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Unformatted text preview: The growing need to quantify tacit knowledge for a sustainable competitive advantage Karym Metwally, MBA Department of Management Pharos University Faculty of Economics and Business Administration Behind Green Plaza Alexandria EGYPT E-mail: bmwclubegypt@yahoo.com Words: 7,120 Keywords: knowledge, competitive advantage, tacit, strategy, resources, luxury, sustainable Electronic copy available at: http://ssrn.com/abstract=1259686 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 Contents: 1. Abstract 3 2. Introduction – why it is important to quantify tacit knowledge? 4 3. Key research Questions 5 4. Literature review 6 5. Discussion of Literature Review 12 5.1 Importance of tacit knowledge as a competitive advantage 13 5.2 The metabolism of low entropy 13 5.3 Luxury as a source of low entropy 13 5.4 Tacit knowledge and culture 14 5.5 How to acquire the implicit 14 5.6 What is Knowledge? 15 5.7 Why transfer Tacit knowledge at all? 18 6. The Model: The Black and Sholes model and its roots 20 7. Sustainable Competitive Advantage and Lead time 28 8. Conclusion 30 References 31 2/34 Electronic copy available at: http://ssrn.com/abstract=1259686 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 1. Abstract Most of the research communities tackle Knowledge Management from a Technological point of view, and neglecting the socio-psychological side of the equation. Psychology and education offered us an invaluable tool namely: the Knowledge Transfer or Cognitive Mapping. It is a tool available to the foreign investor to help him operate in a Cross-cultural Knowledge context. Blumentritt and Johnson set up a framework to measure the degree of difficulty in transferring knowledge. Physics and the law of thermodynamics also offered us the mathematical best fit to understand knowledge acquisition and development. Just like human beings must counteract the effect of oxidation which can be regarded as the depletion of organism cells by regularly extracting anti-oxidants. If the rate of extraction is less than the rate of depletion, the organism will be in a state of degradation and ultimately death. The Firm in a similar way must counteract the effect of deterioration which is a natural process caused by the business environment, products of today are already the products of the past (Drucker). This research seeks a deeper understanding of organizational and psychological phenomena taking place during the adoption and implementation of KM in a cross-cultural context. This initiative is to assist the reader in being able to: 1. Understand the difficulty to access tacit knowledge and this mainly due to the heterogeneity of mind mapping. We refer to the heterogeneity especially with regards to the difficulty of implicit knowledge transfer. Thus, the focus of the research, is to target knowledge resources requirements. 2. But most importantly to help the reader gain lead time in the acquisition and management of tacit knowledge using a mathematical model. 3/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 2. Introduction Every region has its own set of rules and processes that govern how business is done, its own specific and local way of doing business. This research shows the way to the reader to acquire culture-bound tacit knowledge in order to be able to compete. I propose an important knowledge transfer model, namely the tacit knowledge Model (TKM) based on both the entropy Model and Black & Sholes Model. The latter can be considered an evolution of the former. All countries have an implicit side; the implicit knowledge is embedded in every process, which we can informally call secret of the trade. Investors in general and particularly investors in a foreign country face a dilemma that is both difficult and tedious by nature, which is they only get acquainted with the explicit side of the processes, and always have difficulties in getting access to the implicit knowledge of the business processes. It is important to note that the implicit part is by far more important than the explicit part, and that the former is greater in terms of value. 4/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 3. Key research questions ß How to use the information model to calculate the value of implicit knowledge drawn into consciousness, using mapping between intuition and expression that would then give rise to the feeling of understanding? ß How can we mathematically define the “background” (the implicit knowledge and feelings) that both provides the meaning of the rule and the reason for having it in the first place? Can we call the latter “Trust”? ß Does all learning presuppose prior learning? ß Using the information theory, how can knowledge be transmitted or reconstructed by the learner in a crosscultural context? ß What are the mathematical methods for appraising and revising personal beliefs and intuitions? 5/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 4. Literature Review 4.1 Importance of tacit Knowledge as a Competitive Advantage Within the knowledge era, it has become widely recognized that the intangible assets of an organization will be key to both its ability to create competitive advantage, and to grow at an accelerated pace [Itami, 1987][Sveiby, 1996]. The shift of traditional production factors, which used to be capital, land or labor, to the only meaningful resource that can lead to the obtainment of social and economic results, which is knowledge [Drucker, 1993]. Competitive advantage stems from the firm-specific configuration of its intangible knowledge, through which it adds value to the final product/service [Schumpeter, 1942][Penrose 1959][Grant, 1996][Coombs and Richards, 1991][Teece, 1982, 1984]. The importance of knowledge as a strategic resource and its role in the firm’s competitiveness has been widely recognized lately by a large number of scholars [Spender, 1996, 1998] [Drucker, 1992][Grant, 1996][Davenport and Prusak, 1998] [Teece et al, 1997] [Teece 1998][Nonaka et al 2000]. Knowledge plays a fundamental role in the formulation of business strategies, as the only corporate resource that can provide sustainable competitive advantage [Rumelt, 1974] [Grant, 1996]. Knowledge has a more important role than all the others production factors, like capital and labor so much as input as output. Examples of companies in this category are law, accounting firms, management, engineering and computer consultancy companies, advertising agencies, R&D units, and high-tech companies [Alvesson, 1995]. 6/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 For many researchers, KM is seen as a strategic business development practice, in which knowledge and organizational competences are closely interrelated as the source of wealth creation. [Teece, 1998][Spender, 1996][Prahalad and Hamel, 1990]. 4.2 Tacit Knowledge or the “Background” Implicit knowledge or intuition is what provides the “meaning” of a proposition or expression. Learning the formal rules and procedures and explicit knowledge of the discipline does not exhaust or even adequately represent what is implicitly known. To understand an explicit rule on must capture the intuitions, that is the implicit knowledge and feeling, the “background” [Searle, 1983] that both provides the meaning for the rule and indicates the reason having the rule. Polanyi argue "We know more than we can tell” [1966, p.4]. Tacit knowledge is subjective, experiential and hard to formalise and communicate. Tacit knowledge has a personal quality, it is deeply rooted in action and understanding, involves both cognitive and technical elements, and is non-transferable without personal contact [Nonaka, 1994][Nonaka et al, 2000][Senker, 1993]. According to Kay [1999, p.13]: tacit knowledge can take many forms… is unique to an organisation - and therefore cannot be copied...The benefits of such tacit knowledge arise only through a culture of trust and knowledge sharing. There is widespread agreement that tacit knowledge is important. Nonaka and his colleagues regard it as the root of all organizational knowledge [Nonaka & Takeuchi, 1995]; 7/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 4.3 Knowledge Transfer or Cognitive Mapping In fact the issue of sharing the organizational knowledge, what is called transferability of knowledge, is one of the most important ones in the knowledge discussion. It seems that there is a powerful relationship between codification of knowledge and the costs of its transfer; apparently the more a given item of knowledge or experience has been codified, the more economical is its transfer [Teece, 1998]. Whether the transferred knowledge will be considered useful or not by its recipients depend on whether they are familiar with the code chosen as well as the different contexts in which it is used [Teece, 1998][Shannon and Weaver, 1949]. In fact the marginal cost of knowledge transmission rise very rapidly with "distance" from the context in which the knowledge was generated [Pavitt, 1987]. This happens mainly because of the tacit dimension of knowledge: tacit knowledge is less observable in use, more complex and less teachable [Shapiro, 1999]. As a result tacit knowledge transfer is slow, costly and very difficult to take place. Some form of direct personal interaction (either physical or virtual) is necessary for transferring tacit knowledge. Blumentritt and Johnson’s [1999] framework for categorising knowledge puts the primary emphasis on the degree of difficulty in transferring knowledge. They distinguish four different categories of knowledge: ß Codified knowledge, equivalent to information. The knowledge has been made explicit by a human and it is in a readily transferable form; ß Common knowledge, knowledge that is accepted as standard without been formally explicit; ß Social knowledge, knowledge about cultural and interpersonal relationships; Knowledge of social links and shared values ß Embodied knowledge, tacit knowledge related to experience, background and skills of a person. 8/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 According to this framework, the transfer of codified knowledge involves the smallest degree of difficulty while the transfer of embodied (Tacit) knowledge is the hardest task. Learning is never simple acquisition but rather the finding of something in one’s implicit knowledge or intuition of which the knowledge to be acquired is an expression, extension, formulation, or reformulation. [Olson, 1994] We can draw implicit knowledge into consciousness, using mapping between intuition and expression that would then give rise to the feeling of understanding. The “background” (the implicit knowledge and feelings) both provides the meaning of the rule and the reason for having it in the first place. All learning presupposes prior learning. [Olson, 1994] Indeed as Zhu Z [2004 ] notes, the complexity of understanding how best to understand and manage knowledge is further broken down by country differences in each geographic area: being American, Japanese, Chinese and European views, respectively. In addition, Sharif [2005] argue: These two 'Neuro-Hemispherical' worldviews as I will call them, clearly represent a schism within the KM literature, being based upon either Codification or Collaboration concepts. In the former, largely Western-view of KM, there is a strong emphasis on implementing processes and systems that capture and store knowledge from individuals. Here, the benefits of eliciting both primary and secondary sources of knowledge are largely seen as having immediate or at least short-term impact. By codifying and providing information taxonomies, within organisational KM systems say, the means for accessing and making use of knowledge is achieved in a 'pull' sense. In other words, it is up to the seeker of knowledge to seek and find his/her relevant information, via search and data mining tools. In the latter Eastern view of KM, there is conversely a strong emphasis on providing means for individuals and teams with the ability to share knowledge via the concept of communities, within which the sharing or collaboration of knowledge is encouraged, that is, in a 'push' sense. This engenders a long-term approach to the realisation of benefits that such a people-focused view affords. Sharif [2005] 9/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 In their studies Deshpande and his colleagues found significant differences in the way companies operated from one nation to another. “The most successful companies all shared a competitive, achievement-oriented culture” Deshpande notes. Lisa Adent Hoecklin discovered the importance of national cultural differences within organizations and provided practical insights and frameworks to aid successful management across culture and the strategic value of cultural differences. Joint venture learning to cooperate and cooperating to learn joint venture management is a demanding and continuous process in a cross-cultural environment. Relationships between each side will change over time and problems can arise at different stages of development. [Gilbert Probst, Bettina S. T. Buchel, Bettina S. Buchel] Probst and his colleagues emphasizes on learning the Tacit knowledge required for a long term relationship. Global Competition has paved the way to new corporate combinations – and opened up new pitfalls along the way. [Bleek, J. & Ernst] Veiga, Lubatkin, Calori and Very [2000] developed a cultural compatibility index that can be used to foresee the differences in the two existing cultures. 4.4 Culture Definition Hofstede [1991] defines culture as the collective programming of the mind that distinguishes the members of one human group from another. He states that each person as layers of cultural programming and expands upon this idea of “ mental programming “ in a model. Cultural Programming is divided into Human nature, Culture learned, and Inherited Personality. A study done by Hofstede [1984] discovered a consistent pattern in the tendencies and attitudes of workers of different nationalities working within the same multinational firm. He found that all individuals function under 10/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 certain basic assumptions, values and beliefs which Hoefstede divides into the following: 1) Individualism and Collectivism 2) Power distance 3) level of risk avoidance 4) Masculinity and Femininity Deshpande and Farley coined the tacit knowledge in different countries and had put them in the form of animals to explain their differences. He divided them into a tiger culture where it tends to be more achievementoriented and competitive; Rabbits cultures are more flexible, creative and entrepreneurial. Monkey and Elephants cultures are more inward focus, with Monkeys more oriented towards teamwork and loyalty, while elephants respect hierarchy and order. 11/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 5. DISCUSSION OF LITERARY REVUE 5.1 Importance of tacit knowledge as a Competitive Advantage Although many researches in the past emphasized on the Importance of Knowledge starting from the resourcebased organization, through the learning organization by Peter Senge and the latest theories of Knowledge Management. Only recently however, there has been a widespread agreement that tacit knowledge is crucial for a long lasting competitive advantage. Psychology and education offered us an invaluable tool namely: the Knowledge Transfer or Cognitive Mapping. It is a tool available to the foreign investor to help him operate in a Cross-cultural Knowledge context. Blumentritt and Johnson set up a framework to measure the degree of difficulty in transferring knowledge. Physics and the law of thermodynamics also offered us the mathematical best fit to understand knowledge acquisition and development. However, the foreign investor only sees the external shell of the interactions; he cannot see the “background” cultural and intuitive side of the business processes, settings, and rituals. He will attempt to learn the implicit knowledge of the local market and this is quite a difficult and daunting task. Many investors face the everlasting dilemma of not being able to grasp the implicit knowledge in the country where they operate and they usually go for the easier more obvious explicit knowledge that has been codified and indexed. Thus, they take a knowledge stagnant position and stay at the more explicit level. A more adventurous investor will seek to go and operate within the implicit depth and within the business level, where he will be confronted with local attitudes values and beliefs. Tacit knowlegde is thus a vital and an essential energy for the very survival of the firm. Without it the firm is doomed to failure and ultimately economic death. 12/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 5.2 The metabolism of low entropy Just like human beings must counteract the effect of oxidation which can be regarded as the depletion of organism cells by regularly extracting anti-oxidants. If the rate of extraction of anti-oxidants is less than the rate of depletion, the organism will be in a state of degradation and ultimately death. 5.3 Luxury as a source of low entropy Luxury is regarded as a source of low entropy since it counteract the dissipation trend which we call deterioration or in this regard we call impoverishment. All individuals seek to counteract this trend by being as rich as possible. Here we can find a similarity between the dissipation of low entropy and the effect of inflation on the present value of our money in the future. The investor must always extract low entropy by attempting to earn abnormal rents in order to counteract the effect of inflation. Luxury seeking is a way to strive against the natural dissipation effect of nature. Also Luxury is a way to fight the negative feelings with which many people are bombarded through the atrocity of daily news. Persons faced with mortality salience were shown to have a higher tendency overall to affiliate with a luxury brand. Luxury products have embedded tacit knowledge, an expensive watch may convey a message of superiority, the tacit knowledge will be assimilated by a receiver with a common culture. The same watch shown to a commoner will not influence him as much. This is because like we have previously said there must be a high correlation between the sender and the receiver for the transfer of tacit knowledge be successful. Tacit knowledge embedded in Luxury products: ß Exclusivity ß Limited supply ß Snobbism ß Social Value ß Quality ß Prestige 13/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 ß Elegance ß Conspicuous ß Elitism ß Materialism 5.4 Tacit knowledge and culture Many foreign investors will attempt to learn the local tacit knowledge. Unfortunately, this part of the equation is hard to acquire and takes lots of time to comprehend. The foreign investor is confronted with a challenge either to stay at the corporate level or attempt to learn the local tacit knowledge. Armed with the notion that tacit knowledge is the only corporate resource that is unique and therefore can provide competitive advantage. The foreign investor has an inner motive to move downward from the corporate level, this is because the competitive advantage is always present in the tactical or functional level and never in the corporate level. 5.5 How to acquire the implicit Matching what is known with the knower is the key to transfer implicit knowledge. By the former I mean the implicit knowledge embedded in the local country and by the latter I mean the foreign investor or the knowledge recipient. The Implicit knowledge is then codified and incorporated in every process thus gaining a sustainable local competitive advantage. There was an initial belief that there is distinction between the mind and culture, another naïve belief is that the mind is some kind of container where you pour in knowledge. The learner is seen as being ignorant “He does not know” indicates a defect to be remedied by pouring in the knowledge. However by experience those who know discovered that some learner are brighter than others, and they deducted that there must be something other than the mind influencing the learner’s ability to assimilate knowledge. 14/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 The transmission theory have seen many generation of theorists that have adopted the model of sender -> encoding -> message -> decoding -> Receiver or SEMDR Model. The encoding/decoding phase is a mere attempt to re-phrase Tacit knowledge embedding in a message. All knowledge builds on and finds itself in a tradition or culture, the mind is in sense deeply social. Both cognitive psychology and socio-cognitive theory have contributed to knowledge management. Socio-cultural theorists inspired by Vygotsky have shown that infants are not simply cognizers but intrinsically social beings. Social practices, games, family routines, bedtimes and so on provide occasions for the developments of the infant. 5.6 What is Knowledge? Knowledge is the reduction of entropy, not only in a mathematical sense, as in Shannon’s theory, but also in a physical sense. After the entropy theory of information was developed in 1948, its technique has been applied to many different problems in economic and finance. (Theil, 1967; Maasoumi and Racine, 2002 and many others) In this paper I have used the theory of information and applied it in the field of Knowledge Management. After all Knowledge evolution is: Data -> Information -> Knowledge -> Wisdom Wisdom happens when the tacit knowledge is transferred successfully. The rules of information transmission developed in Shannon’s theory, as mathematical rules, apply not only to communication systems, but also to knowledge systems. The value of knowledge is a function of probability and must satisfy the following properties: a) The knowledge value of two events is higher than the value of each of them (synergy). 15/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 b) If two events are independent, the knowledge value of the two events will be the sum of the two. c) The knowledge value of any event is non-negative. The mathematical function that satisfy all the above properties are of the form (5.1) where H is the value of information, P is the probability associated with a given event and b is a positive constant (Applebaum, 1996). Formula (5.1) represents the level of uncertainty. When a signal is received, there is a reduction of uncertainty, which is tacit knowledge. Suppose a random event, X, has n discrete states, x1, x2, …,xn, each with probability p1, p2, …,pn. The knowledge value of X is the average of knowledge value of each state, that is (5.2) The right hand side of (5.2), which is the entropy function first introduced by Boltzmann in the 1870s, is also the general formula for information (Shannon, 1948). In the following, we will discuss some distinct properties. 16/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 First, Tacit Knowledge that is more valuable is in general more expensive to obtain. From the second law of thermodynamics, Maxwell concluded that information of higher value is of higher physical cost. Since economic cost is highly correlated to physical cost, (Georgescu-Roegen, 1971) more valuable tacit knowledge is in general more expensive to obtain. Second, the amount of knowledge one can receive depends on the person’s background knowledge (intuition) about that particular knowledge. The most important result from Shannon’s entropy theory of information is the following formula (5.3) where R is the amount of knowledge one can receive, H is the amount of explicit knowledge a source sent and Hy(x), the conditional entropy, called equivocation is the amount of tacitness in this knowledge. Formula (5.3) shows that the amount of Knowledge one can receive would be equal to the amount of explicit knowledge sent minus the average rate of conditional entropy which is the implicitness of the knowledge. Before Shannon’s theory, it was impossible to accurately assess how much information one can receive from an information source. This formula can be used to discuss how noises (tacitness) affect the efficiency of knowledge transmission. But it can be understood from more general perspective. Hy(x) the equivocation is: ß Tacitness ß Ambiguity ß Complexity 17/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 ß Implicitness ß Untrustful relationship The level of conditional entropy Hy(x) is determined by the correlation between senders and receivers. 5.4.1 Tacit Knowledge at an extreme When x and y are independent, Hy(x) = H(x) and R = 0. No knowledge can be transmitted between two objects that are independent of each other. There is no common background or intuition to facilitate the transfer of knowledge. This empower the theory emphasized by (Chen et Al 2001) on the evolution of knowledge–based clusters, that tacit knowledge is easier to transfer locally and between people with common background (Olson D. 1994). This also enlightens us that knowledge transfer occurs with less cost during social interaction or networking. 5.4.2 Explicit Knowledge at an extreme When the correlation of x and y is equal to one, Hy(x) = 0. No Knowledge loss occurs in transmission or the knowledge is totally explicit. In general, the amount of knowledge one can receive from the source depends on the correlation between the two. The higher the correlation between the source and receiver, the more knowledge can be transmitted. This is why social interaction and social networking facilitate the knowledge transfer between the parties. Hy(x) in Formula (5.3) offers the quantitative measure of information asymmetry (Akerlof, 1970). Since different people have different background knowledge about the same information, heterogeneity of opinion occurs naturally (Chen 2001). Third, the same knowledge, when known to more people, becomes less valuable. 18/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 In the standard information theory, P represents the probability that some event will occur. In this theory, P is generalized to represent the percentage of people or money that is controlled by informed investors. When P = 1, -log P =0. Thus the value of knowledge that is already known to everyone (Explicit Knowledge) is zero. When P approaches zero, -logP approaches infinity. Therefore, the value of Knowledge that is known to few (tacit Knowledge) is very high. “In those cases where animal signals really are of mutual benefit, they will tend to sink to the level of a conspiratorial whisper.” (Dawkins, 1999, p. 59) 5.7 Why transfer Tacit knowledge at all? We all know that tacit knowledge is more valuable when know to few, and it might not be in the interest of the firm to transfer this tacit knowledge or transform it into explicit knowledge. We know that tacit knowledge can be: 1. Embodied 2. Embedded 3. Made explicit in certain cases 4. Transferred to a common mind Thus, Tacit may preserve its value if transferred to a trusted person in the firm like sons and relatives – we see this happening in the Mediterranean countries like in Italy and Greece within the Family business – or it can be transferred into a product (embedded or embodied). 19/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 6. The Black and Sholes model and tacit knowledge 6.1 Thermodynamical Origin Economic evolution directly originated from the Second Law of Thermodynamics, the Entropy Law (GeorgescuRoegen, 1971). Entropy is a measure for the degree of order in a system. Systems that exhibit a high degree of order are said to have low entropy. Systems that exhibit a low degree of order are said to have high entropy. Since it takes energy to create order, low entropy systems represent a higher level of energy than high entropy systems. (Chen 2001) The Second Law of Thermodynamics states that (in the absence of infusion of low entropy into a system) entropy is continuously increasing. This means decay and mediocrity are inevitable unless the firm counteract this tendency. To counteract this tendency, the ordered structure must actively maintain itself by extracting large amounts of energy (low entropy) from its environment. The problem it at an extreme the more ordered and complex the structure and the less resource-rich the environment, this becomes increasingly difficult. 6.2 Log-Normal Processes and Option Pricing The Black-Scholes equation that has been developed for the pricing of options, in essence, is a thermodynamic equation (Chen 2001). It can be used to describe a system that is characterized by a process of tacit knowledge assimilation counteracting a process of tacit knowledge dissipation. 20/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 Underlying the Black-Scholes model is the assumption that the underlying asset, S, follows a random walk. That means proportional changes in S must be normally distributed and S itself, therefore, must follow a log-normal distribution. On one hand, equations require that proportional changes in S are random, on the other hand, they allow for an expected drift rate of tacit knowledge assimilation r per unit of time. This makes it a valid description of entropic systems when S is the value of the firm and the amount of low entropy, r, the rate of extracting low entropy -tacit knowledge-- from the environment, and _, the rate of diffusion of the low entropy (Tacit knowledge) into the environment, it can also be viewed as the rate of depletion, erosion or duplication of the firm’s tacit knowledge. The production of a tacit knowledge involves fixed cost, K, and variable cost, C, which are functions of the value of the firm S. If the competitors rate of tacit knowledge assimilation is q, from Feynman-Kac formula, (Øksendal, 1998) the variable cost, as a function of S, satisfies the following equation We perform a thought experiment about a project with a duration that is infinitesimally small. When the duration of fixed cost is infinitesimal small, the project has only enough time to produce one unit of tacit knowledge. If the fixed cost is lower than the value of the firm, the variable cost should be the difference between the value of the firm and the fixed cost to avoid arbitrage opportunity. If the fixed cost is higher than the value of the firm, there should be no extra variable cost needed for this firm. Since the log-normal distribution of proportional changes in S is the result of the interaction of growth and dissipation rate as described in (2), it follows that a new value of S is given by (6.1) 21/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 Here, S0 is the initial value of the firm, and ST is the value of the firm S grows to over a time period of length T. Based on the above assumptions about the behavior of S, Black and Scholes developed their option pricing formulas as solutions to the following equation, the Black-Scholes differential equation: (6.2) This differential equation has many solutions. Any of these solutions establishes the value of a derivative based on the value of the underlying asset and the structure of the derivative. The Black-Scholes formula for a (European) call option is one such particular solution to the Black-Scholes equation: (6.3) (6.4) Where 22/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 The function N(x) is the cumulative probability distribution function for a standardized normal random variable. When q, the discount rate (the competitor rate of tacit knowledge assimilation), is equal to r (our rate of tacit knowledge assimilation), the rate of change, Formula (3.4) becomes (6.5) The Black-Scholes formula for call options is a tool for describing evolutionary development. In order to apply the theory to entropic processes, the variables in formula must be interpreted in the following ways: S: S is the underlying asset in a financial context. In our context it is the value of the firm, or more precisely its level of low Entropy in the firm. q: In the financial context, r is the discount rate or the risk-free growth rate of S. In this paper it is a measure for the rate at which the competitor firms extracts low entropy (Tacit Knowledge) from their immediate environment, this is because q is also called the opportunity cost of capital. r: In the financial context, r is the rate of change. In this paper it is a measure for the rate at which our firm extracts Tacit Knowledge or low entropy from our immediate environment. This rate depends on the following factors: ß Patents ß Monopoly ß Franchise ß Brand ß Commercial Secrets ß Scarcity ß Luxury 23/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 K: In a financial context K is the strike price at which the underlying asset, S, can be acquired if a call option is exercised. For our purpose, K is the level of irreversible resource commitment, or tacit knowledge procurement fixed costs. s : s measures the volatility in S and in a broader sense is a measure of uncertainty. In our framework s measures the rate of dissipation of low entropy or in knowledge management the rate of depletion of our firm tacit knowledge it measures the uncertainty in the immediate environment. This rate depends on the following factors: ß Abundance ß Substitutability ß Number of producers ß Duplication t: t is a measure of the time period or the duration of the project in both contexts. C: The value of a financial call option measures the benefit of having the choice but not the obligation to acquire the underlying asset in the future. In the light of a our interpretation, C can be regarded as the variable resource commitment necessary to extract low entropy from the environment, or variable costs to acquire tacit knowledge. 1. When the fixed cost of extracting Tacit knowledge increases the variable cost of extracting tacit knowledge decreases. This is because the fixed cost of extracting provide a lead time where variable cost is not needed by the firm. 2. For the same amount of tacit knowledge, when duration of project is longer, the variable cost of acquiring tacit knowledge increases, this is because when the duration is longer the level of uncertainty (knowledge depletion) increases and the firm must increase its effort to maintain its level of low entropy. 24/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 3. When the diffusion of knowledge increases, the variable cost of extracting tacit knowledge increases. This because the firm must counteract the rate of depletion with an increase effort of extracting low entropy from the environment. 4. When the fixed cost of Tacit knowledge K = 0 (No lead-time). The variable cost of extracting tacit knowledge = the value of the firm or C= S 5. When the rate of depletion -> Infinity , the variable cost of Acquiring tacit = value of the company. In addition the fixed cost of acquiring Tacit knowledge = 0 6. When the value of the company -> 0, the variable cost of extracting tacit ->0. 6.3 A numerical Example: For example, a product can be manufactured with a new technology. It needs ten million dollars of tacit knowledge assimilation fixed cost (K). Assume the other parameters are unit value of the product, to be one million, the competitors rate of tacit knowledge assimilation (q) is 10% and the duration of the project, is twenty-five years (T=25). When the rate of tacit knowledge duplication in the environment is 30% per year, variable cost for project C is 0.14 million, calculated from (3.5). When the rate of tacit knowledge duplication in the environment is 90% per year, variable cost for the project C is 0.94 million. 6.4 Efficiency of Tacit knowledge extracting Efficiency depends on the type of environment the firm deals with, an environment with high uncertainity (high duplication) favors the variable cost of acquiring tacit knowledge. Conversly, an environment with low uncertainity (low duplication) favors fixed commitments. 25/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 hen the Black-Scholes formulas are applied to entropic economic processes, C is a measure of the variable resource commitment (variable costs) necessary in order to extract one unit of low entropy (tacit knowledge) from the environment. Based on this assumption, any growth in S comes at the cost of C_Q + K, where Q is the number of units of low entropy (tacit knowledge) that can be extracted from the environment at a given level of K (fixed cost of acquiring tacit knowledge). In other word, the efficiency of the entropy extracting process is given by (6.6) (6.7) The variable cost, C, is an increasing function of volatility. In the extreme case where s reaches infinity, C is equal to one and C_Q is equal to Q, the value of the total output. Environment with high duplication rate of tacit knowledge In an environment with high duplication of tacit knowledge, any long-term commitment of tacit knowledge fixed cost does not reduce the variable resource commitment necessary for the extraction of (low entropy) tacit knowledge from the environment significantly. 26/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 When s approaches infinity the return on any long-term resource commitment (Fixed cost of acquiring tacit knowledge) in fact becomes zero. Environment with low duplication rate of tacit knowledge Structures that however sacrifice some flexibility and commit resources for long-term usage will experience increasing returns when they increase the scale of their activities. The more stable the environment the more attractive it is to commit fixed resources to acquire tacit knowledge (Invest in a franchise, a patent or an agency). A structure that does not commit any of its available fixed resources for long-term utilization will earn a return of zero. As fixed costs increase the structure becomes more sensitive to environmental changes. 27/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 7. Sustainable Competitive Advantage and Lead Time 7.1 Lead Time (Incurring fixed Cost of acquiring tacit knowledge K) Tacit knowledge unlike many traditional resources, it is not readily acquired. To acquire similar knowledge competitors have to engage in similar experiences. However, acquiring knowledge through experience takes time, investment and effort, and competitors are limited in how much they can accelerate their learning merely through investments (Zack). Long lead times give the innovating firm a window of opportunity that allows them to generate high initial profits and build on their initial advantages before competitors enter the industry. (Ghemawat 1991). One cannot buy, rent or hire more time. The supply of time is totally inelastic. No matter how high the demand, the supply will not go up. There is no price for it. Time is totally perishable and cannot be stored. Yesterday’s time is gone forever, and will never come back. Time is always in short supply. There is no substitute for time. Everything requires time. All work takes place in, and uses up time. Yet most people take for granted this unique, irreplaceable and necessary resource. (Drucker) Long lead time explains the attraction of strategic alliances and other forms of external ventures as potentially quicker means for gaining access to knowledge. The long learning lead time or “knowledge friction” highlights the importance of benchmarking the organization current knowledge platform. Sustainability comes from knowing more about some things than do competitors, combined with the time constraints faced by competitors in acquiring similar knowledge regardless of how much they invest to catch up. 28/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 7.2 Lead Time The firm’s advantage comes from being able to absorb external tacit knowledge (extract low entropy) and integrate it with their internal tacit knowledge to develop new insights faster than the competitors. Knowledge flows between individual firms & industry at large quickly and only those firms with the best learning capabilities and the greatest capacity for absorbing external tacit knowledge will survive. We should note that Competitive advantage is not necessarily enduring: A firm’s competitive advantage may erode over time. It is in the very nature of competition that rivals attempt to duplicate or eliminate a firm’s competitive advantage in this paper we refer this process in our model to the rate of uncertainity or the rate of tacit knowledge dissipation( s). 29/34 Karym Medhat Metwally. The growing need to quantify tacit knowledge for a sustainable competitive advantage. 2008 8. Conclusion We believe the results will be of importance to foreign investors. It will help them acquire and calculate by mathematical formulas the implicit knowledge essential in gaining a sustainable local competitive advantage. Matching what is known with the knower is the key to transfer implicit knowledge. By the former I mean the implicit knowledge embedded in the local country and by the latter I mean the foreign investor or the knowledge recipient. The Implicit knowledge is then codified and incorporated in every process thus gaining a sustainable local competitive advantage. 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