Exploitation versus Exploration in Market Competition

Transcription

1 1 Explotaton versus Exploraton n Market Competton Abstract John Debenham Unversty of Technology, Sydney debenham@t.uts.edu.au Ian Wlknson Unversty of New South Wales.wlknson@unsw.edu.au A general smulaton model of market competton s developed to explore the effectveness of and nteractons between dfferent types product exploraton and explotaton strateges.e. nnovaton, mtaton and process mprovement. The model, lke real markets, s hghly nonlnear such that analytcal solutons n the form of optmal marketng strateges are not possble. Hence, we use smulaton experments to examne frm survval and the effectveness of dfferent strategy mxes and show how these depend on the length of tme t takes for each strategy to bear frut, the speed of new product dffuson and the duraton of product lfe cycles and the tmng of new product entry. The model s mplemented on the Internet and provdes the bass for further experments to examne the mpact of dfferent combnatons of frm strateges on survval and performance and as a means of honng management senstvtes regardng the mpact of dfferent market response functons on the outcomes of strategy. Introducton It s the unendng search for dfferental advantage whch keeps competton dynamc (Alderson 1957 p 102). Wth these words Wroe Alderson, one of the poneers of modern marketng theory begns hs dscusson of the essental nature of the compettve process. Frms are contnually seekng to create and delver advantage or value to customers that are better than alternatves.

2 2 They attempt to do ths n many ways; n terms of market segments.e. the customers and ther partcular needs and problems they target, and n terms of the means of meetng these targeted needs and problems they offer prospectve customers. It s a contnung struggle because customers' needs are contnually changng, n some markets faster than others, and the means of meetng customer s needs are also changng as a result of technologcal change and entrepreneural acton that recognzes and explots new opportuntes as they arse. As Alderson descrbes t, there s a contnung prolferaton of opportuntes as the satsfyng of exstng needs begets new needs and opportuntes and the development of new technologes and means of satsfacton begets new problems, needs and opportuntes. Ths concepton of competton les at the heart of Porter s (1985) dentfcaton of three generc types of compettve strateges n terms of the twn dmensons of compettve scope and type of advantage. Compettve scope relates to the focus on a partcular market segment or to a broad mass market and compettve advantage refers to the form of dfferental advantage offered ether low cost or some other form of dfferentaton matchng the target markets requrements. The same concept s reflected n Kench Ohmae s (1982) depcton of competton n terms of a strategc trangle of three elements of a frm, customer and compettors and the way the frm seeks to offer customer advantage (or value) to target customers that s superor, n the eyes of the customer, to the customer advantage offered by compettors. The ablty to offer such dfferental advantage n turn depends on the suppler advantage, whch may be traced to varous types of frm, relatonshp and network resources, and dstnctve competences (e.g. Dyer 1998, Hamel and Prahalad 1994, Hunt 2000, and Rtter 1999). Our understandng of the dynamcs of compettve strategy s lmted because tradtonal analytcal technques have tended to be comparatve statc n nature, focusng on the way frms can compete by seekng out and occupyng nches n the market place by creatng and delverng a sutable market offer n terms of product/servce functonaltes, prcng optons, promotonal strateges and dstrbuton optons. Many sophstcated models of markets have been developed

3 3 to gude optmal choce among the multple dmensons of marketng strategy under varous assumptons regardng the compettve stuaton (e.g. Carpenter et al 1988; Llen et al 1995, Mdgley et al 1997). These nclude varous types of olgopoly models that examne the effects of dfferent response functons among closely competng frms on frm behavour and performance (Baye 2000). The model presented here s dfferent from prevous models n that we focus on two fundamental types of compettve strateges: the extent to whch resources are used to explot current means of meetng customer needs and the extent to whch they are used to search or explore for new way of meetng customer needs (ncludng new needs to meet). In the next secton we provde a bref overvew of these strateges and ther relaton to marketng strategy. Exploraton versus Explotaton Ths dstncton between explotaton and exploraton les at the heart of compettve strategy (Nelson and Wnter 1982). For example, consder Ansoff s (1965) classc competton matrx, whch dstngushes between offerng the same or dfferent products to the same or dfferent markets. Strateges focusng on the same products n the same markets are examples of explotaton strateges. All the rest nvolve some form of exploraton, be that new means of servng exstng markets, new markets for exstng products or new product and market combnatons. The tradeoff between explotaton and exploraton s a fundamental dmenson of any strategy and s a concept that has been used to help understand the evoluton of ecologcal systems as well as economc systems. For example, studes of socal nsects have revealed dfferences n the mx of exploraton and explotaton among dfferent types of ant colones that have evolved n envronments wth more or less turbulence n the sources of food avalable (Bonabeau et al 1999). In stable envronments wth relatvely fxed sources of food more resources are devoted to the explotaton of known food sources and less to exploraton whereas, n more dynamc

4 4 envronments, ant speces evolve that devote more resources to exploraton. In the same way frms n a market can adopt a mx of exploraton vs explotaton strateges and the optmal balance or trade-off between the two wll depend on the strateges of other compettors and the nature and dynamcs of the market demand. Furthermore, algorthms based on socal nsect foragng behavor have been used to solve complex search problems other types of approaches cannot solve (Bonabeau and Meyer, 2001) James March (1991) summarzed the key dfferences between explotaton and exploraton strateges n the followng way. The essence of explotaton s the refnement and extenson of exstng competences, technologes and paradgms. Its returns are postve, proxmate and predctable. The essence of exploraton s expermentaton wth new alternatves. Its returns are uncertan, dstant and often negatve (p. 85). The strateges of explotaton versus exploraton may be pursued n varous ways. For example frms may choose to devote more resources to workng more closely wth fewer supplers, customers and dstrbutors.e. explotng exstng relatons or they may choose to devote more resources to fndng new potentally valuable relatonshps. Determnng the optmal balance of exploraton and explotaton strateges s mpossble because of the hghly non-lnear systems nvolved and the fundamental uncertanty that arses. The benefts of each strategy revolve around the probablty of success of each type of strategy and costs and sacrfces nvolved. Ths n turn depends on the nature of the market and compettve stuaton, ncludng the degree of turbulence and responsveness of the envronment and the strateges adopted by compettors. There are uncertantes regardng the tmng and payoffs of dfferent strateges and there are nonlneartes resultng from the nteractons among dfferent frm strateges and between these strateges and market demand. In order for management to deal wth ths knd of problem there s a need to use new ways of understandng a frm's market envronment and to develop and hone managers' senstvtes regardng the effect of dfferent market parameters on the outcomes of strategy. Tradtonal

5 5 analytcal technques rely on mathematcal methods desgned to deal wth lnear systems n whch analytcal solutons are possble. But as Robert May (1976), one of the poneers of non-lnear systems analyss ponts out n a classc early paper publshed n Nature: " the mathematcal ntuton so developed ll equps the student to confront the bzarre behavour exhbted by the smplest of dscrete nonlnear systems Yet such nonlnear systems are surely the rule, not the excepton, outsde the physcal scences" (p 467). The same apples to management, as "students" of ther own nonlnear compettve market envronment. To better develop our ntuton regardng the behavour of nonlnear systems, Robert May advocated the ntroducton of non-lnear systems nto elementary mathematcal educaton and over the last decade there has been a rapd growth and spread of general purpose smulaton modellng tools such as Starlogo, Stella and Ithnk, SWARM and Repast, that enable students, researchers and manager to buld and explore models of nonlnear systems For management, the soluton s to develop smulaton models of ther market envronment that enables them to explore the mpact of dfferent combnatons of strateges and market condtons on market outcomes. In ths way they can greatly enrch ther ntuton about such systems and be n a better poston to more effectvely partcpate n and adapt to changng market crcumstances. Ths approach corresponds to modern developments n management theory that stress the role of partcpaton and learnng and adaptaton and mprovsaton (Brown and Esenhardt 1997; Chelaru, et al 2002; Moorman and Mner 1998a, 1998b; Wlknson and Young 2002) Hence, n lne wth ths approach, we develop a model of compettve dynamcs to examne the condtons under whch dfferent types of exploraton and explotaton strateges are lkely to succeed. The model allows frms to pursue dfferent types of explotaton and exploraton strateges n terms of devotng resources to mprove the effcency of supplyng exstng products (explotaton) as aganst usng resources to develop new products (exploraton). Two forms of

6 6 exploraton are consdered: (a) nnovaton n whch a frm devotes resources to the nventon of new products and (b) mtaton n whch the frm devotes resources to copyng the products offered by other frms n the market. We use smulaton technques to examne the condtons under whch dfferent mxes of exploraton, ncludng both nnovaton and mtaton, and explotaton perform best and how ths compares to the stuaton of a frm that devotes no resources to explotaton or exploraton and smply contnues to supply the same types of products n the same way. A crtcsm of these types of smulaton models s that they are senstve to small changes n parameters and that "anythng" can be made to happen. Ths senstvty to parameter values and startng condtons s the very hallmark of the behavour of nonlnear systems. It s from ths the celebrated butterfly effect s derved, whereby the flappng of a butterfles wngs n the Amazon jungle can lead to a storm system movng nto New York. The problem s to nvestgate the pattern of behavour that can occur under dfferent, plausble parameter settngs and to gan nsght nto how a system may be coaxed nto exhbtng desrable behavour characterstcs. Ths can only be done by systematc smulaton experments because of the nherent nonlnear nature of the system and t requred the advent of modern computers and software systems to permt such smulatons to be run n any realstc tme frame. Thus we need to abandon our prejudces borne of smulatons n the past where the full repertores of behavour of a system could not be nvestgate or even contemplated. Moreover researchers n marketng are startng to make more use of ths types of modellng (e.g. Goldenberg et al 2001, Hbbert and Wlknson 1997, Mdgley et al 1997, Wlknson et al 2001). Prevous Olgopoly Models Our model s a form of olgopoly model. Such models address the problem of nterdependence among a lmted number of compettors n a market and the performance of any

7 7 one frm depends on what other frms are dong and how they respond to each others actons (Baye 2000). It s beyond the scope of ths paper to revew ths vast lterature but some general observatons may be made (see for example Baye 2000 for an overvew). Varous types of models have been proposed regardng how an ndvdual frm should behave so as to maxmze ts performance under varous assumptons about rvals behavour and responses. The models nclude ones based on comparatve statc analyss such as the Sweezey and Cournot models as well as dynamc models based on game theory. These models focus on how frms adjust aspects of ther marketng strategy for exstng products such as prce, quantty suppled, promotonal effort etc. Dependng on the response functons assumed complex dynamcs can result, ncludng chaos, wth no clear wnnng strateges for ndvdual compettors (Hbbert and Wlknson 1994, Mdgley et al 1997). Another type of model s of the type poneered by Nelson and Wnter (1982) and are based on the work of Schumpeter. These are evolutonary models n whch frms nnovate and mtate other frms strateges and products. These once agan produce complex dynamcs and admt of many possble evolutonary paths. Models of ths latter type are part of the fast growng area of complex systems analyss or complexty scences, sometmes referred to as artfcal lfe. They focus on dynamc systems comprsng nterdependent nteractng elements n whch order emerges n a bottom up selforgansng fashon, rather than beng mposed on the system by any central authorty. Ths s exactly the form of olgopoly models. As Tefatson (1997) characterses these types of models: "[T]he actons of each unt depend upon the states and actons of a lmted number of other unts.. The complexty of the system thus tends to arse more from the nteractons among the unts than from any complexty Inherent n the ndvdual unts per se" (p534)

8 8 The model developed here s desgned to contrbute to our understandng of the effects of nnovaton and mtaton strateges on frm performance. We seek to examne how the outcomes from pursung dfferent exploratons and explotaton strateges depends on how other frms n the market are competng for dfferental advantage. In order to do ths we buld a model of a market nvolvng a lmted number of compettors and use a systematc set of smulaton experments to examne how dfferent combnatons of compettors n a market affect the nature of the optmal compettve strateges frms should adopt. Thus we provde gudance for frms operatng n real markets n terms of the approprate compettve strateges to adopt under dfferent compettve regmes. Our model s dfferent from prevous models of olgopoly competton. Innovaton and mtaton strateges formed part of Nelson and Wnter s models but they dd not examne the effect on frm performance of dfferent mxes of such strateges. Further, nnovaton and mtaton strateges are not lke the marketng strateges that form the bass of most olgopoly models as they cannot be drectly observed and coped by compettors. Only the results of these strateges can be observed n the form of new products, successfully coped products and, to a lesser extent, process mprovement n the form of ncreased productvty. Moreover, the results of such exploraton strateges are delayed and uncertan, as the precedng dscusson makes clear. Hence, frms have to trade off the gans from explotaton, n the form of devotng more resources to the makng and sellng of exstng products usng exstng process, or to devote some resources to exploraton strateges n the antcpaton of future benefts. To our knowledge no exstng models of market competton attempt to do ths. The smulaton model developed must necessarly be a smplfcaton of real world markets. But ths s ts purpose. By extractng from the real world key dynamc processes we are able to examne ther role and mpact n ways that are otherwse mpossble. Ths approach to analyss s ganng ncreasng favour amongst scentsts n many dscplnes as they seek to understand the

9 9 key processes underlyng the development of economc, socal and busness systems (Anderson and Valente 2002, Cast 1997, Langton 1996, Ianst 2002, Tesfatson 1997, 2002) and as researchers attempt to fnd solutons to complex nonlnear dynamc problems. There has also been some work n marketng usng such models (Goldenberger et al 2001, Wlknson et al 2001). As Chrs Langton (1996), one of the founders of the scence of Artfcal lfe observes n the context of research bology: We trust mplctly that there are lawful regulartes at work n the determnaton of ths set [of realzed enttes], but t s unlkely that we wll dscover many of these regulartes by restrctng ourselves only to the set of bologcal enttes that nature actually provded us wth. Rather, such regulartes wll be found only by explorng the much larger set of possble bologcal enttes (p x). The same may be sad for studes of busness ecosystems and markets n whch we are restrcted to studyng the knds of behavour that managers happen to have manfested n the marketplace, rather than the knds of behavour that could exst and perhaps may be preferable. The model n outlne The model descrbed here s desgned to enable the performance of frms to be compared when they allocate resources dfferent mxes of explotaton and exploraton strateges. The explotaton strateges are (a) producng exstng products wth exstng technology, or (b) process mprovement.e. usng resources to mprove the effcency of producton for exstng products. The exploraton strateges are (a) nnovaton.e. usng resources to dscover new types of products, or (b) mtaton.e. usng resources to copy new products produced by compettors. The market model s of a closed economy that s, a tradng envronment n whch a fxed total amount of resources, modeled here n terms of a frm's number of employees, s used by

10 10 frms for generatng product. Furthermore, a form of Say's Law apples n that supply creates demand (Sowell 1972). Demand s completely endogenously determned because the frms' employees are also the source of market demand for products. No external source of demand exsts. Usng the money they receve for ther labour servces people purchase the products offered by frms n the market.. All ths takes place n successve, dscrete tme perods. At the begnnng of each tme perod each frm has a budget for ts labour. Each frm hres labour to the full extent of ts labour budget. In the fnal few moments of each tme perod the followng thngs happen: labour s pad by the frms n exchange for ther work durng that tme perod at ths stage labour has all the money and the frms have none; the frms are pad by labour n exchange for the product all product s ether sold or wrtten off before the next tme perod starts at ths stage the frms have all the money and labour has none; the frms are now cashed up and they commt all of ther money by hrng labour for the next tme perod. If no one buys a frm's products n a perod t receves no ncome. It wll have spent all of ts budget on hrng labour for that tme perod, wll have nothng left for the next tme perod, and so t wll go out of busness. A frm s proft n a tme perod s the amount that t receves for sellng ts product at the end of that tme perod less the amount that t spent on hrng labour at the begnnng of that tme perod. If a frm makes a proft durng a tme perod then ts budget s ncreased n the next tme perod and so t wll hre more labour than n the prevous tme perod. If t makes a loss then ts budget s decreased and sze of ts labour force contracts n the next tme perod. The objectve of each frm s to survve. The total amount of money n the economy remans constant n tme and s all placed on the table at the end of each tme perod as descrbed above. The sze of the labour force also remans constant as does the total and per capta

11 11 remuneraton that labour receves. At the begnnng of each tme perod all money s commtted by frms to hrng labour. The frms dffer n the way n whch they allocate resources at the begnnng of each tme perod to the four types of strateges. The four strateges are realsed by allocatng labour to four job types: workers who produce product the proporton of frm s money spent on workers s w. process mprovers who mprove work processes by generatng process knowledge that s knowledge of how to produce product better the proporton of frm s money spent on process mprovers s p. mtators who desgn processes for producng products that have been dscovered by other frms the proporton of frm s money spent on mtators s m. nnovators who dscover new products the proporton of frm s money spent on nnovators s n. If a frm dscovers a new product durng a tme perod then, at the end of that tme perod, other frms may decde to attempt to copy that product. The objectve of the smulaton experments descrbed here s to understand the effect of values for the four basc varables w, p, m and n on a frm s performance. These varables are constraned by: 0 {w, p, m, n} 1 w + p + m + n = 1 for = 1,..,n where n s the number of frms.

12 12 Structure of the model The basc structure of the model, from the pont of vew of the economy, s shown n Fgure 1. It owes much to [Andersen and Valente, 2002]. At the begnnng of each tme perod a labour force of fxed sze s fully employed by a number of frms at a fxed wage rate. Durng each tme perod, the total costs for each frm are the amount t spends on hrng labour. The total costs for frm are C. The total costs for all frms s C, and ths amount of money s entrely spent on hrng labour and so ths s also the amount of money that the entre labour force wll spend at the end of the tme perod when they purchase products. In each tme perod frm allocates the effort of ts workers across the range of products that frm knows how to produce. That allocaton of workers wll lead as determned by each product s process knowledge to the generaton of actual product Q for frm where the underlnng notaton denotes a vector Q = [q,1, q,2, q,3,...] that s, q,j s amount of the j th product that frm produces n the tme perod. The total quantty of the j th product that s avalable at the end of the tme perod s q,j = q. The total output, produced by all frms, at the end of the tme perod s represented as the vector Q = [q 1, q 2, q 3,...]. The prce of the varous types of product s determned so that the total cost of all products s exactly the same as the amount of money that labour has to spend. That s, prce s set to ensure that supply equals demand. At the end of the tme perod the entre labour force goes shoppng and purchases all of the output Q. The Q vector s unbounded n length although at any tme only a fnte number of entres n t wll be non-zero. Innovaton takes place when one frm begns producng a product that has not been produced before. For example, f: Q = [2, 3, 0, 2, 0, 0, 0, 0,...] then ths means that 2 unts of product 1 are avalable, 3 unts of product 2 and 2 unts of product 4. New products dscovered as a result of nnovaton are ntroduced to the rght of the marker,

13 13 and the marker s moved along so that t remans to the rght of the most-recently-dscovered product. So n the Q shown above product number 3 s out of producton. Suppose that, n addton to the products n Q, one of the frms s an nnovator and that t commences producton of a new product. Ths new product wll be numbered 5. Suppose that the nnovatng frm produces 2 unts of product 5 then the augmented product vector s: Q = [2, 3, 0, 2, 2, 0, 0, 0,...] Havng revewed the range of products that are avalable at the end of a tme perod, labour wll have preferences over whch partcular products they desre. These preferences are expressed by labour attachng a relatve demand measure [descrbed below n the sub-secton Determnng demand ] across the range of avalable products n Q. The relatve demand D s used drectly to determne the relatve prce per unt. For example, f the relatve demand of product 1 s 0.8 and the relatve demand of product 2 s 1.2 then the prce per unt for product 2 wll be 1.5 tmes the prce per unt for product 1. At the end of each tme perod labour also places the total amount of money avalable, M, on the table. M remans constant n tme. The actual prces P are set n proporton to the relatve demand so as to clear the market. So the only way n whch a product wll be unsold s f ts relatve demand, s zero. For example, suppose that the total amount of money s 100, consder the followng output and relatve demand vectors: Q = [2, 3, 0, 2, 2, 0, 0, 0,...] D = [30, 30, 0, 0, 25, 0, 0, 0,...] Ths wll result n product 1 beng sold at 15 per unt, product 2 beng sold at 15 per unt and product 5 beng sold at 12.5 per unt. The 2 unts of product 4 are unsold, and are wrtten off by the frms that produced them. The total proceeds from sellng at these prces s 100, whch s also the total amount of money avalable.

14 14 Total Output Q = Q Prce P Total Money M Relatve Demand D Fgure 1. The model from the pont of vew of the economy. Havng determned the prce vector P, the model from the pont of vew of frm s shown n Fgure 2. Consder the tme perod [t 1, t]. At the begnnng of ths prevous tme perod the frm wll have carred over ts revenue R t 2 derved n the prevous tme perod and wll have fully commtted ths revenue to hrng labour. The way n whch the output vector Q t 1 and the costs C t 1 are determned for the products produced durng the tme perod [t 1, t] s descrbed below n Fgure 3. Havng determned the output vector, and havng calculated the prce vector P t 1 so as to clear the market as descrbed above, the revenue for frm, whch s derved at the end of the tme perod [t 1, t], s: R t 1 = ( p 1 _ q,1 ) + ( p 2 _ q,2 ) + = j ( p j _ q,j ) Hence the proft for ths tme perod, S t 1, s determned and so s the revenue that wll be carred over to the next tme perod. The ant-clockwse loop shown n Fgure 2 goes round and round from one tme perod to the next.

15 15 carred over R t 2 carry over t 1 R See Fg 3. Budget t 2 R Costs C t 1 Prce Proft S t 1 = R t 1 C t 1 P j Output Revenue Q t 1 t 1 R = j p j _ q,j Fgure 2. The model from the pont of vew of a partcular frm. Fgure 2 does not show how the carry over amount R t 2, avalable at the start of tme perod [t 1, t], generates output Q t 1 and costs C t 1 by the end of that tme perod. Ths s shown n Fgure 3. The horzontal dashed lne n Fgure 3 dvdes the fgure nto two tme perods: [t 2, t 1] n the upper part, and [t 1, t] n the lower part. Frst, the carry over amount R t 2 from [t 2, t 1] becomes the budget for the tme perod [t 1, t]. The budget R t 2 s entrely commtted to hrng labour n the tme perod [t 1, t]. That s: L t 1 = Rt 2 c where c s the constant wage rate. For smplcty, c s set to unty. So a unt of money s the cost of a unt of labour for one tme perod. Labour s splt n the proportons w : p : m : n nto the four categores workers, process mprovers, mtators and nnovators. The mtators attempt to buld processes for producng products that have been dscovered by other frms. If they are successful then they create a level of manufacturng expertse, or process knowledge, that s represented as a vector:

16 16 Im t 2 For example: Im t 2 = [0, 0, 1.0, 0, 0, 0, 0, 0,...] contans process knowledge wth value 1.0 concernng product 3. The value 1.0 s added to the thrd place of the frm s process knowledge vector ths s descrbed below. The value of a frm s process knowledge for a product wll be 0.0 f the frm can not produce that product, and 1.0 f t has dscovered how to produce that product by ether nnovaton or mtaton. The value of the process knowledge may then be ncreased to an nteger value greater than 1.0 by the frms process mprovers. The process mprovers generate process knowledge for products that the frm already produces. A frm s process mprovers are allocated to mprovng the manufacturng processes for partcular products. The th frms process knowledge s denoted by a vector A. In the tme perod [t 1, t] the process mprovers may have found new process knowledge Pro t 1 as for Im t 2 ths knowledge s represented as a vector denotng the product(s) that are the subject of the generated process knowledge. Lkewse the nnovators N may dscover process knowledge for new products, Inno t 1. All knowledge generated durng one tme perod may only be used n subsequent tme perods, and so each frms process knowledge avalable n the perod [t 1, t] s: A t 1 = A t 2 + Im t 2 + Pro t-2 + Inno t 2 That s, each frms process knowledge accumulates from one tme to the next. It remans to descrbe how a frm s workers use ths knowledge. Frm s workers are dstrbuted across the range of products that the frm can produce as represented by the vector W t 1. [The way n

17 17 whch ths dstrbuton s done s descrbed below n the sub-secton Determnng supply.] The quantty of output that the workers generate n the tme perod s: Q t 1 = A t 1 _ W t 1 where the _ symbol means that the vectors are multpled together element by element. carred over R t 2 Costs t 1 C = c _L t 1 Total budget R t 2 Labour L t 1 [t 2, t 1] [t 1, t ] Imtators M = m t 1 _ L t 1 Process specs P = p t 1 _ L t 1 Innovators t 1 t 1 N = n _ L Coped knowledge Im t 1 Process knowledge Pro t 1 Dscoveres t 1 Inno Productvty A t 1 Workers t 1 t 1 t 1 W = w _ L Output t 1 Q = A t 1 t 1 _ W Fgure 3. An allocaton of resources leads to output and costs for frm. The dashed lne separate two tme perods, and dashed arrows mean that the new knowledge s not avalable untl the followng tme perod.

18 18 The model n detal Determnng demand The prce of each type of product s determned at the end of each tme perod by the amount of product generated n that tme perod, by the total amount of money avalable, and by the relatve demand for the dfferent types of product whch s determned by labour s preferences. Relatve demand reflects the preferences of labour for dfferent types of product. So a model of relatve demand for each product s requred to calculate unt prce, as s a model of supply e: the product generated. Relatve demand s consdered now, and supply s consdered n the next subsecton. A modfed Bass model or penetraton model (Fourt and Woodlock 1960; Mahajan, Muller, and Bass 1990) wth repeat purchase s used to model relatve demand for dfferent products n the market subject to a fxed total overall market demand. The rate of new product dffuson the rate of repurchase depends on the type of product or servce, as numerous studes of new product dffuson and adopton have ndcated. Thus the rate of development of the demand for automobles s not the same as that for a new beverage because at best each member of the populaton wll purchase one or two automobles but may purchase a beverage repeatedly. The type of products that we have n mnd n developng our model are packaged food products n a market wth fxed total demand. In each tme perod there s a total demand for a fxed s unts of product (eg: s packaged dnners). s called the market sze. Gven a partcular product (eg; a partcular packaged dnner), n a partcular tme perod [t 1, t], the ntal penetraton, P t 1, s the sze of the populaton who has purchased ths product at least once ether durng or before ths tme perod. In tme perod [t 1, t], the frst-tme sales, N t 1, are sales made of ths product durng ths perod to those who have not purchased ths product prevously. Suppose that the growth of ntal penetraton t s proportonal, for some penetraton constant, to the sze of the

19 19 populaton that has yet to purchase ths product. Then ntal penetraton n tme perod [t 1, t], P, satsfes: P 0 = _ P 1 P 0 = _ ( P 0 ) P 2 P 1 = _ ( P 1 ) Or as a contnuous approxmaton: dp dt = _ [ P ] Solvng ths dfferental equaton gves the ntal penetraton: P t = _ (1 exp( t ) ) Frst-tme sales s the rate of change of ntal penetraton. So f N t s frst tme sales at tme t: N t = P t P t 1 and as a contnuous approxmaton: N t = dpt dt = _ _ exp( t ) ) (1) Frst-tme sales for a market of sze = 100 and penetraton constant 0.1 s shown n Fgure 4. Fgure 4. Frst-tme sales, N t, for a market of sze 100 and = 0.1.

20 20 Now suppose that once labour has purchased a product, labour contnues to purchase that product wth a probablty of. That s, f T s total sales n tme perod [ 1, ]: T +1 = N +1 + _ T where N s frst tme sales n tme perod [ 1, ]. Then: T 0 = N 0 T 1 = _ N 0 + N 1 T 2 = 2 _ N 0 + _ N 1 + N 2 etc Or as a contnuous approxmaton: T t t = =0 t _ N _ d Evaluatng ths usng equaton (1): T t = _ ln( + _ [ t exp( t _ ) ](2) Whch, for a market sze of = 100 gves total sales values for each tme perod as shown n Fgure 5 for varous and. The sales graphs n Fgure 5 are now used to model relatve demand. The dscovery of a new product by an nnovatng frm can lead to a substantal shfts n demand for dfferent frm s products, dependng on how rapdly the new product dffuses through the market and the peak demand acheved, whch depend on the values of the parameters and. For example, wth = 0.2 and = 0.9, there s a rapd growth n demand for a new product to nearly 50% share wthn 8 tme perods. The choce of and n the smulatons descrbed below substantally effects the speed and extent of new product dffuson and the duraton of the lfe cycle of the product, as can be seen from the llustraton n Fgure 5. Ths affects the results of frm s usng dfferent strateges as we wll show.

21 21 = 0.05 and = 0.4 = 0.05 and = 0.7 = 0.05 and = 0.9 = 0.1 and = 0.4 = 0.1 and = 0.7 = 0.1 and = 0.9 = 0.2 and = 0.4 = 0.2 and = 0.7 = 0.2 and = 0.9 Fgure 5. Total sales for each tme perod for a market of sze = 100 and varous and. For a gven market sze, equaton (2) has two varables: and. Gven the values of a total sales functon n the frst two tme perods, f 0 and f 1, t s easy to calculate and : = f0 = f1 f0 0 f and so knowng the frst two values of a total sales functon s to know all there s about t.

22 22 Returnng now to the problem of modellng relatve demand. The general shape of the total sales functon n Fgure 5 s a far descrpton of how nterest n a new product, such as packaged foodstuffs, mght be expected to develop. Equaton (2), for some values of and s used here to model relatve demand. So each product has a relatve demand determned by equaton (2), wth ts own values of and, for some fxed arbtrary, say, = 1. Consumers dstrbute ther money over the dfferent products n proporton to ther relatve demand D for each product as descrbed above. The prces per unt of the products s n proporton to ther relatve demand, and are set so as to clear the market. Determnng supply The only flexblty that a frm has s frst to choose ts parameters: w, p, m and n, and second to decde what products ts workers should produce. Ths second queston s consdered now. At the begnnng of each tme perod each frm knows all about the relatve demand for the products that t s able to produce. A ratonal choce of whch product to produce n whch quanttes may not be obvous. For example, consder the choces n the llustratons shown n Fgure 6 all of whch were produced usng equaton (2). In (a) and (b) the functon that appears to be the most valuable turns out not to be by tme 6 or 7. In (c) the functon that appears to be the most valuable remans so untl tme 28 so choosng between those two functons s not smple as the choce wll depend on whether anythng nterestng occurs between tme 1 and tme 28. (a) (b) (c) Fgure 6. Choosng output on the bass of relatve demand.

23 23 Suppose a frm has to choose between two products such as those whose relatve demand functons are shown n any of the three pars n Fgure 6. Consder Fgure 6(a) n whch the graphs cross at tme 6: a ratonal decson could be to produce the product wth the hgher relatve demand up to tme 6 and then to change to the product wth hgher demand after tme 6. But f a frm were to behave n ths way then the second product functon should have been drawn startng at tme 6. Some smplfyng assumpton s requred to prevent these consderatons from overcomplcatng ths nvestgaton. After all, the objectve of ths nvestgaton s to explore changes n performance resultng from modfcaton of the four basc parameters. So each frm n the smulatons wll produce all of the products for whch t possesses process knowledge, and wll do so n quanttes proportonal to ther relatve demand. Analyss Innovaton and Tradng Off Exploraton and Explotaton Suppose a number of dentcal frms commence producton of a range of products at the same tme, and each produces ther ar share of products as descrbed n the prevous sub-secton. As tme passes the relatve demand of each product wll rse and then declne as determned by (2), as llustrated for a number of dfferent values of and n Fgure 5. If the frms manage the producton of ther respectve products n the same way then ther market share wll reman the same; customers (labour), on the other hand, wll become less enthusastc about purchasng the products but wll contnue to do so as there s no choce. Ths stuaton s remnscent of collusve olgopoly that operate through an nformal wnk and a nod or by some, possbly llegal, collusve agreement. Ths state of affars wll be perturbed f one of the frms dscovers a new product. Intally the relatve demand of ths new product may rse well above that of the establshed products whose product lfe cycles may now

24 24 be well nto ther declne stages. On ntroducton of ths new product the nnovatng frm wll beneft by beng a monopolst and gan from the demand for ths new product, but monopolstc prcng strateges are ruled out by our market clearng prce system. But, nnovaton comes at a prce. In order to nnovate, the th frm must allocate some of ts labour to nnovaton by settng n > 0. Suppose that two frms commence producton of the same, sngle product at the same tme. Suppose that the frst frm allocates all of ts labour as workers, w 1 = 1, and that the second frm dvdes ts labour equally between workers and nnovators, w 2 = n 2 = 0.5. The role of the nnovators n the second frm s to dscover a new type of product, and, untl they do, they contrbute nothng. If the nnovators fal to dscover a new type of product then the sze of the second frm wll declne. Suppose that both frms ntally have 100 unts of labour that are pad one unt of money each per tme perod, and suppose that each frm's process knowledge s 1.0 for each product. At the end of the frst tme perod the frst frm wll produce 100 unts of product and the second frm 50. So two thrds of the revenue of 200 wll go to the frst frm and one thrd to the second. In the second tme perod the frst frm wll employ 133 unts of labour and the second frm 67. The contnung development of ther respectve szes s shown n Fgure 7. In nne tme perods the second frm s less that one per cent of ts orgnal sze. However, f the second frm had set w 2 = 0.9 and n 2 = 0.1 then t would have taken 52 tme perods for the sze of the frm to become less than one per cent of ts orgnal sze. In general f L t 1 2 s the sze of the second frm at the end of tme perod [t 1, t] then: L2 t = TR _ (1 n 2 ) _ Lt 1 2 TR (L t 1 2 _ n 2 ) where TR s the total revenue, e: 200 n the example above. One advantage of defnng relatve demand usng equaton (2) s that a frm can only go out of busness analytcally by choosng to have no workers; e: by settng w = 0. The sze of the frm llustrated n Fgure 7 becomes smaller and smaller wthout actually reachng zero.

25 25 Fgure 7. The development of the szes of a non-nnovator frm and an nnovator frm each of whch has an ntal sze of = 100. The nnovator frm allocates 50% of ts labour to nnovaton, fals to dscover a new product and des. Suppose that the second, nnovatng frm dscovers a new product n tme perod 10. Ths may or may not be a good thng n the medum term as Fgure 8 llustrates. Even f a new product s valuable, an nnovatng frm may fnd that t s so depleted that t s unable to produce suffcent quanttes to beneft from ths new product n the medum term. The problem here s classc tradeoff between exploraton and exploraton.. It s a problem of tradng off the future benefts to exploraton, n ths case nnovaton, aganst the more mmedate benefts of greater explotaton of the demand for exstng products,.e. devotng more resources to producng current products. The tradeoff n turn depends on the tmng of new product dscoveres and the speed and sze of the market that wll result. For example, Fgure 7 shows that settng n = 50% results n a frm havng no resources left to explot the results of ts nnovaton.

26 26 Fgure 8. Two new products ntroduced at tme 10 the fgure shows the relatve demand of the three products. In rough terms, we thnk of a tme perod as beng one week. The rate at whch the th frm can expect to dscover a new product wll depend on the amount of person-hours spent on nnovatng, and ths wll depend on both ts total labour force and on the proporton of ts labour force allocated to nnovaton, n. For example, suppose that at the begnnng there are two frms that have the same sze and that the frst frm sets w 1 = 1, and that the second sets w 2 = 0.9 and n 2 = 0.1. If the mean of the random dscovery process s twenty weeks then by tme 20 the second frm wll be 23.8% of ts orgnal sze by tme 30 t would have shrunk to 9% f ts orgnal sze. The trade-off between nnovaton and explotng the demand for exstng products depends on the speed and amount of market penetraton for new products, as well as the tme between new product dscoveres noted already. Ths can lead to frst mover advantages and dsadvantages, as s llustrated n the followng example. Frst Mover Effects Suppose two frms start at tme zero each producng a product wth = 0.1 and = 0.8, and that n tme perod [20, 21] the second frm dscovers a new product wth the same and. The relatve demand curves are shown n Fgure 9(a). From tme 21 onwards the second frm wll produce the orgnal product and ts new product n quanttes that are proportonal to ther

27 27 relatve demand as descrbed above. How wll the second frm fare? Not badly t would seem, as s shown n Fgure 9(b). The second, nnovatng frm s sze reaches a low of 19 n tme perod [21, 22] and then turns up qute sharply reachng 99.6% of the labour force by tme perod [29, 30]. The frst, non-nnovatng frm has vrtually been oblterated by tme 40. The problem for the frst frm s that the second frm has a new product whose relatve demand remans above that of the only product that the frst frm can produce. Thus nnovaton s rewarded. However, both frms may survve dependng on the pattern and sze of dffuson of the new product. Fgure 10 shows the results for a market n whch the parameter settngs for the orgnal product's demand functon are = 0.1 and = 0.8 and for the new product for the second frm they are = 0.2 and = 0.7. Under these condtons, by tme 200 the benefcal effect of the second, nnovatng frm s new product has passed and t s oblterated. The reason for ths beng that the graphs n Fgure 10(a) cross at tme 45, after whch the orgnal product has a hgher relatve demand, but the second frm contnues optmstcally to make a mx of both products. What happens wthn 200 tme perods s shown n Fgure 10(b). (a) (b) Fgure 9. For two frms a new product wth = 0.1 and = 0.8 s ntroduced at tme 20. (a) shows the resultng relatve demand of the two products and (b) shows the resultng szes of the two frms.

28 28 (a) (b) Fgure 10. For two frms a new product wth = 0.2 and = 0.7 s ntroduced at tme 20. (a) shows the resultng relatve demand of the two products and (b) shows the resultng szes of the two frms. Clearly, the benefts of a new product must be great enough to allow the nnovatng frm to recover ts nvestment. The nsght from the smulaton s how ths depends on the tmng of the new product ntroducton and from the pattern of growth of demand over tme of the new product relatve to exstng products. In Fgure 10, f the new product entered later t would sustan ts superor demand over the exstng product for longer but ths would be at the cost of ncreased nvestment n nnovaton. In a later secton we examne n more detal the return on nvestment from dfferent types of strateges and how ths s depcted n the smulaton results. In the smulatons descrbed here, a frm dscovers an nnovaton when the total amount of ts labour perods allocated to nnovaton reaches an nnovaton target. The nnovaton target may be a fxed amount or may be randomly determned n some nterval. Once a frm has dscovered an nnovaton, ts nnovaton counter s decreased by the amount of the nnovaton target for the next dscovery. If two nnovatng frms are competng then what s the optmal value of n? Ths wll depend on the values of, and the nnovaton threshold. These proved dffcult to calculate. Perhaps ths s due to computatonal round-off errors, or perhaps there are only approxmate optma.

29 29 These matters are not resolved here and awat further research nvestgaton. The optmal percentage to allocate to nnovaton, for varous nnovaton thresholds and dfferent values of the two demand parameters, are shown n Table 1. The table shows us that the hgher the nnovaton threshold the greater the percentage of resources that should be devoted to nnovaton. It also shows that the more rapd and greater s product dffuson [see Fg 5] the lower the optmal value for the nnovaton allocaton n. The latter result occurs because there s more to be ganed (and hence lost) by focusng resources on explotng the demand for exstng products or any new product developed than there s to devotng resources for developng new products.

30 30 = 0.4 = 0.7 = 0.9 = 0.05 = 0.1 = 0.2 = 0.05 = 0.1 = 0.2 = 0.05 = 0.1 = Table 1. Optmal values of n for values of nnovaton threshold between 20 and 100 where = 0.1 and = 0.7. Imtaton and Tradng Off Explotaton and Exploraton The knd of mtaton descrbed here s that of usng labour to copy new products ntroduced by other frms, rather than, say, purchasng technology from other frms. So f a frm allocates resources to mtaton then they can only be employed as mtators f there s a product n producton that ther frm can not produce. If a frm allocates resources to mtaton then those resources are re-appled to the worker category untl a new product s dscovered when the mtaton allocaton s fully appled to mtaton untl the requred knowledge s found. On

31 31 observng a new product dscovered by another frm the mtators work untl they can produce that product, at whch tme t becomes an output of ther frm wth a process knowledge value of 1.0. As for nnovaton, mtatons are dscovered when the total amount of ts labour perods allocated to mtaton reaches an mtaton target. The mtaton target may be a fxed amount or may be randomly determned n some nterval. Once a frm has dscovered an mtaton, ts mtaton counter s reduced by the mtaton target value for the next dscovery. There s lttle to be ganed by nvestng n mtatng a product f that product s relatve demand s low. Fgure 6 shows that selectng the best relatve demand functon s not smple. For want of a better crteron, an mtatng frm wll choose the most recently dscovered product to attempt to mtate. If two mtatng frms are competng then what s the optmal value of m? For ths to make sense at least one frm needs to be nnovatng, as otherwse there wll be nothng to mtate. If nether frm s nnovatng then all of the products n the system are those that were there at the begnnng. So the reward for a frm that nvests n mtaton wll be products that are as old as the products that t already has. Unless the relatve demand functons for the mtated products are sgnfcantly dfferent from those of ts exstng products such an nvestment wll not be worth whle. If the relatve demand functons of all products are the same then mtaton s certanly not worth whle. So the queston of an optmal value of m only really makes sense f both of the frms are nnovatng. Consder two frms, each of whch allocates an optmal 7% to nnovaton wth an nnovaton threshold set at 70.0 as ndcated n Table 1, = 0.1 and = 0.7. The frms now allocate dfferng proportons of staff to mtaton for dfferent values of the mtaton threshold. The result s zero even for small values of the mtaton threshold. It appears that f a frm allocates the optmal proporton of ts resources to nnovaton, n, then mtaton s not worth dong. Therfore we consder what happens f two frms have an dentcal, sub-optmal allocaton to nnovaton and dfferent allocatons to mtaton. Suppose that both frms allocate 4% to

32 32 nnovaton [threshold 70] and dfferent amounts to mtaton [threshold 20]. A local optmal mtaton allocaton s around 8% whch does better than 7% and 9%. But 0% does better than the 8%! It seems that f two frms are both nnovatng to the same extent then mtaton s not worth whle t s better to allocate resources to the generaton of new products. But ths does not mean that mtaton s not worth whle generally. Below we show that, under certan crcumstances, an mtatng frm can lve off an nnovatng frm. A related queston s the level of mtaton that leads to the slowest declne. If two frms allocate 6% to nnovaton [threshold 70], wth he frst allocatng 0% to mtaton [threshold 5], then 22% allocated to mtaton for the second frm leads to the slowest declne wth the frm s sze at 0.2% of ts orgnal sze at tme 100. Ths s slower even than allocatng a very small amount to mtaton, say 0.1%. The reason for ths s not clear to us at present and serves as a demonstraton of the sometmes non-ntutve outcomes of nonlnear systems behavour that Robert May (1976) descrbes. Process mprovement: Tradng off further explotaton Investment n process mprovement enables a frm to produce output at lower cost. Each frm has a level of process knowledge for each product. Frm s workers are dstrbuted across the range of products that the frm can produce as represented by the vector W t 1. The quantty of output Q t 1 that the workers generate n the tme perod s: Q t 1 = A t 1 _ W t 1 where A t 1 s the frms process knowledge, and _ means that the vectors are multpled together element by element. Each frm s process knowledge for a gven product ether remans constant or ncreases from one tme to the next. Intally the process knowledge s set to 1.0 n whch case one worker wll produce one unt of product n one tme perod. If a frm allocates labour to

33 33 process mprovement then t s reasonable to allocate those process mprovers to (one of) the most recent product(s) that the frm has learned to produce. In ths way an mprovng frm wll derve returns from such nvestments for products whose relatve demand s lkely to be large. In any case, ths makes sense as the more recent the product the greater the lkelhood of dervng beneft from nvestng n process mprovement for that product. The model chosen for process mprovement s smlar to that chosen for both nnovaton and mtaton. That s, an nvestment of a certan proporton of labour on the mprovement of a partcular product untl the labour/tme exceeds a set mprovement threshold wll cause the process knowledge for that product to ncrease by one. The reason for ths choce s to ensure a unform bass for nnovaton, mtaton and mprovement. For example, f two frms are both producng ther own sngle product wth the second frm allocatng 10% of ts labour to process mprovement, then ths leads to an ntal decrease n the sze of the second frm. Fgure 11(a) shows what happens wth a process mprovement threshold of 50 the two graphs cross n tme perod [33, 34]. Fgure 11(b) shows a threshold of 100. These calculatons are nvarant to the values of alpha and gamma. (a) (b) Fgure 11. Two frms wth an ntal sze = 100, the second frm allocates 10% of ts labour to process mprovement. In (a) wth a process mprovement threshold of 50, and n (b) wth a process mprovement factor of threshold of 100. If two mprovng frms are competng then what s the optmal value of p? Suppose that two frms allocate 5% to nnovaton [threshold 70]. Then the more allocated to mprovement

34 34 [threshold of 20] the better, up to 30% when a dfference of 5% s not suffcent to domnate wthn 160 tme unts although the equlbrum reached s alarmngly unstable. See Fgure 12. Fgure 12. Two frms wth an ntal sze = 100, both frms allocate 5% to nnovaton [threshold 70], the frst frm allocates 30% to mprovement [threshold of 20] and the second frm allocates 25%. The Return on Investment of Dfferent Strateges The return on nvestment (ROI) of dfferent strateges may be ndcated n terms of the area beneath the relatve demand curve for a product. For example an nnovator nvests for a perod of tme and dscovers a new product. That drectly benefts the nnovator untl an mtator learns to mtate that product, at whch tme the nnovator wll share the beneft wth the mtator. The nnovators relatve beneft s shown as the hashed area n Fgure 12(a). Lkewse the mtators relatve beneft s shown n Fgure 12(b). (a) nnovator (b) mtator (c) mprover Fgure 12. Return on nvestment for an nnovator, an mtator and an mprover.