Cognitive Time Distortion on the Performance of Economic Organizations

■ Research Paper

Cognitive Time Distortion on thePerformance of Economic Organizations

Fabian von Schèele2 and Darek M. Haftor1*1Department of Informatics, Linnaeus University, Växjö, Sweden2School of Business, Stockholm University, Stockholm, Sweden

This paper introduces a novel conception of an economic organization, where its TotalProfit Equation accounts for the phenomenon of cognitive time distortion—this beingunderstood as the discrepancy between physical and cognitive time. Cognitive timedistortion is unconditionally inherent in all human beings and everything they do, andtypically produces economic inefficiencies as well as human stress; all this may now beconceptualized, detected, and acted upon. The novel Total Profit Equation as introducedhere, including its underlying Total Revenue Equation and the Total Cost Equation, echoesa call of the founders of Systems Sciences that non-trivial systems manifest several kindsof temporal experiences. This call has largely been ignored by the various disciplines thatstudy organizations and their management, particularly economic organizations, wherethe temporal experience of economic organizations is reduced to physical time. In thissense, this contribution offers an alternative to remedy that reductionism. Copyright ©2013 John Wiley & Sons, Ltd.

Keywords economic organization; contract; productivity; cognitive time distortion; reductionism

INTRODUCTION

This paper presents a novel conception of an eco-nomic organization where its Profit Equation isendowed with a rigorous account of cognitive timedistortion; this phenomenon is understood as thediscrepancy between physical time and cognitivetime that is unconditionally inherent in all humanbeings and everything they do. The model intro-duced here articulates significant organizationalinefficiencies caused by temporal misperceptions,

which may now be conceptualized, detected andacted upon; as a consequence, this economicmodel offers a novel contribution to a number oforganization-related disciplines.

The remaining part of this Introduction is madeup of a brief system theoretic contextualization ofthe topic addressed here, which is followed by abrief disposition of the whole paper.

Manifestation of several kinds of time

The early twentieth century system science theor-ists (see Hammond, 2003) have sent a clearsignal: non-trivial systems manifest several kinds

*Correspondence to: DarekM. Haftor, Department of Informatics, Lin-naeus University, Växjö, SwedenE-mail: [email protected];[email protected]

Received 15 August 2012Accepted 22 January 2013Copyright © 2013 John Wiley & Sons, Ltd.

Systems Research and Behavioral ScienceSyst. Res. 31, 77–93 (2014)Published online 21 March 2013 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/sres.2173

of temporal experience, or time. For instance, theso-called father of the General Systems Theory,von Bertalanffy (1968, p. 100), stated that ‘Experi-enced time is not Newtonian. Far from flying uni-formly (aequilabiliter fluid, as Newton has it), itdepends on physiological conditions’. This con-ception articulates the experiences of differentkinds of time and also the gap between physicaland cognitive time, yet without being preciseabout it. In the same line of this message, butmore specifically, the Living Systems Theoryproposes the existence of a set of kinds of time,depending on system level, hence eight kindsof time, each kind of time for each kind ofsystem level, i.e. cell, organ, organism, group,organization, community, society, and the supra-national system (Miller, 1990). The message hereis that each kind of system must contain a subsys-tem (i.e. process) called the Timer. Its function is to‘measure elapsed time, set the pace of rhythmicprocesses like the heartbeat, and underlie changesof components from state to state in oscillatingprocesses in order to keep the system synchro-nized with its environment and to coordinate theinteractions of its subsystems and components’(Miller, 1990, p. 164). This message recognizes theexperience that mechanical time may differ frombiological time or cognitive time: ‘Engineers, how-ever, point out that clocks and timers are not neces-sarily the same sort of thing in the mechanicalsystems they work with and may not be in livingsystems either’ (Miller, 1990, p. 164). In this sense,the Living Systems Theory also accounts for theexperience that there exist different kinds of time,including physical and biological time, and thatthese have different rhythms. However, no morespecificity will be provided here, with regard toexactly what the difference is, and particularlyhow the various kinds of time interrelate.

While systems thinkers have directed their at-tention to the experience that non-trivial systemsmanifest several kinds of time, this messageseems to have been ignored by the various disci-plines that study economic organizations andtheir performance, such as firms, governmentalorganizations and non-governmental organiza-tions. Hence, orthodox economic thinking andpractices assume the existence of one kind of timeonly: physical time. This ignorance is challenged

here with an alternative notion that accounts fortwo kinds of time: physical and cognitive time.

We show here that all human activity systems(e.g. Checkland, 1981; Eriksson, 2004), whetherthey be business organizations, governmental andnon-profit organizations or inter-organizationalcollaborations, manifest situations where more(or less) time is consumed by its staff than plannedfor but also perceived and paid for. Even thoughthere may be several reasons for this, one key rea-son is the so-called cognitive time distortion, wherehuman cognitive time perception relates in a non-linear and non-expected manner to physical time,i.e. the latter typically called clock time. Cognitivetime distortion has been well known to psycholo-gists for at least a century (e.g. Lavie and Webb,1975; Ceci et al., 1988; Campbell, 1990; Eisler andEisler, 1992; Block and Eisler, 1999) and constitutesamajor challenge for themanagement and econom-ics of any operations conducted by human beings.As cognitive time distortion has escaped the noticeof management, organization, business, and eco-nomic studies, this paper represents an initial steptowards remedying this unmet demand throughan elaboration of economic profit and loss, by expli-citly incorporating the everyday phenomenon ofcognitive time distortion into the conventionalProfit Equation. This incorporation offersmore just-ice to how economic organizations actually operate,rather than reducing them to a mechanical concep-tion of time; it also provides an initial formalcharacterization of the structure and function ofeconomic organizations with regard to revenueand cost, and profit and loss that account for thiscognitive time distortion. In this way, the modelproposed here indicates a novel approach thataccounts for key economic deficiencies presentin contemporary societies and their variousorganizations.

The next section elaborates briefly on the notionof time and its kinds; this is followed by a summar-ized characterization of the phenomenon of cogni-tive time distortion, which is fundamental for themodel introduced here. The section after thisshows the probabilistic character of cognitive timedistortion, accounting both for individuals and forcollectives of individuals, i.e. organizations. Allthis is then incorporated into the economic profitand loss equations, in terms of the Total Revenue

RESEARCH PAPER Syst. Res.

Copyright © 2013 John Wiley & Sons, Ltd. Syst. Res. 31, 77–93 (2014)DOI: 10.1002/sres

78 Darek M. Haftor and Fabian von Schèele

Equation, the Total Costs Equation, and then theTotal Profit Equation. The paper endswith sectionswhere the model proposed here is positionedwithin the context of current academic discourseson management and organizations, articulatingthe theoretical contribution advanced here. Finally,a handful of key areas that may merit furtherresearch are exposed in brief, and a summary ofthe key message is provided.

TIME

On the one hand, time holds a special position inscience, as it is central to physics while being atthe same time notoriously difficult to define(Whitrow, 2003). On the other hand, most humanbeings intuitively know what time is. A commondefinition of time, in physics, is that ‘time is whata clock measures’ (Whitrow, 2003). This defin-ition is not exhaustive, as a consequent questioneasily emerges: what is a clock then? The typicalanswer to this is that a clock is a mechanicaldevice that measures time (Whitrow, 2003). Thiscircularity between time and clock is, however,not especially penetrating; therefore, we assumehere a notion of time as a measure of somechange (e.g. Le Poidevin and MacBeath, 1993;Oaklander and Smith, 1994; Mellor, 1998). In theWestern civilization, time has become the implicitcontext for all sorts of change, e.g. speed (km/h),growth rate (numbers/year), profit (MU/year),frequency (oscillations/s), acceleration (speed/time-unit squared), and heart rate (beats/min).In the present context, a differentiation is madewith regard to physical time, which is under-stood as the time that is measured by a clock,and cognitive time, which is understood as themental perception of time. Physical time and cog-nitive time are relevant both for a retrospectiveassessment of elapsed time and for prospectiveprognoses of time needed for any reason.In the study of time, several scholars have

introduced various kinds of time. For example,Dooyeweerd (1955–58) holds that human realitymay be understood in terms of a set of interre-lated temporal aspects, or modalities, and thateach of these aspects has its own temporality.Dooyeweerd (1955–58) proposed that human

reality may be understood in terms of the follow-ing 14 modalities, each accounting for its specialkind of time: arithmetic; spatial; kinematic; phys-ical; biotic; sensitive or psychic; logical; historical;lingual; social; economic; aesthetic; juridical; eth-ical and creedal or pistic. This is not the place fora detailed account of Dooyeweerd’s proposal,but rather only to highlight a key point maderelevant for the present study: all human beingsseem to experience various kinds of time. Anillustration exemplifies this as follows.

When Jane, in her work, travels from Europe tothe USA on an airplane, she will experience phys-ical time and its geographically induced alternation,i.e. time zones, such as the 6-h time difference be-tween London and New York. Further, she mayalso experience biological time manifesting itselfas so-called jet lag, when her body wants to sleepin the early afternoon upon arrival. Thirdly, Janemay then experience cognitive time, for example,when embarking early in the morning in Europeand, after a flight-long sleep, disembarking on theeast coast of USA, she may feel that the trip tookonly 2h rather than 6h. Further, as in such a par-ticular flight, Jane moves backward in the assumedphysical–geographical time spectrum, and know-ing that her flight is conducted as part of her workwhere each working hour induces a certain cost tothe employer, she technically considers that thisflight may induce less cost to her employer whencompared with a situation where she would stayin Europe and not fly to the USA, or when shewould fly from Europe to Japan. Hence, there isan economic aspect to time aswell, often articulatedin the expression ‘time is money’. The presentinquiry focuses its particular attention on, andbuilds its argumentation upon, the distinctionbetween physical (or clock, or objective) time andpsychic (or cognitive, or subjective) time, and thenits relation to costs and revenues.

As suggested above, physical time is some-thing that is measured by a clock. To be sure, aclock is a recent mechanical invention of humankind (i.e. fifteenth century; e.g. Whitrow, 2003).This kind of time is characterized by regularity,continuity, and a steady pace; it is abstract and ir-reversible and measured with dedicated devicesexternal to the human being (Whitrow, 2003).Psychic or cognitive time, on the other hand,

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Cognitive Time Distortion and Economic Organizations 79

may be understood as a human being’s mentalexperience or perception of time. Hence, a dur-ation measured by the physical clock may beexperienced by a human being, without beinginformed by an external clock, as an hour, as lessthan an hour, or as more than an hour. Unlikephysical time, psychic time passes in jerks andjumps and has no standardized measurementother than the mental experience, whether con-scious or not (e.g. Ashoff, 1985).

COGNITIVE TIME DISTORTION

We would now like to introduce a crucial empir-ical phenomenon, which typically passes un-noticed by most human beings, namely, that therelation between physical time and cognitivetime may give rise to the phenomenon herecalled cognitive time distortion. The divergencebetween the two kinds of time is well known inthe medical and psychological disciplines (e.g.Levin and Zackay, 1989; Block and Eisler, 1999),yet to our knowledge, it has not been elaboratedby the various management and economicsciences, which we will also show later in thispaper. More specifically, cognitive time distor-tion is understood here as the difference betweenthe cognitive time of an individual and the phys-ical time as measured by a clock. As mentioned,the cognitive time of an individual tends tomovein jerks and jumps, while the physical timepasses smoothly and at an even pace. Therefore,when individuals estimate time durations, theytypically, unintentionally and unknowinglycommit errors resulting in significant differencesbetween the self-assessed cognitive time and thecorresponding physical time. A review ofcurrent research into cognitive time distortionsuggests that the gap, or the error, in correctassessment of 1 h may vary between 1.08–2.14 h(see Table 1 for a summary of that literature; seealso Block ,1990, p. 5).

In general terms, this inquiry assumes cogni-tive time distortion to be the ratio between thecognitive, or psychic, time (tc) and the physical, orclock, time (tp). Consequently, cognitive time dis-tortion may be formalized in the following way:

Cognitive Time Distortion ¼ tc=tp

In appraising time distortion, it is necessarythat the psychic and the physical time havethe same frame of reference, and that theyaddress the same event, whether retrospectivelyor prospectively. Thus, frame of reference andevent may signify, for example, an activity, aprocess, a project, or a service contract. Timedistortion is a relative measure and can beinterpreted as the difference, here the error, thatoccurs when a human individual assesses atime duration in relation to its correspond-ing physical time, whether retrospectively orprospectively. Therefore and more specifically,time distortion, here denoted as ti, is definedas the ratio between the psychic time, tc, andthe physical time, tp, of a certain event i; hence,formally

Time Distortion : ti ¼ tc=tp� �

i (1)

Specifically, in the context of a businessagreement, tp denotes the time agreed upon ina certain contract, where i denotes a contractnumber in the given context. From this defin-ition, it follows that time distortion, ti is limitedby [0. . .L], where L is a large number, and that avalue of ti corresponding to unity signifies thetotal conformity between psychic and physicaltime. Thus, ti=1 signifies that there is a perfect

Table 1 Various studies’ mean value of one psychic hour,obtained by individual’s self-assessment versus a physical

clock measurement

SourceMean value of one psychic

hour (h)

Macleod andRoff (1936) 1.22Vernon and McGill(1963)

1.08

Siffre (1964) 2.14Lavie andWebb (1975) 1.12Hartley et al. (1977) 1.24Ashoff (1985) 1.47Campbell (1990) 1.12




compliance between the cognitive and physicaltime, which can also be denoted as ti=100%.Anticipating the forthcoming elaboration below,we wish to highlight that the nature of this corres-pondence constitutes a key erroneous assumptionmade within present managerial and economicconceptions.Now, a question that easily emerges here iswhat

is the cause of the cognitive time distortion? A setof central factors are mentioned here to orient thereader and also to account for the non-trivialitythat characterizes the emergence of cognitive timedistortion. Research has found several factorsinfluencing time distortions of an individual. Forexample, a time distortion may depend uponwhether the assessment of the duration is relatedto an empty or a filled time interval (c.f. Eislerand Eisler, 1992). During an empty time interval,no noise or interruptions distract the cognitiveprocesses of the individual. However, time assess-ments of filled time intervals tend to have poorervalidity with a larger standard deviation of theerror. Thus, the time distortion corresponding toassessments of filled time intervals might betterreflect situations in real life. For example, timeplanning activities taking place in settings wheretelephones, noise and interruptions frequentlydisturb the cognitive processes of individuals.Another cause, explored in a study of paramedicperception of elapsed field time (Jurkovich et al.,1987), shows that time distortion varies dependingon task, such as transport of patient or site activity,with an overestimation of time durations between11% and 61%; the estimated time durationswere 1.5–5min. For instance, Collopy (1996)shows that the amount of (computer) system useinfluences time perception, where frequent usersunderestimate the time while light (infrequent)users overestimate it. This may be in contrastto previous studies where system users tendedto overestimate the use time (Robinson, 1985;Pentland, 1989) while other studies (Hyett, 1979;Rice et al., 1989) suggested underestimation ofsystem use. In a study of pain mitigation (Thornand Hansell, 1993), the cognitive time distortionvaried between an underestimation by 42% to anoverestimation by 10%. Yet another study reportedtime distortions varying between 50% and 500%during assessments of filled time intervals of

3–5min (von Schéele, 2001). Further factorsinfluencing the emergence and dynamics oftime distortion include body temperature,gender, perceived stress, perceived pain, age,and mode of reproduction of time interval—e.g.verbal reproduction or mechanical reproductionby means of pressing a button controlling abuzzer (von Schéele, 2001).

This elaboration has so far introduced theeveryday phenomenon of cognitive time distor-tion. In the context of this inquiry, at least threekey insights may be highlighted. Firstly, cogni-tive time distortion is, unconditionally, prevalentin human daily life. Second, the scope of the timedistortion is extensive; that is, time distortioninfluences all human activities and operationswhatever their context, be it human, social, orbusiness and industrial. Thirdly, cognitive timedistortion is not constant and is influenced by aset of different factors. Taken together, theseinsights suggest that cognitive time distortionmay have significant yet little known conse-quences for the planning, managing, executionand control of any organized human activity,whether in or between organizations. Therefore,the nature of time distortion will be investigatedin the next section.

THE NATURE OF COGNITIVE TIMEDISTORTION

It is now time to turn our attention to a key char-acteristic of cognitive time distortion. This maystart with the leading question: what is the pat-tern of cognitive time distortion within a givenpopulation of human actors? This question maybe further qualified in terms of whether there isany difference in the patterns of cognitive timedistortion when comparing an individual actorversus a group of actors. The following addressesthese questions.

The Probabilistic Nature of Cognitive TimeDistortion

Recalling the empirical research of von Schéele(2001), Figure 1 shows a crucial insight: that the




variation of cognitive time distortion, within agiven population of human actors, and measuredat the level of an individual human actor, manifestsa stochastic pattern. Figure 1, upper panel, showsthe distortion measured at individual subject level.Out of 224 monitored subjects, very few showednon-distortion (i.e. t =100%), the majority showeda positive distortion (i.e. t> 100%) and a minorityshowed a negative distortion (i.e. t< 100%).

Figure 1, lower panel, shows the cognitive timedistortion at the level of a group of human actors,here measured as the conduct of service contracts.1

As at the individual level, of 233 conductedcontracts, very few, only 37 contracts, showed amoderate distortion (i.e. 80%< t< 120%). Instead,111 contracts showed a positive distortion (i.e.t> 120%), while 85 contracts exhibited a negativedistortion (i.e. t< 80 %) (see von Schéele, 1999).

These results show that cognitive time distor-tion has a stochastic pattern both at the level ofan individual subject and at the level of a groupof subjects; however, these deviations are morepronounced at group level (lower panel) than atthe individual subject level (upper panel). Inour experience, the data presented in Figure 1show a counter-intuitive outcome discord witha frequently assumed common opinion that anerror in time assessment will level off over time.The data in Figure 1 show that the stochasticpattern displays a large variation in amplitudefor t yet has a general positive tendency, i.e. thecognitive time> the corresponding physical timeframe, for a given event. All these imply that theempirical phenomenon of cognitive distortion,both at the level of an individual human actorand at the level of a group of human actors,corresponds to the mathematical statistical prop-erties of a stochastic variable; hence, an additionof mean values of stochastic variables impliesan addition of standard deviations as well.

The Asymmetric Nature of Cognitive TimeDistortion

To further elucidate the statistical nature of thetime distortion t, consider P(t) as the probability

function of the stochastic time distortion variable t.Let p(t) express the probability that a timedistortion of magnitude t occurs. The expectedvalue E(t) of the time distortion t in a set consistingof i events, where [i=1. . .r], can then be defined asE(t) =Σp(ti) ti. Provided that the individuals of agiven population are unbiased or randomly biased,the time distortion will then exhibit a probabilitydistribution P(t) with the following properties:

(1) P(t) is not symmetrically distributed aroundt=1, which implies that the arithmetical meanvalue mt 6¼ 1 and the expected value E(t) 6¼ 1.There exist several examples of empirical evi-dence supporting this, showing that individualsassessing time exhibit a tendency to overesti-mate the passage of time (e.g. Ashoff, 1985;von Schéele, 2001).

(2) P(t) is not Gaussian-distributed but exhibitsinstead an asymmetric distribution with along tail for values of t> 1. In such distribu-tions, it should not be expected that the arith-metical mean value mt corresponds to theexpectancy value E(t). Serious errors will becommitted if a Gaussian distribution of timedistortion is assumed in economic calculus,as such an assumption, in turn, builds on pre-suppositions that both the arithmetical meanvalue mt and the expected value E(t) are equalto unity. To illustrate this point, an investiga-tion of five service organizations (vonSchéele, 2001) showed that both the arithmet-ical mean value mt and the expected value E(t) of P(t) were larger than 2 (see Figure 2).Thus, the time estimations of the employeesexceeded the actual contracted time, whichindicates a general overestimation of the pas-sage of time. Furthermore, only 16% of thecustomers received a service time thatmatched contractual time. The practical con-sequences of this were large deviations frombudgeted economic outcome as well as poorprofitability of the investigated service opera-tions (see von Schéele, 2001, for details).

(3) The statistical distribution of cognitive time dis-tortion is sensitive to time-related feedback. Asa consequence of the generic causes for the ac-tual emergence of cognitive time distortions, to-gether with its stochastic character as discussed

1 Each of the Service Contracts measured was conducted by two ormore individual subjects; see von Schéele (2001).




earlier, we may conclude that the standard de-viation SD(t) and the arithmetical mean valuemt can efficiently be manipulated by means ofpriming techniques (e.g. von Schéele, 2001, p.309–310). Among other things, this inducesthe hypothesis that time distortion in humanoperations may be minimized by cognitivetechniques, thereby significantly influencingand hence changing the profit level of an eco-nomic organization.

Before moving on to the next section, to elabor-ate the economic implications of the properties ofthe probability distribution P(t) presented here,we wish to observe briefly that these last proper-ties are counter-intuitive. This is so, as we haveexperienced a frequent assumption in real-lifeorganizations that ‘the loss of time in a businesswill be proportional to the gains’. However, the

empirical data presented here shows that such anassumption cannot be supported. People have alltoo often sustained the idea that occurrences thatpass by chance follow some kind of ‘Gaussian dis-tribution law’; i.e. good balances evil in life andnight balances day. Such intuition-based rules ofthumb lack empirical support; instead, the datapresented here imply that the asymmetrical prop-erty of P(t) influences any human activity system,including its human actors and the economicproperties assigned to such a system. It is nowtime to turn our attention to the implications thatcognitive time distortion may have on aneconomic organization (Foss, 2010), such as a firm.

ECONOMIC PROFIT IMPLICATIONS

In society, economic transactions are typicallyunderstood in terms of the goods and servicesproduced and exchanged. The key message of theresearch presented here is that cognitive time distor-tion, as introduced above, has important, and prob-ably profound, implications on the production of

Figure 1 Empirical results from measurements of the cognitive time distortion at the level of an individual human actor(upper panel) and at the level of a group of human actors (lower panel) (the empirical data is based on von Schéele (1999,2001)). Both data sets clearly show the stochastic nature of cognitive time distortion. The upper panel results show thevariation of cognitive time distortion of individuals in a laboratory experiment (N= 224), while the lower panel results showthe variation of cognitive time distortion prevalent in service contracts (N= 233) for five service organizations,2,3 The ordinateindicates the time distortion t ; 100% corresponds to when cognitive time equals physical time (upper panel) or when cogni-tive time equals contracted time (lower panel). The abscissa indicates the subject number (upper panel) or project contractnumber (lower panel). This elementary indicator clearly shows that that there is a significant deviation between the physicaland the cognitive time, both at individual and at group levels. While the distortion pattern is clearly stochastic, there is a pro-nounced elevation of the deviation as the physical time increase, and as the time assessments are made in business settings.4

These data sets challenge clearly the convention of contemporary economic and management thinking and practices

2 The lower panel excludes 18 customer contracts with 500< t< 5862 (% t).3 Note that t in the field study consists of multiple time assessmentsmade by different employees, the sum of which were added up for eachservice contract.4 The other important trait to consider is that there exists amarked asym-metrical quality in the statistical distribution of cognitive time distortion.This asymmetry in statistical distribution is demonstrated in Figure 2.




both goods and services when human actors aresignificantly involved in such a production.

Given the space limitation here, this account fo-cuses only on how cognitive time distortion influ-ences the production of services. This is for tworelated reasons: First, cognitive time distortioninfluences service production more profoundlythan the production of goods, mainly because ofthe typical extent of human actor involvement inthe service production process. Second, and as aconsequence of the above, the articulation of theimplications that cognitive time distortion has onthe production process is more direct when pre-sented in the context of services production. How-ever, the elaboration that follows here also hassimilar implications for the production of goods.

The dissimilar effects of cognitive time distor-tion, due to the contractual form,will be addressedfirst. This is followed by an elaboration of the TotalRevenue Equation and the Total Cost Equation, re-spectively, both of which account for the cognitivetime distortion. A synthesis of the two equationsgives rise to a modified Profit Equation, which issubsequently presented.

The Dissimilar Effects of Cognitive TimeDistortion on Economic Outcome

One starting point for the conceptualization of aneconomic organization is the contract (e.g. Coase,1937; Williamson, 2002). Cognitive time distor-tion, then, causes an economic distortion in theproduction of services in two alternative ways,related to the nature of the contract between theservice supplier and the customer, and is specific-ally linked to the irreversible property of time.The two different economic agreements appliedon the service market are typically as follows:

(1) Service delivery at a fixed price (fixed-price con-tract). The service provider and the customerhave agreed upon the total time volume of theservice (tp), the price, and the date ofdelivery, after which the service deliverycommences. The service delivery ends whenthe contracted time volume has been deliv-ered. The time distortion t is here consideredwith reference to the predefined time in thefixed-price contract (tp).

(2) Service delivery on current account (current ac-count contract). The service provider and thecustomer have agreed upon the price per timeunit for the service. The total time volume (tp),

Figure 2 Shows the asymmetrical probability distribution P(t) of cognitive time distortion. The upper panel illustrates the dis-tribution of cognitive time distortion for individual time assessments in a laboratory experiment (N= 224), while the lowerpanel illustrates the distribution of cognitive time distortion at the level of a group of individuals (here service contracts, whereN= 233 in five service organizations5,6). Arrow ‘A’ indicates the mean value, 23mt, of a Gaussian distribution, arrow ‘B’ theapproximate mean value, mt, and arrow ‘C’ the approximate expectancy value, E(t), of the probability distributions P(t) (data

from laboratory experiment and service contracts in von Schéele, 2001).

5 The lower panel excludes 18 customer contracts with 500< t< 5862 (% t).6 Note that t in thefield study consists ofmultiple time assessments bydiffer-ent employees, the sum of which were added up for each service contract.




however, remains unspecified. For each per-formed additional hour of the service delivery,the service provider will charge the customer.For this economic agreement, the time distor-tion t is considered with reference to the phys-ical clock time (tp).

The total revenues per time unit (TR) and thetotal costs per time unit (TC) are both influenceddifferently by cognitive time distortion in thesetwo distinct contractual forms, as illustrated inFigure 3. As practical experience demonstrates,that which is specified in a contract (prospect-ively) typically differs from that which is actu-ally delivered (retrospectively), especially withregard to the time volume. An underlying rootto such differences is the cognitive time differ-ence, as specified here (e.g. Formula 1). Specific(mathematical) mechanisms relate the economicoutcome to the cognitive time distortion, as willbe elucidated below.Consider first the fixed-price contract. Should

employees overestimate the time volume deliv-ered, leading cognitive time, tc, to exceed thecontracted or physical time, tp, the time distor-tion, t, will be greater than unity, thus decreasingTR per time unit (‘A’ in Figure 3). On the otherhand, an underestimation of the time deliveredaffords a time distortion, t, less than unity, andTR per time unit will increase (‘B’ in Figure 3).Thus, the time distortion, t, is inversely propor-tional to TR per time unit for the fixed-pricecontractual model.Consider then the contract on current account.

Here, the customer is charged for the contractor’scognitive time assessment, tc, regardless ofwhether it equals the actual physical time deliv-ered, tp, or not. Underestimation of the passageof time—leading to undercharging—causes adecrease in TR per time unit (‘C’ in Figure 3),and the time, tc, reported to the customer willbe less than the actual physical time delivered,tp. The opposite will occur if time is overesti-mated (‘D’ in Figure 3). Therefore, the influenceof time distortion, t, on TR per time unit is linearfor contracts on current account.This distinction between the fixed-price con-

tract and the current account contract induces arule of dissimilar effects due to contractual mode,

which also applies to the total costs, TC per timeunit. The time distortion in the total costs, TC pertime unit, however, always refers to the em-ployee contract. Thus, the temporal frame ofreference to the cognitive time distortion is thecustomer contracts (for the total revenues, TR)and the employee contracts (for the total costs,TC). This latter distinction forms the basis forthe mathematical lever effect due to time distor-tion, an effect that is demonstrated below.

In summary, we have decomposed the TotalRevenue Equation (Formula 2) into two specificcontract categories, where each category mani-fests a unique mathematical property, namely,the category of ‘customer contracts’ (that refersto Total Revenues, TR, per time unit) and the cat-egory of ‘employee contracts’ (that refers to TotalCots, TC, per time unit). Next, each of the twocontract categories is further decomposed intotwo subgroups, respectively: the subgroup of

Figure 3 Relation between Total Revenues (TR) and TotalCosts (TC) per time unit vs. Cognitive Time Distortion.Cognitive time distortion generates dissimilar effects, whichare determined by the contractual category: current accountvs. fixed price. There is a variation of TR and TC per timeunit due to contractual category and as a function of thecognitive time distortion t, d (for further details, see vonSchéele, 2001). Figure 3 focuses on a phenomenon hithertolittle observed, illustrating the lever effect between linearcognitive time distortion and curve linear economicoutcome. While the relation between volumes of goods andeconomy is assumed to be linear, this does not apply tovolumes of time and economy. Instead, as Figure 3 demon-strates, there exists a curve linear relation between the

volume of time and economy.




fixed-price contracts and the subgroup of currentaccount contracts. All these distinctions form thevery basis of the mathematical mechanisms andthe lever effect that cognitive time distortiongenerates, as presented below.

Before moving on to elaborate on the conse-quences of the dissimilar effects of cognitive timedistortion due to the contractual form, however,we wish to make a brief observation. The key roleof the mode of contract for economic results of anorganization, as we understand it, appears so farto have been unnoticed in economic research (e.g.Buckley and Michie, 1996). Subsequently, any re-lation between the cognitive time leakage and theeconomic outcome would be assumed as linear. Itis, however, the mathematical properties of thecurves in Figure 3 that render linear equationstheir non-linear properties. This discussion iscarried further in the following paragraph, wherethe properties of the Total Revenue Equationare analysed.

The Total Revenue Equation

Given that statistical and contract-determinedeconomic effects of cognitive time distortion havebeen elucidated, a mathematical time distortionmodel for an analysis and prediction of profit inproduction economy will now be presented. Thisexpression is revenue oriented and targets thetotal contractual time volume, tvol, here of aservice delivery organization. The basis for themodel is the notion of profit (Hadar, 1971):

p ¼ TR� TC (2)

Here, p signifies profit per time unit, TR thetotal revenues per time unit, and TC the totalcosts per time unit. The parameters are expressedin monetary values, preferably defined for thetime unit of 1 year. We shall now return to ourdiscussion of contracts and define the total con-tract time to customers, tvol, of an economicorganization on a yearly basis, while the marketprice for each hour delivered, p, is consideredon an hourly basis. Accordingly, the expression

TR= p tvol denotes the total annual revenues ofone service organization that charges its cus-tomer the price of p MU per hour, for the totalcontractual time volume of tvol hours in a year.

A service organization will often have severalcustomers, in which case the total contractualtime volume, tvol, denotes a sum of the contracttime of all customers in a year. Therefore, it isuseful to consider a single customer i as holdinga fraction, ei, of the total customer contract vol-ume, tvol, where i signifies the number of servicecontracts in a service organization, i= {1,2,. . .,n},and Σ ei= 1. Thus, TR for a service organizationwith i customers becomes TR= p tvol Σ ei.

In order to distinguish between contracts oncurrent account and fixed-price contracts, thevariable a, where [0≤ a≤ 1], is used, where avalue of unity signifies 100% of fixed-price con-tracts. Consequently, considering the linear andinverse effects of cognitive time distortion dueto contractual category, the mathematical expres-sion for total revenues, TR, becomes

TR ¼ ptvol aX

ei=tið Þ þ 1� að ÞX

eitið Þ� �

(3)

Before proceeding, we wish to make an obser-vation. It is assumed here that a cognitive timedistortion in the context of a fixed-price contractcorresponds to a cognitive time distortion in thecontext of a current account contract. While thisassumption is deliberate here, to simplify thepresentation, our empirical studies suggest thatthis assumption be modified to account for differ-ent kinds of cognitive time distortion, includingTR with a fixed-price contract, TR with a currentaccount contract, TC with a fixed-price account,and maybe TC with a current account contract.

The Total Cost Equation

The expression for time distortion of total costs,TC, follows a similar pattern as for TR above.However, only TC on fixed-price contracts isconsidered, since this contractual form is themost commonly used for employment contracts




in contemporary economic organizations (themodel proposed below, however, may easily beadapted to those particular situations where TCis based on a current account contract). The cog-nitive time distortion of Total Costs is definedas d= ep/ec, where ep signifies the planned, or tar-get, capacity per physical time unit that serves asthe norm for estimation of salaries and ec is theemployee’s cognitive, or perceived, capacity pertime unit. The expression ‘capacity’ signifies thefraction of the Total Employee Time that isplanned for customers. From our experience, weknow that it is not uncommon that the perceivedcapacity, ec, falls well below the planned capacity,ep, thereby increasing the total costs, TC, per timeunit. To explicate here, the addressed cost-relatedtime leakage has its origin in the failure toadequately plan for physical time consumption.This in contrast to the revenue-related time leak-age as elaborated above that originates in the fail-ure to adequately monitor and report actuallyconsumed physical time. While the former hasits prospective origin in the abilities of time con-ception, the latter has a retrospective origin inthe abilities of time perception.Advancing the model, we may notice that the

time distortion of total costs, d, is inversely pro-portional to the total costs, TC, since an employeecontract is typically a fixed-price contract. Theemployee salary per time unit is related to themarket price, p, by the weight vp, where [0< vp< 1],so that the salary cost per time unit of one em-ployee becomes vp p. The weight vp connects tothe concept of ‘margin’ and is called here a ‘PricePolicy Margin’.As we now address the contract category of

TC, it is useful to consider a single employee jas holding a fraction, ’j, of the total employeecontract time volume tvol, where j signifies thenumber of employee contracts in a serviceorganization, j= {1,2,. . .,r}, and Σ ’j = 1. Conse-quently, considering the inverse impact of cogni-tive time distortion on each employee contract,the expression for total costs, TC, becomes

TC ¼ ptvolX

vpj’j=dj (4)

Again, we wish to recall that cognitive timedistortion relates to a physical time frame of

reference of an empirical event. Therefore, timedistortion on revenues, TR, refers here to the cus-tomer contract while time distortion on costs, TC,refers here to the employee contract. Our ownpractical experience suggests that it is commonin business organizations that the perceived cap-acity per time unit merely amounts to 60%–90%of the target capacity per time unit.

The Profit Equation

The above-elaborated Total Revenue Equationand Total Cost Equation account for the cognitivetime distortion. This in turn constitutes a founda-tion for the formulation of an updated ProfitEquation, Equation (5). Substitution of Equation(2) with Equations (3) and (4) affords the generalmathematical expression for how profit in aneconomic organization is affected by cognitivetime distortion (for further elaboration, see vonSchéele, 2001).

p t; dð Þ ¼ ptvol�aX

ei=tið Þ þ 1� að ÞX

eitið Þ�X

vpj’j=dj� �

Þ(5)

We may now see that cognitive time distortionaffects profit in two ways:

• The distortion of the profit based upon incor-rect time assessment of customer contract.

• The distortion of the profit based upon incor-rect time assessment of employee contract.

An important conclusion may be identifiedfrom this novel Profit Equation (Equation (5)).Namely, since cognitive time distortion is a sto-chastic variable, any other variable that forms afunction of the time distortion is also a stochasticvariable, exhibiting a probability distribution, amean value, and a standard deviation dependenton time distortion. As a result, influencing theprobability function of the cognitive time distor-tion of a group of employees corresponds to in-fluencing the fluctuations of total revenues, TR;total costs, TC; and thus profit, p, of an economicorganization. This implies that there is a need for




other and new means of managing operationsand their economy, namely, to manage the timedistortion of contracts in economic organizations.

CONCLUSIONS

This final part of the paper will first present ashort summary of the model proposed here, fol-lowed by a brief positioning of that model in rela-tion to some mainstream discourses onmanagement and organizations, aiming to articu-late the model’s novelty and potential contribu-tion. Finally, a few avenues that may meritfurther research will be provided.

Summary of the Model

The argument developed here builds on the empir-ical phenomenon of cognitive time distortion,which is the difference between physical time andcognitive time, and emerges unconditionally whenhuman agents assess the time interval of an event,both retrospectively and prospectively. Empiricalresearch presented here shows that retrospectiveperceptions of time may be both positive and nega-tive yet are more often positive, i.e. human timeassessments tend to overestimate the amount ofphysical time consumed by an event.

We have then shown that cognitive time distor-tionmanifests a stochastic behavior that is asymmet-ric, i.e. not Gaussian-distributed, and that cognitivetime distortion shows a similar pattern both at thelevel of an individual human actor and at the levelof a group of human actors. In the context of an eco-nomic organization, we have introduced the distinc-tion between fixed-price customer contracts andcurrent account contracts, and shown their differ-ence with regard to economic outcome, namely, thattime distortion is inversely proportional to totalrevenues (or total costs) for the fixed-price contrac-tual mode, while the time distortion to total reven-ues (or total costs) is linear for contracts on currentaccount. This implies that a linear cognitive timedistortion creates a curve linear economic distor-tion—a counter-intuitive outcome.

All this has provided us with a firm foundation forthe elaboration of an alternative Total Revenue Equa-tion and an alternative Total Cost Equation where

both equations incorporate the cognitive time distor-tion. This, in turn, has given rise to an alternativeProfit Equation that accounts for cognitive timedistortion, including its non-linear characteristics.

Positioning of the Proposed Model

The theoretical position of the model advancedhere is presented in this section by means of itsjuxtaposition with current mainstream scholarlydiscourses on management and organizations; inthis way, the novelty and value of this proposalwill be explicated. This is not the place to providea comprehensive review on the elaboration of timein the context of management and organizations(such reviews may be found elsewhere, e.g. Berg-mann, 1992; Couzens Hoy, 2009). The juxtaposeddomains are as follows:micro-economics, strategicmanagement, management sciences (MS), opera-tions research (OR) and operations management(OM), management accounting and organizationsociology; we recognize that these domains do, tosome extent, overlap.

Before proceeding though, we wish to articu-late in generic terms the key contributionadvanced here: the Profit Equation as introducedhere is novel, as it incorporates cognitive timedistortion and thereby accounts for the temporalexperiences of economic organizations; as far aswe understand it, no other attempt has beenmade to offer such a justice to the empiricalexperiences of economic organizations. This con-tribution may be related to the various economicand managerial discourses as follows.

If we understand micro-economics in broadterms to be the branch of economics that studiesthe behavior of how individualmodern householdsand firms decide to allocate limited resources (Badeand Parkin, 2001), then Boland’s (1978) review ofthe conception of time in this contextmay be instru-mental to our purpose here. Typical economicconceptions of time include the basic static standardeconomic models that implicate time only, at leastfor reasons of comparison (e.g. Boland, 1978).Micro-economic approaches that address timemore explicitly include time-based variables suchas making reference to the point in time at whichthe goods are consumed (e.g. Koopmans, 1957;




Debreu, 1959), and the idea of including time as acommodity (e.g. Becker, 1971). Then, there is theapproach to determine a time path trajectory ofthe endogenous variables, and that change is sug-gested because of a change in the parameters or inthe exogenous variables along time (e.g. Hicks,1970). Yet another approach is one that extends astatic notion of a model to a dynamic one by insert-ing differential equations (e.g. Barro andGrossman,1971). These and other conceptions of economictime all seem to follow the same path, which is ei-ther to conceive economic time in terms of a simpletimeline for economic activities and/or to focus onthe use of time as a commodity.Whichever the case,there is no recognition of, or account for, the distinc-tion between physical and cognitive time and thuscognitive time distortion. This limitation is furtherillustrated in the review below, as the black box ofeconomics is opened further.The domain of strategic management is con-

cerned with, among other things, the question ofwhat makes a firm, or an economic organization,successful in the longer term (e.g. Barney andClark, 2007). While various approaches have beenadvanced to this end—e.g. the industry-basedapproach (Porter, 1985), the resource-based ap-proach (Barney and Clark, 2007), or more recentlythe institution-based approach (Meyer et al.,2009)—the notion of time is not really addressed.More specifically, time-related discourse is limitedhere to the conceptions of cycles of an industrialevolution and, as a consequence, to the timingfor an entry into, or exit from, an industry (e.g.Schoenecker and Cooper, 1998), or for makingvarious strategic investments (e.g. Souder andBromiley, 2011), and recently to the notion of tem-poral strategic advantage (D’Aveni et al., 2010). Also,the more recent conception of dynamic capabilities,as a source of a firm’s sustainable profitability(Teece, 2007), does recognize change, hence impli-citly time, in a firm’s inner and outer environment;however, this kind of change implies only a mono-lithic notion of time, derived from the occurrence ofstrategic events. In this sense, contemporary strategicmanagement discourse does not provide anyaccount for a firm’s success being founded in its abil-ity tomanage the inevitable cognitive timedistortion.The domain of OM, understood as the govern-

ance of the various production-related activities in

a firm, is typically concerned with the researchand development of products, their manufacturingand supply, and other related activities (e.g. Naylor,2002; Hill, 2010). In a certain sense, these activitiesrepresent the core of a firm, i.e. ‘what it is doingfor a living’. In this context, time has received recur-ring attention from both practitioners and scholars.Taylor’s (1911/2007) well-known time studies infactories may be understood as the canonicalexample of this time obsession in the context of afirm’s operations and productivity. Later, morespecialized efforts have been pursued, such as thedevelopment of firms’ research and developmentprocesses focusing on the lead time from idea toready product in the market, hence the ‘time-to-market process’ (e.g. Hartley et al., 1997, Cohen,et al., 1996); the flexibility and lead time of the in-bound logistics that provide the inputs needed forproduction, hence the so-called just-in-time man-agement (e.g. Huson and Nanda, 1995); and thelead time ofmanufacturing of virtually any product(e.g. Koufteros et al., 1998). Whichever part of afirm’s operations is addressed, the concern seemsto be common to all: to shorten the lead time ofwhatever that is being conducted, and also to allowa more flexible execution of operations (e.g. Vossand Blackmon, 1998). Thus, the cognitive time perse has not been the subject of investigation in thedomain of OM.

Management science and operations researchmay be understood as the application of scientificmethods to the solution of operational issues inhuman, social, industrial and military affairs (e.g.Gass and Harris, 1996, p. xxxix). In contrast toOM, MS/OR typically focuses primarily on thevarious models and methods for the solution ofan operational problem (Gass and Harris, 1996),while OM focuses primarily on characterizationof the operations as such, and as a whole (Hill,2010). An iconic illustration may be the challengesoffered when scheduling a machine or any humanwork activities so as to arrive at some optimumproduction efficiency, where time is typicallyregarded as a resource where use of a worker or amachine over time generates costs. A considerablenumber of methods and solutions have beenadvanced byMS/OR, from simple network or arrowdiagrams, throughvarious generic optimization algo-rithms and simulation models, to specific dynamic




and thus time-dependent pricing models (e.g. Taha,2010). Unfortunately, the standard employed notionof time, in OM and MS/OR, is orthodox: physicalor clock timeonly,which is also the case for the subsetof OR, called ‘systems thinking’ (e.g. Jackson, 2000).With regard to the this last, understood here to bemethodologies based upon the idea of a system andaimed to guide the intervention in our world, it is apity that such approaches as systems analysis, sys-tems engineering and systems dynamics, while oftenrelying on the existence of time in their respectivemodel building approaches, do fall into the trap of re-ducing all time experience to physical time only.

In this sense, the proposal advanced here mayprovide a significant contribution; as with man-agement and operations practices and discourse,it accounts for physical or clock time. However,unlike this orthodox approach, the modeladvanced here recognizes the cognitive time ofa human agent and the gap between the physicaland the cognitive time. Further, the model alsooffers a conceptual link between the two kindsof time and an incorporation of that interrelationinto the conventional Profit Equation. As currentdiscourse and practices on organizational opera-tions and their management collapse, or reduce,cognitive time to physical time, they are unableto establish any rational link between the twoand are thus incapable of incorporating it intothe Profit Equation.

Management accounting, and particularly costaccounting,may be regarded as the understandingof costs in the context of an economic organization(Horngren et al., 2010). When inputs are trans-formed into outputs, by means of activities exe-cuted by resources, the use of these resourcesover time induces costs (Horngren et al., 2010).While various approaches have been advancedas to the conception of such costs (Horngrenet al., 2010), and this is not the place to reviewthem, the most recent and also most capableapproach seems to be the so-called Time-drivenActivity-Based Costing (Kaplan and Anderson,2007). This approach, as the more conventionalActivity-Based Costing approaches, explicitly uti-lizes time as a base for the understanding of anoperation’s usage of resources. By understandingthe costs of a standard temporal unity, e.g. an hour,a day, or a month, for a given resource, of a

machine or a worker, one can derive the costsinduced by a certain operation, when the time con-sumed by such an operation is known (Kaplan andAnderson, 2007). As with the discourse and prac-tice in the context of operations and management,cost accounting recognizes physical time only,ignores cognitive time, and is therefore unable toaccount for or manage the cognitive time distor-tion, including the consequent inefficiencies andchallenges to human well-being.

Finally, we consider the domain of organizationsociology, also understood as organization studies.A significant amount of elaborations of the tem-poral understanding and praxis of organizationshave been pursued, including journals devoted tothat end (e.g. Time & Society, KronoScope). An earlyand more generic example of such elaboration isDurkheim’s (1915/1965) The Elementary Forms ofthe Religious Life, while amore recent and local casestudy is the conception of temporality in e-mailexchanges in social life (Flaherty and Seipp-Williams, 2005). In summary, these and manyother conceptions articulate the fundamental chal-lenge and debate of the notion of time within asociological organization, namely, the divide be-tween the objective time and the subjective time(Clark, 1985; Bergmann, 1992). Here, an objectivenotion of time assumes the form of regular orhomogenous rhythm that is external to humans,typically articulated in a linear, mechanical andquantitative manner (Clark, 1985; Bergmann,1992). A subjective notion of time, on the otherhand, typically assumes the form of events thatoccur sequentially and/or in parallel, in relation tosubject’s own experiences of events and their flow;it is often regarded as discontinuous and heteroge-neous (Clark, 1985; Bergmann, 1992). In the fieldof rhetoric, a similar distinction is made in terms ofchromos and kairos, respectively (Kinneavy, 1986).While various attempts to establish a bridge be-tween the two notions of social time have beenattempted (Clark, 1985; Bergmann, 1992), they alltend to be less successful and fail to provide a fairaccount of the actual empirical experiences of timein social context (Orlikowski and Yates, 2002). Morerecently, however, a powerful attempt to deal withthe two notions of time in social affairs was put for-ward by Orlikowski and Yates (2002). Based on theso-called practice theory, they propose that time in




social contexts may be regarded as an interplay ofsocial structures,where a subjective time componentmay give rise to an objective time component, andvice versa. In several senses, this resolution of thetemporal divide in social affairs is ingenious, as itoffers a coherent and plausible interpretation ofhow time is actually embedded in social affairs.However, that proposal is too generic in the contextof an economic organization and its producingoperations, where the latter has a starting point ina legal contract, which in turn implicates a relationto the physical notion of time, as our current soci-eties have accepted it as a common denominatorfor the measurement of time and coordinationbetween the various social actors. In this sense,current organization sociology discourse does notaccount for cognitive time distortion and hence forhow it may be managed positively to improveproductivity and thewell-being of humansworkingin organizations.This positioning of the model of economic

organization as introduced here shows that the sug-gestions of some of the fathers of SystemsSciences—e.g. L. von Bertalanffy and J.Miller—thatnon-trivial systems manifest various kinds of timehave been ignored by the various domains of aca-demic discourses that focus on organizations.Whilevon Bertalanffy’s notion of the General SystemsTheory andMiller’s notion of Living Systems The-ory opened the door for the introduction of mul-tiple temporal accounts, Systems Sciences did notoffer any suggestion for how such multi-temporalaccounts could be elaborated. To this end, themodel of Profit Equitation proposed here, whichaccounts for cognitive time distortion, both opera-tionalizes the suggestion provided by SystemsSciences, thus advancing their message, and com-plements and extends the current discoursesoffered by the various academic domains thatfocus on organizations and their behavior.

Further Research

The time-related model of economic behavior ofhuman activity systems as proposed here maybe regarded as only a first and foundational stepfor a new research program on the role of, andthe interplay between, physical and cognitive

time and organizational economics. The follow-ing can be regarded here as central domains forfurther research.

While the model introduced here offers a ProfitEquation that accounts for cognitive time distor-tion, alternative price models deserve a similar al-ternation. Secondly, as the key producing resourceof a human activity system is the human agent andhis/her work, a workload model, accounting forcognitive time distortion, would provide insightsinto workforce efficiencies. This in turn may openan avenue for the elaboration of the work timeplanned for, and actually realized by, humanagents in organizations. Such a conception wouldmost likely also contribute to the understandingand management of health conditions, as thosecaused by stress or work overload. Thirdly, thetime-accounting Profit Equation proposed here,together with the suggested Price Equation andWorkload Equation, may constitute a scientificfoundation for the development of managerialtechniques to support managers in their manage-ment of cognitive and physical time in a consciousand deliberate manner, thereby enabling theachievement of improved operational efficienciesand improved workforce health. Fourthly, theProfit Equation proposed here opens up forimproved understanding of risk managementand reduction of volatility with regard to creditsgranted to the service sector.

ACKNOWLEDGEMENT

The authors wish to thank Dr. Eva M. K. Hedin,Stockholm, for her valuable technical assistanceduring the formulation of the proposal herepresented; the authors also wish to thank the twoanonymous reviewers whose comments and sug-gestions has helped to clarify this paper.

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Cognitive Time Distortion on the Performance of Economic Organizations