . The square roots of 300 and come about because the individuals utility function for this example is specified as , where , in this case , corresponds to a win outcome of 200 , and ' corresponds to a loss outcome of 100 . Lastly , the values and , respectively , BEHAVIORAL ECONOMICS PRACTICUM 87

correspond to the 60 probability of the win outcome occurring with lottery , and the 40 probability of the loss outcome occurring . Thus , via the expected utility form , we have ( 1111 ) 172 ) The expected utility values for lotteries and are derived in the same manner . Since ( in this example , the result naturally follows . The utility expression indicates that our individual exhibits risk aversion with respect to total wealth level , This is due to the utility expression itself exhibiting diminishing marginal utility in , Thus , diminishing marginal utility in , is synonymous with risk aversion . To further understand this relationship between diminishing marginal utility and risk aversion , we turn to a graphical analysis . In Figure below , we depict defined on a continuum from the lowest total wealth of at the graphs origin to the largest total wealth of 300 . We also indicate the other total wealth levels of 30 , 80 , 120 , and 200 associated with lotteries and . Note that indeed exhibits diminishing marginal utility in 11 ) or to state it yet another way , wy , concave in , Figure . Utility Function Defined Over Wealth Levels 88 ARTHUR

30 so 120 200 300 Wi For sake of example , let now superimpose the values associated with lottery on this graph , as shown in Figure . Figure . Utility Function Defined Over Wealth Levels with Superimposed Lottery Values . Wi ) 200 ' I air . 115 BEHAVIORAL ECONOMICS PRACTICUM 89

Begin by noting that with lottery the individuals total wealth when she wins equals 200 ( which , as indicated on the graphs vertical axis , corresponds to ( 200 ) and equals 30 when she loses ( corresponding to ( 30 ) We already know from the information provided in the example that ( as indicated on the graphs vertical axis . What the example did not tell us is that the midpoint on the line segment connecting the individuals utility values at lottery loss outcome of 30 and win outcome of 200 corresponds to ( 200 ) 30 ) We can identify two values in this graph that provide quantitative measures of an individual risk aversion . As shown in Figure , the measures are known as certainty equivalent and ( to avoid having to play the lottery in the first place . Figure . Certainty Equivalent and . Note that our reference point for this midpoint of the line to lottery . 50 split in probability of a win and a loss . If , for example , the lottery split had instead been 60 in favor of winning , then the reference point would be located further to the northeast on the line segment , corresponding to a of ( 200 30 ) 138 . 90 ARTHUR

( As depicted in the graph , the individuals certainty equivalence is found by drawing a line horizontally from the midpoint of the line segment to its intersection with the utility function . Mathematically , this intersection corresponds to the value of , in the graph denoted as LE ) that solves for the expected utility value of lottery , This value is 96 , which , because the individual in this example is risk averse , is less than The individuals is then calculated as 100 96 . In other words , the individual is willing to pay ( out of his initial wealth of 100 ) to avoid having to play lottery in the first place . Before leaving this discussion of the expected utility form , consider the following thought experiment . By contrast , if the individual had been assumed risk neutral , in which case her utility function would be drawn linear with respect to wealth ' certainty equivalent would per force be equal to 115 . What would be the result if our individual was instead risk seeking , also known as risk loving ?

BEHAVIORAL ECONOMICS PRACTICUM 91 Choose between lotteries A and A 80 chance to win win for certain If you chose lottery , then you are considered risk averse . That because the expected value of playing lottery A ( is larger than the certain value of lottery , If you weren averse to risk you would have chosen lottery A . Because we are precluded from ever deriving your utility function , we can not calculate your certainty equivalence , per se . So , this type of thought experiment an admittedly expedient way to gauge whether you are risk averse . Can you think of an alternative experiment that would enable us to actually obtain your certainty equivalence ?

Suppose I would have confronted you with the following lottery 80 chance of Winning and 20 chance of losing . I then ask you two questions ( What is your initial wealth , and ( what are you willing to pay to avoid having to play this lottery ( Suppose you answer that your initial wealth is and your is 100 . Recalling our previous graphical analysis , We could stop right here . Because your is greater than zero , We know that for this particular lottery , you are risk averse . But We can also go a bit further and calculate your corresponding certainty equivalence for this lottery . From our graphical analysis we learned that certainty equivalence is the difference between your expected total wealth from playing the lottery and your . Given that your initial wealth is , and you have an 80 chance of winning and a 20 chance of losing , your total expected wealth from playing the lottery is ( Subtracting your 92 ARTHUR

HOMO AND THE INDIFFERENCE CURVE Before concluding this chapter on the rationality of Homo , we introduce another important concept in Figure indifference In doing so , we depart from the world of expected utility defined over Homo possible Wealth levels and venture into a world where Homo chooses different levels of actual commodities to consume . In other words , we model Homo choices in the context of a marketplace rather than the context of a lottery . Figure . Homo Indifference Curves In Figure , let variables and represent the of 100 from results in a certainty equivalence of . BEHAVIORAL ECONOMICS PRACTICUM 93

physical amounts of any two commodities and that Homo might choose to consume ( as a bundle ) at some given point in time , and constant 71 represent some predetermined utility level , say 100 . An indifference curve defined for ' 100 depicts the Homo is willing to make between the respective amounts of commodities and that still result in 100 of Or , alternatively stated , the indifference curve depicts all of the bundles that yield Homo the same utility level 100 . Thus , Homo would feel indifferent about owning any of the bundles on the indifference curve . Hence its name . For those of you with a background in theory , you will recall the stylistic version of Homo indifference curves as shown in Figure . By stylistic we mean that the curves are everywhere and convex ( from the graphs origin . In this graph , we have drawn two indifference curves for the same corresponding to a utility level of 100 , the other to a utility level of 200 . It is no coincidence that the indifference curve associated with 200 lies everywhere above ( to the northeast of ) the indifference curve associated with 11 100 . It is also no coincidence . For those of you who have seen indifference curves before , recall that the slope of the indifference curve at any given bundle of commodities and is the curves marginal rate of substitution ( which can be shown to equal the negative ratio of the individuals marginal utilities at that bundle . The , then , is a marginal or continuous measure of the rate at which the individual is willing to tradeoff commodity for more of . 94 ARTHUR

that the two curves are ( they are parallel and do not intersect each other ) The reason why the indifference curve lying to the northeast is associated with larger utility is because of what is known as , specifically the assumption cum property that an individual obtains more utility by consuming larger amounts of the commodities . Recalling that a given indifference curve depicts all of the different bundles of goods ( in our case bundles of goods and ) that provide an individual with the same level of utility , if we pick any bundle on curve 11 100 ( say , bundle A ) we can always find a bundle on curve 17 . 200 ( say , bundle ) that includes more of both goods and thus , by the Property , implies that utility is indeed higher on 12 200 . The fact that Homo indifference curves for 11 100 and 200 in Figure do not intersect bears further mention . To see why , we need to recast our previous definition of the Transitivity Axiom we learned about in the context of lotteries to the context of commodities and . As a reference point for the Transitivity Axiom , recall the earlier definition provided in the context of lotteries if i and , then . In other words , if an individual weakly prefers lottery to lottery , and also weakly prefers lottery to lottery , then it must also be the case that the individual weakly prefers lottery to lottery . In the case of actual commodities , this definition of the . The shape and location of the indifference curve is directly related to the individuals utility function as it is defined over and ) For example , it can be shown that indifference curves such as those depicted in the figure can be derived from what known as a Douglas utility function , where ( I ( BEHAVIORAL ECONOMICS PRACTICUM 95

Transitivity Axiom changes as follows if an individual weakly prefers commodity bundle A to bundle , and also weakly prefers bundle to bundle , then it must be the case that the individual weakly prefers bundle A to bundle as well . See the parallel between these two ?

Now , assuming both the Transitivity Axiom and Property they do for Homo can prove by contradiction that 11 100 and 200 do not intersect . Or , to state it another way , we can show that if the two curves do intersect , then transitivity and can not hold simultaneously . To see this , consider Figure below , which includes two purposefully unlabeled indifference curves and three different consumption bundles A , and Figure . of the Transitivity Axiom 96 ARTHUR

351 Begin by noting that , via the definition of an indifference curve itself , because bundles A and lie on the same indifference curve , the individual prefers the two bundles equally ( obtains the same level of utility from each bundle ) Similarly , because bundles A and lie on the same indifference curve , the individual also values these two bundles equally . Now , according to the Transitivity Axiom , it must be the case that the individual prefers bundles and equally as well . But wait , by the Property , bundle lies to the northeast of bundle and therefore has more of both goods and in its bundle . So , this property tells us that the individual instead prefers bundle over bundle , which contradicts the earlier conclusion reached by the BEHAVIORAL ECONOMICS PRACTICUM 97

Transitivity Axiom . We have a contradiction here , one which can not stand . Thus , the indifference curves can not intersect each other when the Transitivity Axiom and Property hold simultaneously . Alternatively stated , the indifference curves for Homo can not intersect . HOMO AND CHOICE The previous analyses of Homo preferences and choice behavior have been strictly static in the sense that we have restricted our representative individual to making decisions during a single time period the . But decisions are typically not made in such a vacuum . Instead , we ( both Homo and Homo sapiens ) consider how decisions made today will affect future decisions . In other words , we take into account how money spent today ( for a new shirt ) will affect our ability to purchase something else in the future ( the latest book about behavioral economics ) Choices that span multiple time just the , but also the known as , and the analysis of these choices is dynamic rather than static . Certainly , the span of time we could conceivably account for in our dynamic analysis of Homo choices is long , an entire lifetime . But to keep things tractable , and yet enable key comparisons between the choice behavior of Homo and ( later , in Chapter ) Homo sapiens , we make some simplifying assumptions . First , the time span under consideration is three periods rather than what could 98 ARTHUR

instead be considered a lifetime , or effectively an infinite number of Second , we assume preferences are stable , in particular , that the individuals utility function does not change shape ( functional form ) from one period to the next . Lastly , we assume that the individuals annual income level remains constant over time , as do relative prices . As a result , our analysis loses no generality by assuming that all prices are normalized to a value of one . These last two assumptions imply that Homo exhibits perfect foresight , which should come as no surprise . Perfect foresight means that Homo can accurately predict how her preferences , annual income , or prices of the different commodities will change over time , and thus account for these changes in her decision problem at the outset . Therefore , Homo can not be tricked into making what appear to be inconsistent choices over time . To see this , recall our earlier definition of an individual utility function , which allows us to model Homo decision problem as follows , Mao Subject to , where , and represent the amount of a composite consumption good consumed by the individual in each period , and , respectively to ( 171 ) 614 ( 172 ) Technically speaking , only two time periods are necessary to conduct dynamic analysis ( today and tomorrow , or this year and next year ) Hence , we could claim that our time span extends beyond what is necessary here . BEHAVIORAL ECONOMICS PRACTICUM 99

function represents the individuals utility defined over a given period consumption level parameter ( represents the individuals discount factor , indicating the extent to which he is impatient for present , as opposed to future , consumption prices , and are the given , constant prices for periods , and , respectively and aggregate income 31177 where ) 1112 11 ) the string of imposes the previously mentioned constant income level ) As with the utility function defined earlier over an individual consumption bundle , the function is assumed to be increasing and concave in its respective consumption levels . An impatient Homo is represented by ( yes , as with risk aversion , rational choice theory permits Homo to be an impatient consumer ) As such , in solving her decision problem ( choosing at the outset ( and to maximize aggregate utility across the three periods ( Su ( 372 ) 621 ( Homo discounts her utility level more than her , and in turn discounts her utility more than her second period . Such is the nature of impatience in the context of an choice problem . Because discount factor is constant across time but is nevertheless reduced in value through time exponentially ( if there were a fourth period in our model , discounted utility would enter the individuals aggregate utility as ( and so on for additional periods ) this pattern of discounting future utility is known as exponential time As Figure shows 100 ARTHUR

below ( for ) the schedule of discounted discount factors over time charts out a negative exponential curve that is convex to the graphs origin and asymptotically zero with respect to the passage of time . In other words , as time stretches out further into the future , future utility is discounted progressively to a point where Homo severely minimizes the of additions to his aggregate utility obtained in the distant future . Figure . Exponential Time Discounting Discount Factor 10 15 20 Time Periods Three particular features of Homo exponential discounting problem bear mentioning . First , in solving her choice problem stated above , Homo will choose , and such that her discounted marginal utility levels are equated across time . Let these optimal levels of consumption be denoted , and , respectively . This result ensures a choice profile where LE BEHAVIORAL ECONOMICS PRACTICUM 101

, which is what we would expect the consumption profile of an impatient consumer to look like . For those of you familiar with calculus , in particular solving constrained optimization problems , you will note that you can write this problem in its form as ( du ( 13 ) where , the problems multiplier , and for simplicity , we have normalized all prices to one ( Obtaining the associated system of conditions for this problem results in ( 902 ) 303 ) where denotes the individuals marginal utility function . This string of indicates that discounted marginal utility levels are equated across time . Given our underlying assumptions of and diminishing marginal utility , the string of in turn implies an Second , Homo choice profile abides by what known as In other words , her preferences for any increments to a given level of consumption in two different time periods depends upon the interval of time that passes between the two time periods ( between periods and ) and not the specific points in time when the two respective . Since ' fi ) in the face of the underlying assumption that ' we effectively assume the individual borrows against future income ( without interest penalty ) to obtain the larger consumption level in period . Because the roles of borrowing and saving are extraneous to the insights we seek from the choice problem , we lose nothing by casting the borrowing and savings decisions as implicit . 102 ARTHUR

increments could conceivably be consumed ( periods and ) For example , suppose Homo chooses to consume the same base amount I in each period , and let the two different increments to base consumption be denoted as ' and . implies that if 21 ) in ( ac ) where ( 95 11 ) represents the corresponding utility level in period and ( represents discounted utility level in period , then 611 . 35 ) 6211 ( ig ) by exactly the same amount as ( 512 ( or ig ) where du ( 11 ) represents a discounted utility level in period and ( ac ) represents a discounted utility level in period . This result is easy to see since du ( 21 ) 5211 ( ig ) for periods and reduces to ) for periods and after cancelling from each side of the former inequality . Since the two inequalities are identical through time , Homo preferences are stationary through time . Note that the time intervals under comparison must be of equal length for to be assessed . For example , if ( I ) du ( I ) for consecutive periods and , this does not necessarily imply that ( 21 ) 6211 ( by the same amount across periods and ( convince yourself of this fact ) To further test your understanding of , suppose there was a fourth period of consumption . You should be comfortable seeing that if ( at 11 ) or ) between periods and , then 672 ( 21 ) 331 ( between periods and by the same amount . Third , Homo preferences are time consistent , In other words , given that he has chosen BEHAVIORAL ECONOMICS PRACTICUM 103

, and at the outset for any given set of , and prices , and , then if after having consumed at level 261 in period , the individual decides to his decision problem from that point forward ( now starting in period ) he will not deviate from choosing and In this case , the individual effectively solves the problem , Max , subject to , 2111 ( which results in the same 51 and as before . To see this result , first note that we can pull ( from the string of three derived from the individual original decision problem ( 11 , and then cancel from each side of the equality , resulting in ( But ( 172 ) is precisely the equality that results from the conditions for this problem . Given that nothing else has changed in this problem ( the values for , and , and are the same , as is the functional form of and the fact that 301 has already been chosen ) no values for and 333 , respectively , solve ( except and And if after having consumed at levels 171 and for the first two periods , he then decides to his decision problem from that point forward ( now starting in period ) he does not have a problem left to has effectively locked himself into consuming at that point . Therefore , because he chooses not to alter his consumption profile over time by having embarked on du ( 104 ARTHUR

these decision problems , we say that his choices are time consistent . KEY TAKEAWAYS ON HOMO So , what have we learned about Homo thus far ?

For starters , we have learned that she is inviolable when it comes to making the miscalculations and , exhibiting the biases , and falling victim to the fallacies and effects that bedevil Homo sapiens . Furthermore , Homo is inextricably bound by the rationality axioms of Completeness , Transitivity , Dominance , Invariance , Independence , and the Principle . And when confronted with the uncertainty of having to play a lottery , Homo chooses to maximize expected utility derived over her total wealth . In the face of uncertainty , Homo can be risk averse . And when it comes to a deterministic setting , such as when Homo enters the marketplace to purchase actual commodities , the family of indifference curves that represent her preferences for different bundles of commodities are not permitted to intersect with each other . In other words , Homo borrow the title of Sade hit smooth operator . Her expected utility function and indifference curves are smooth , and when it comes to navigating the challenging choice situations that often confound Homo sapiens , she smoothly the pitfalls . Nevertheless , as we pivot to learning about the behavioral economic theories that have emerged to explain the in choice behavior between the two species , bear in mind that to a great extent the reason why Homo seems so smooth BEHAVIORAL ECONOMICS PRACTICUM 105

is because the world explained by the rational choice model is perforce restrictive of many of the characteristics that define the human , sensation , distraction , a world whose complications seem to demand imperfection and roughness ( as opposed to smoothness ) As a result , Homo couldn help but perform well within a bubble of . Fortunately , as we are about to learn , the adjustments to the framework devised by behavioral economists are quite efficacious , not to mention eloquent . STUDY QUESTIONS Note Questions marked with a are adopted from Cartwright ( 2014 ) State the Completeness and Independence Axioms in two separate , sentences . Recall that Figures are depicted for utility function , indicating that Homo exhibits risk aversion with respect to total wealth level . a ) Suppose instead that ) Reconstruct Figures for this utility function and interpret your results in relation to the figures in the text derived for Can you think of any reason why 11 , might not be representative of Homo preferences ?

Explain . Now let Reconstruct Figures for this utility function and interpret your results in 106 ARTHUR relation to the figures in the text derived for as well as those you derived in part ( a ) for ( wi ) wi . Can you think of any reason why ) might not be representative of Homo ?

Explain . Suppose Henry the Homo is presented with the following lotteries Lottery A Win with a probability of . Lottery Win with a probability of . Lottery Win with a probability of . Lottery Win with a probability of . Show why it would be inconsistent for Henry to choose Lottery over Lottery A together with Lottery over Lottery What pattern do you notice in the four lotteries ?

In Figures , Homo indifference curve is drawn . Suppose instead that the indifference curve is sloping , as depicted in the figure below . Interpret this figure . Hint One of the two goods is actually a bad rather than a Would Homo ever exhibit an indifference curve ?

BEHAVIORAL ECONOMICS PRACTICUM 107 . Given the indifference curve in Question , does satisfying the Transitivity Axiom still imply that indifference curves can not intersect one another ?

Explain . What does satisfying the Invariance Axiom imply about Homo susceptibility to Framing Effects studied in Chapter ?

What does satisfying the Principle imply about Homo susceptibility to Priming Effects studied in Chapter ?

What would you call an individual whose time discounting path is depicted in the figure below ( it fits the shape of a positive exponential curve rather than negative exponential curve as 108 ARTHUR depicted in Figure ) Discount Factor 15 20 10 Time Periods Media Figure ( Chapter ) Arthur is licensed under a BY Attribution ) license Figure ( Chapter ) Arthur is licensed under a BY Attribution ) license Figure ( Chapter ) Arthur is licensed under a BY Attribution ) license Figure 10 ( Chapter ) Arthur is licensed under a BY Attribution ) license Figure Arthur is licensed under a BY Attribution license Figure Arthur is licensed under a BY Attribution license Figure BEHAVIORAL ECONOMICS PRACTICUM 109

Figure Arthur is licensed under a BY Attribution license Figure Arthur is licensed under a BY Attribution license Figure Arthur is licensed under a BY Attribution license Figure for Study Question ( Chapter ) Arthur is licensed under a BY Attribution license Figure for Study Question ( Chapter ) Arthur is licensed under a BY Attribution license 110 ARTHUR