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Investment in new technology: Modelling the decision process
Technovation 26 (2006) 345–350 www.elsevier.com/locate/technovation
Investment in new technology: Modelling the decision process Gregorio Gimenez* Department of Applied Economics, University of Zaragoza, Gran Vı´a, 2, 50005 Zaragoza, Spain
Abstract This paper presents a model designed to throw light on the economic mechanisms determining the decision to acquire a new technology to replace an existing one. The investment decision is governed by a cost-benefit analysis, which is influenced by the factors analysed in the model described. These factors are the lapse of time between the acquisition of the technology currently in use and the moment at which the new technology becomes available; the useful life of the new technology; the speed of the innovation process; interest rates; the acquisition cost of the new technology; and learning costs. A static comparative analysis is performed on the basis of these factors with the aim of recommending the most appropriate instruments for technology policy measures. q 2005 Elsevier Ltd. All rights reserved. Keywords: Investment in technology; Technology use; Innovation
1. Introduction There has been a proliferation of studies treating technology as a key factor for economic growth in recent years, among which we may cite the contributions of Romer (1990), Grossman and Helpman (1991) and Aghion and Howitt (1992, 1998). If technology plays such a significant role in growth and economic convergence between countries, it will clearly be essential to understand in detail the decision-making process behind investment in technology. This is the objective of this paper, which proposes a microeconomic model to explain the technology investment process.1 The first part of the argument examines the factors determining the process of new technology acquisition. This requires an analysis of costs and benefits. Users will purchase a technological innovation if it generates positive net gains. The second part applies a static comparative analysis to observe how each of the factors considered affects the investment decision process. Finally, the measures that governments might take to encourage * Tel.: C34 976 762 223; fax: C34 976 761 840. E-mail address: [email protected]. 1 A broad review of the literature on innovation and technological change is provided in Freeman (1982) and Dosi et al. (1988). Published studies of the diffusion of new technologies among potential users include Mansfield (1968) and Mansfield et al. (1971, 1977), which focus on the diffusion of new technologies in industry, and Dosi (1991), which is more general.
0166-4972/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.technovation.2005.03.008
the acquisition of new technologies are considered in light of the results obtained from the study. Conclusions are presented in Section 4 of this paper. 2. Basis for the model Technological innovations may be used either by producers, applying the technology as an intermediate input for the production of some other consumer good, or by consumers as final goods. For the purposes of this section, let us take the case of an entrepreneur using a given production factor (with an associated technology) to manufacture certain goods or services.2 For example, we may imagine an economist using a computer program to manage his clients’ investment portfolios or a reprographics business that acquires a photocopier. Embedded in these intermediate inputs is a specific technology. Let us also assume that this embedded technology is subject to a process of incremental development. These productive inputs are, then, offered for sale in the market in each period, but incorporating successive technological improvements.3 In the examples given, this assumption translates into the appearance of new versions of 2 The results obtained from the model would be exactly the same where we take the case of a consumer of final goods obtaining a given utility from the use of the new technology. 3 This is similar to the Schumpeterian process of creative destruction. The studies by Grossman and Helpman (1991) and Aghion and Howitt (1992, 1998) cited above are based on this concept.
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G. Gimenez / Technovation 26 (2006) 345–350
the computer program used by the economist and new, more sophisticated models of photocopier that could be acquired by the reprographics business. These improvements would raise the productivity of users of the technology. If the entrepreneur opts to purchase the program or photocopier incorporating technical improvements, business returns will rise either because it becomes possible to boost the quality of outputs or because the costs associated with the production process will fall, or for both reasons. Let us suppose that the entrepreneur is offered a new version of the input used in the production process in each period. This version will include a series of technological improvements that would raise the profits obtained in each period. This section presents a model to explain how the producer makes the decision to acquire the new embedded technology. In the first place, the entrepreneur starts up the business in period 0, acquiring a technology A0 at a cost C0. In addition, he will have to learn to use this technology, which means incurring learning costs (time, effort and money invested) equal to Ap0. The technology will enable the entrepreneur to obtain a profit of B0 monetary units in each period in which it is utilised. Chart 1 provides an outline of this account. What, then, occurs in the following period, 1? The entrepreneur is offered the opportunity to acquire a new, more developed technology, A1 which incorporates the technology of the preceding period. The price of this new technology is C1. In order to adapt to the new technology, the entrepreneur will also incur learning costs of Ap1. This innovation would make it possible to generate higher profits. To simplify, let us assume that additional returns equal to the initial profit (B0) are obtained each time a new technology is acquired. Thus, profits B1Z2B0 would be generated if the new technology A1 was acquired. This is the same as assuming that the incremental technological improvements incorporated are of the same magnitude, which is to say the impact of each innovation is similar to the preceding one and the developments included bring the entrepreneur an identical increase in profits to that provided by the adoption of earlier technologies. Let us assume that the entrepreneur decides not to adopt the new technology offered in period 1. He will thus continue to utilise the technology pertaining to the prior period, A0. The entrepreneur incurs no costs, because he is already familiar with the technology and knows how to use it. The profits obtained in period 1 using technology A0 will be equal to those earned in the initial period, B0. What happens when we reach the second period 2, with technology A0? In this period, the technology offered, A2, includes the technology developments A1 and A2. The purchase price of this technology is C2, and the associated learning costs are ApZAp2CAp1. We may note here that these learning costs are incremental. This means that in taking up a new technology we incorporate earlier technical improvements (in this case A1), which we must also learn to use. Let us now suppose that a period n is reached with a technology adopted in previous period m. In n,
the entrepreneur considers acquiring technology An. This would involve paying P an acquisition cost of Cn and learning costs equal to ApZ niZm Api . These costs reflect the need to recycle knowledge and skills since the period of the last upgrade, m, in order to learn how to use technological developments incorporated in each of the intervening periods. The increase in profits that would be achieved in each period with the adoption of Pnthe new technology, An, can be quantified as follows: iZm Bi . This includes all additional profits that would be obtained from the adoption of the new technologies incorporating all of the innovations developed since m, the period in which the last technology acquisition took place (Fig. 1). Hence, if the technology offered is adopted, the net additional profit obtained in period n will be: n X iZm
Bi K Cn K
n X
Api
iZm
Fig. 1. Technology acquisition.
(1)
G. Gimenez / Technovation 26 (2006) 345–350
Using technology An, the total profit obtained in any period nCk following the nth period will be equal to BnCk Z
n X
Bt
(2)
tZ0
where CnCkZ0 and ApnCkZ0. It does not, however, seem reasonable to assume that the technology applied has an unlimited useful life. This is a consequence of physical wear and tear and the increasing difficulty of obtaining supplies or finding personnel with the skills to maintain the technology in question, as might be the case with a photocopier. The goods or services produced using a given technology might also lose their attractiveness for consumers. In the case of our hypothetical economist, for example, it might not be possible to adapt the computer program used to tax reforms or new financial products. In view of this, we shall assume that the useful life of the technology adopted in a period n is limited to T periods. After this time, the technology will be obsolete and unusable. On the basis of the factors discussed above, we may now consider whether the entrepreneur should acquire the new technology developed in the nth period. He will in fact make the switch if the following condition holds: T X n n X X ½Bit ð1 C rÞKt O Cn C Api tZ1 iZm
(3)
iZm
that is, the change will be justified if the present value of the sum of total additional profits generated from the acquisition of the new technology over the whole of its useful life exceeds the sum of all acquisition and learning costs. Pn The additional profits, iZm Bi , will be generated annually until the useful life of the invention ends in period T. These additional profits should, of course, be discounted using an interest rate, r.4 If the foregoing inequality is expressed over a time continuum, we have: ðT ðn
ðn Bit e
Krt
tZ1 iZm
didtO Cn C
iZm
Api di
(4)
Since Bit and Api are equal in each period (i.e. BitZB and ApiZAp), we may rewrite the expression as follows: ðn ðT ðn B eKrt didtO Cn C Api di (5) tZ1 iZm
Let us consider two further assumptions in order to flesh out the model. The first assumes that the new technology includes an increasing number of innovations in each period. We may call this the speed of the innovation process.5 Thus, innovation increases exponentially, possibly as a result of the positive externalities generated by existing technologies.6 Increasing technical developments will translate into higher productivity, thereby raising the potential profits to be earned in each period. Hence, we may assume that profitability gains due to technological developments are determined by a parameter r. Because the technology is increasingly complex, however, this assumption also implies that it will become more difficult to use, raising learning costs. Let us assume, then, that these costs will rise in proportion to profits depending on the value of r. The second assumption is that the annual profits provided by the adoption of the new technology will decline period by period after its acquisition due to obsolescence and emerging substitute technologies that provide consumers with new alternatives. The erosion of profits in each period of the technology’s life cycle will also be given by r, the parameter that determines the evolution of technological developments. To sum up, the entrepreneur may acquire an increasingly sophisticated technology in each period, which will raise his profits although learning costs will also be higher. The entrepreneur also knows that the annual benefit provided by a new technology will begin to decline from the moment of its acquisition due to obsolescence caused by the speed of innovation. On the basis of these assumptions, the entrepreneur will benefit from acquiring a new technology An in period n if: ðT ðn tZ1 iZm ðT
di0
ri
ðn
B e e e didtO Cn C Ap eri iZm ðn ðn ri KðrCrÞt Be e didtO Cn C Ap eri di
tZ1 iZm
Krt
Krt
iZm
ð6Þ Thus, the entrepreneur will benefit from the technology if the present value of the sum of all additional annual profits generated as a result of acquiring the technology over the whole of its useful life exceeds the sum of acquisition and learning costs, taking into consideration that the technology incorporates further developments in each period providing higher profits, despite the increase in learning costs, and that it is subject to obsolescence. In order to make expression (6) easier to work with, let us express the acquisition and learning costs of the innovation
iZm
P P Note that neither of the sums niZm Bi and niZm Api are discounted. This is because the additional benefits and costs derived from the innovations embedded in the new technology arise in the nth period or thereafter, in which case a discount factor is implicit. 4
347
5 This concept is similar to the technology growth rate described in a number of studies, including the eminent paper by Mankiw et al. (1992). 6 Weitzman (1998) analyses how new concepts may be formed from the combination of existing ideas. Stoneman (1995) provides further evidence of the importance of cumulative learning processes for scientific and technical progress.
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in terms of profits: Cn Z l1 B;
Ap Z l2 B
(7)
where liO0 0Ap Z
l2 C ; l1 n
Cn Z
l1 Ap l2
(8)
On the basis of (7), we may rewrite Eq. (6) as follows: ðT ðn ðn B eri eKðrCrÞt didtO l1 B C l2 B eri di (9) tZ1
iZm
the entrepreneur affect incentives to invest in innovation at the time the possibility of purchasing a new technology is raised. This, of course, refers to changes in the parameter m. To this end, it is necessary to find the derivative of G with respect to m
iZm
dG Z dm
h i KrðrCrÞl1 CeKð1CTÞðrCrÞ ðemr Kenr ÞðerCr KeTðrCrÞ Ceð1CTÞðrCrÞ ðrCrÞl2 Þ d ½ rðrCrÞ dm mr
Z
e ½Ke
KrKr
KTðrCrÞ
Ce rCr
Solving expression (9), we find that the entrepreneur will benefit from acquiring a new technology in the market where the net gains obtained from technology investment, G, are greater than zero. This will only be the case if: GZ
GZ
(12)
B½Krðr C rÞl1 C eKð1CTÞðrCrÞ ðemr K enr ÞðerCr K eTðrCrÞ C eð1CTÞðrCrÞ ðr C rÞl2 Þ O0 rðr C rÞ
Since BO0 is a necessary condition for the business to be viable, the entrepreneur will only invest in technology if:
3. Static comparison and design of technological innovation policy This section examines how the net gains obtained from technology investment are affected by changes in the technology uptake periods, in general lifestyles, interest rates, the speed of technological change, and the amount of technology acquisition and learning costs. On this basis, we shall go on to discuss the possible economic policy instruments derived from the model. These effects will be examined assuming that: nOm; mO0; T O0; rO0; rO0; l1 O0; l2 O0 This assumes a period (n) when a given technology that could replace another purchased in an earlier period (m) is acquired; the interest rate (r) is positive; the technology has a useful life (T); technological innovations incorporate ever more developments (r), as a result of which both profits and learning costs increase and inventions become obsolete; and the technology is associated with acquisition costs (l1) and learning costs (l2). All these assumptions fit the model described. (A) In the first place, we shall consider how changes in the period in which the technology currently used by
(10)
The sign of this derivative is indeterminate, depending as it does on the specific values taken by the remaining
½Krðr C rÞl1 C eKð1CTÞðrCrÞ ðemr K enr ÞðerCr K eTðrCrÞ C eð1CTÞðrCrÞ ðr C rÞl2 Þ O0 rðr C rÞ
Furthermore, the entrepreneur will have a greater incentive to invest in the new technology as the value of G increases.
8 9 >O > CðrCrÞl2 < = ! 0 > : > ; Z
(11)
parameters. This is because the increments in the profits that would be obtained by switching technologies will be greater as the time elapsed between technology acquisition periods increases. On the other hand, the learning process required to assimilate the new technology will be more difficult. If learning costs are not too high, it would be logical to suppose that the first of these effects will predominate. Thus, the older the technology currently used by the entrepreneur, the greater the net gains derived from the acquisition of a new technology. (B) Changes in the period in which the new technology is offered, n 8 9 >O > nr KrKr KTðrCrÞ dG e ½Ke Ce C ðr C rÞl2 < = ZK ! 0 > dn r Cr ; : > Z (13) The sign of this derivative is also indeterminate for the reasons given in the preceding point. In this case, however, if learning costs are relatively low, the net gains obtained will be greater if the new technology is acquired. (C) Changes in the length of the technology’s useful life, T 8 > O05 nO m KTðrCrÞ mr nr < dG e ðKe C e Þ (14) Z !05 n! m > dT r : Z 05 n Z m Taking into account the restrictions placed upon the parameters, it will generally be the case that net gains will increase as the useful life of the new technology acquired
G. Gimenez / Technovation 26 (2006) 345–350
349
increases, because the present value of future profit flows will In this way, we may establish that the useful life of the be higher. technology (T) has a positive effect on the net gains derived (D) Changes in the speed of the innovation process, r from the acquisition of an innovation, while the interest rate 2 38 9 eKð1CTÞðrCrÞ ðerTCðmCTÞr ðrð1 Cr KmrÞ Crð2 Cr KmrÞÞ CerTCðnCTÞr ðrðK2 CðK1 CnÞrÞ >O > = < > 6 7> dG 1 6 7 rCrCmr Z 2 ðrðK2 Cmr KTrÞ CrðK1 Cmr KTrÞÞ CrðK1 CðK1 CnÞrÞÞ Ce 6 7 ! 0 2 > 5> dr r ðr CrÞ 4 > ; : > Z CerCrCmr ðrð1 Knr CTrÞ Crð2 Knr CTrÞÞ Cðr CrÞ2 ðemr ðK1 CmrÞ Cenr ð1 KnrÞÞl2
The effect is indeterminate and depends on the value of the parameters. This is because of the increasing difficulty of learning to use new technologies due to the incorporation of ever more innovations, even though their application in the production system will raise the profits that can be obtained. Furthermore, the effect of obsolescence results in a decline in the present value of the flow of future profits over the useful life of the technology. (E) Changes in the interest rate, r
(15) (r), the cost of acquisition (l1) and learning costs (l2) have a negative impact. The effects of the remaining factors are indeterminate. In light of the above effects, then, it is possible to design technological innovation policy measures (Fig. 2). Many arguments have been advanced in favour of the application of technological innovation policies with a view to achieving sustained economic growth. As mentioned above, numerous theoretical models attach fundamental
dG eKð1CTÞðrCrÞ ðemr K enr Þ½eTðrCrÞ ð1 C r C rÞ K erCr ð1 C rT C rTÞ Z !0 dr rðr C rÞ2 When interest rates rise, net gains will fall because of the reduction in the present value of future profits. (G) Changes in the amount of technology acquisition costs, l1 dG Z K1 dl1
(17)
Logically, any increase in acquisition costs will translate into a reduction in net gains. (G) Changes in the amount of technology learning costs, l2 dG emr K enr !0 Z dl2 r
(18)
Hence, any increase in the costs incurred in learning to use the new technology will result in a reduction in net gains.7
ð16Þ
importance to technology as a factor that contributes to, even determines, development. Let us assume that a government wishes to provide entrepreneurs with incentives for investment to acquire new technologies. Based on the model described, this would mean seeking to ensure that the net gains derived from the investment in new technology are positive or, in other words, that G is greater than zero. A series of economic policy measures might be proposed to this end. In view of the parameters affecting the decision to invest in technology, the most viable and useful policies would act on interest rates and acquisition and learning costs. These measures are reflected in Chart 2. The useful life of new technologies and the speed of the innovation process, on the other hand, are affected by numerous factors that are not strictly economic.
7
The amount of acquisition and learning costs are fundamental considerations for any entrepreneur in the decision to purchase new technology. The cost of acquisition is, of course, immediately known to the technology user. The entrepreneur will also have some information concerning learning costs, because he already uses technologies of the same kind and this cost is initially assumed to be constant for each periodic innovation. It is, then, an interesting exercise to find the values of l1 and l2 at which the acquisition of a new technology would generate a positive return, assuming a given value for the remaining parameters. These are obtained from expression (11): GO 0 8 ðemr K enr ÞðKeKrKr K eKTðrCrÞ C ðr C rÞl2 Þ > > < l1 ! rðr C rÞ 5 > eKð1CTÞðrCrÞ ½Kðemr K enr ÞðerCr K eTðrCrÞ Þ C eð1CTÞðrCrÞ rðr C rÞl1 > : l2 ! ðemr K enr Þðr C rÞ Fig. 2. Technological innovation policy.
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G. Gimenez / Technovation 26 (2006) 345–350
Finally, technology acquisition periods are a consequence of the policies applied rather than variables related with government intervention. Measures to reduce interest rates (r), acquisition costs (l1) and learning costs (l2) will provide an incentive for the acquisition of new technologies.
4. Conclusions The foregoing discussion presents a model designed to throw light on the economic mechanisms determining the decision to acquire a new technology to replace an existing one. Such acquisitions, of course, involve costs and benefits. The final decision will depend upon whether the investment in the new technology will generate net gains. According to the model, these gains will, in turn, depend on the period in which the technology in use at the time the possibility of acquiring a new one is raised was acquired, as well as the period in which the new technology is offered, its useful life, the speed of the innovation process, interest rates, acquisition costs and learning costs. Benefits will arise from the technology if the present value of the sum of all additional annual profits generated as a result of acquiring the technology over the whole of its useful life exceeds the sum of acquisition and learning costs, taking into consideration that the technology incorporates further developments in each period providing higher profits, despite the increase in learning costs, and that it is subject to obsolescence. The static comparative analysis reveals that of the factors considered only the useful life of the technology, the rate of interest, the cost of acquisition and learning costs have a definite effect on net gains (positive in the first case and negative in the rest) and, therefore, on the investment decision. The discussion of the most appropriate economic policies that a government might adopt to foster investment in the acquisition of new technologies is based on this analysis.
These policies would involve measures to reduce interest rates or to act on acquisition and learning costs.
References Aghion, P., Howitt, P., 1992. A model of growth through creative destruction. Econometrica 60 (2), 323–351. Aghion, P., Howitt, P., 1998. Endogenous Growth Theory. MIT Press, Cambridge, MA. Dosi, G., 1991. The research of innovation diffusion: An assessment. In: Nakicenovic, N., Gru¨bler, A. (Eds.), Diffusion of technologies and social behaviour. Springer, Berlin, pp. 179–208. Dosi, G., Freeman, C., Nelson, R., Silverberg, G., Soete, L. (Eds.), 1988. Technical Change and Economic Theory. Pinter Publishers, London. Freeman, C., 1982. The Economics of Industrial Innovation. Penguin, London. Grossman, G., Helpman, E., 1991. Innovation and Growth in the Global Economy. MIT Press, Cambridge, MA. Mankiw, N., Romer, D., Weil, D., 1992. A contribution to the empirics of economic growth. Quarterly Journal of Economics 107 (2), 407–437. Mansfield, E., 1968. Industrial Research and Technological Innovation: An Econometric Analysis. Norton, New York. Mansfield, E., Schwartz, M., Wagner, S., 1971. Research and Development in the Modern Corporation. Norton, New York. Mansfield, E., Rapoport, J., Romeo, A., Villani, E., Wagner, S., Husic, F., 1977. The Production and Application of new Industrial Technology. Norton, New York. Romer, P., 1990. Endogenous technological change. Journal of Political Economy 98 (5, part 2), S71–S102. Stoneman, P. (Ed.), 1995. Handbook of the Economics of Innovation and Technological Change. Blackwell, Oxford. Weitzman, M.L., 1998. Recombinant growth. Quarterly Journal of Economics 113, 331–360.
Gregorio Gimenez has a degree in Economics (summa cum laude) and a PhD degree from the Faculty of Economics of the University of Zaragoza, where he is currently working as an assistant professor. He has been visiting fellow at several universities in Latin America. His research interests include economic growth, human capital and innovation; topics on which he has several research projects and publications.
Investment in new technology: Modelling the decision process Gregorio Gimenez* Department of Applied Economics, University of Zaragoza, Gran Vı´a, 2, 50005 Zaragoza, Spain
Abstract This paper presents a model designed to throw light on the economic mechanisms determining the decision to acquire a new technology to replace an existing one. The investment decision is governed by a cost-benefit analysis, which is influenced by the factors analysed in the model described. These factors are the lapse of time between the acquisition of the technology currently in use and the moment at which the new technology becomes available; the useful life of the new technology; the speed of the innovation process; interest rates; the acquisition cost of the new technology; and learning costs. A static comparative analysis is performed on the basis of these factors with the aim of recommending the most appropriate instruments for technology policy measures. q 2005 Elsevier Ltd. All rights reserved. Keywords: Investment in technology; Technology use; Innovation
1. Introduction There has been a proliferation of studies treating technology as a key factor for economic growth in recent years, among which we may cite the contributions of Romer (1990), Grossman and Helpman (1991) and Aghion and Howitt (1992, 1998). If technology plays such a significant role in growth and economic convergence between countries, it will clearly be essential to understand in detail the decision-making process behind investment in technology. This is the objective of this paper, which proposes a microeconomic model to explain the technology investment process.1 The first part of the argument examines the factors determining the process of new technology acquisition. This requires an analysis of costs and benefits. Users will purchase a technological innovation if it generates positive net gains. The second part applies a static comparative analysis to observe how each of the factors considered affects the investment decision process. Finally, the measures that governments might take to encourage * Tel.: C34 976 762 223; fax: C34 976 761 840. E-mail address: [email protected]. 1 A broad review of the literature on innovation and technological change is provided in Freeman (1982) and Dosi et al. (1988). Published studies of the diffusion of new technologies among potential users include Mansfield (1968) and Mansfield et al. (1971, 1977), which focus on the diffusion of new technologies in industry, and Dosi (1991), which is more general.
0166-4972/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.technovation.2005.03.008
the acquisition of new technologies are considered in light of the results obtained from the study. Conclusions are presented in Section 4 of this paper. 2. Basis for the model Technological innovations may be used either by producers, applying the technology as an intermediate input for the production of some other consumer good, or by consumers as final goods. For the purposes of this section, let us take the case of an entrepreneur using a given production factor (with an associated technology) to manufacture certain goods or services.2 For example, we may imagine an economist using a computer program to manage his clients’ investment portfolios or a reprographics business that acquires a photocopier. Embedded in these intermediate inputs is a specific technology. Let us also assume that this embedded technology is subject to a process of incremental development. These productive inputs are, then, offered for sale in the market in each period, but incorporating successive technological improvements.3 In the examples given, this assumption translates into the appearance of new versions of 2 The results obtained from the model would be exactly the same where we take the case of a consumer of final goods obtaining a given utility from the use of the new technology. 3 This is similar to the Schumpeterian process of creative destruction. The studies by Grossman and Helpman (1991) and Aghion and Howitt (1992, 1998) cited above are based on this concept.
346
G. Gimenez / Technovation 26 (2006) 345–350
the computer program used by the economist and new, more sophisticated models of photocopier that could be acquired by the reprographics business. These improvements would raise the productivity of users of the technology. If the entrepreneur opts to purchase the program or photocopier incorporating technical improvements, business returns will rise either because it becomes possible to boost the quality of outputs or because the costs associated with the production process will fall, or for both reasons. Let us suppose that the entrepreneur is offered a new version of the input used in the production process in each period. This version will include a series of technological improvements that would raise the profits obtained in each period. This section presents a model to explain how the producer makes the decision to acquire the new embedded technology. In the first place, the entrepreneur starts up the business in period 0, acquiring a technology A0 at a cost C0. In addition, he will have to learn to use this technology, which means incurring learning costs (time, effort and money invested) equal to Ap0. The technology will enable the entrepreneur to obtain a profit of B0 monetary units in each period in which it is utilised. Chart 1 provides an outline of this account. What, then, occurs in the following period, 1? The entrepreneur is offered the opportunity to acquire a new, more developed technology, A1 which incorporates the technology of the preceding period. The price of this new technology is C1. In order to adapt to the new technology, the entrepreneur will also incur learning costs of Ap1. This innovation would make it possible to generate higher profits. To simplify, let us assume that additional returns equal to the initial profit (B0) are obtained each time a new technology is acquired. Thus, profits B1Z2B0 would be generated if the new technology A1 was acquired. This is the same as assuming that the incremental technological improvements incorporated are of the same magnitude, which is to say the impact of each innovation is similar to the preceding one and the developments included bring the entrepreneur an identical increase in profits to that provided by the adoption of earlier technologies. Let us assume that the entrepreneur decides not to adopt the new technology offered in period 1. He will thus continue to utilise the technology pertaining to the prior period, A0. The entrepreneur incurs no costs, because he is already familiar with the technology and knows how to use it. The profits obtained in period 1 using technology A0 will be equal to those earned in the initial period, B0. What happens when we reach the second period 2, with technology A0? In this period, the technology offered, A2, includes the technology developments A1 and A2. The purchase price of this technology is C2, and the associated learning costs are ApZAp2CAp1. We may note here that these learning costs are incremental. This means that in taking up a new technology we incorporate earlier technical improvements (in this case A1), which we must also learn to use. Let us now suppose that a period n is reached with a technology adopted in previous period m. In n,
the entrepreneur considers acquiring technology An. This would involve paying P an acquisition cost of Cn and learning costs equal to ApZ niZm Api . These costs reflect the need to recycle knowledge and skills since the period of the last upgrade, m, in order to learn how to use technological developments incorporated in each of the intervening periods. The increase in profits that would be achieved in each period with the adoption of Pnthe new technology, An, can be quantified as follows: iZm Bi . This includes all additional profits that would be obtained from the adoption of the new technologies incorporating all of the innovations developed since m, the period in which the last technology acquisition took place (Fig. 1). Hence, if the technology offered is adopted, the net additional profit obtained in period n will be: n X iZm
Bi K Cn K
n X
Api
iZm
Fig. 1. Technology acquisition.
(1)
G. Gimenez / Technovation 26 (2006) 345–350
Using technology An, the total profit obtained in any period nCk following the nth period will be equal to BnCk Z
n X
Bt
(2)
tZ0
where CnCkZ0 and ApnCkZ0. It does not, however, seem reasonable to assume that the technology applied has an unlimited useful life. This is a consequence of physical wear and tear and the increasing difficulty of obtaining supplies or finding personnel with the skills to maintain the technology in question, as might be the case with a photocopier. The goods or services produced using a given technology might also lose their attractiveness for consumers. In the case of our hypothetical economist, for example, it might not be possible to adapt the computer program used to tax reforms or new financial products. In view of this, we shall assume that the useful life of the technology adopted in a period n is limited to T periods. After this time, the technology will be obsolete and unusable. On the basis of the factors discussed above, we may now consider whether the entrepreneur should acquire the new technology developed in the nth period. He will in fact make the switch if the following condition holds: T X n n X X ½Bit ð1 C rÞKt O Cn C Api tZ1 iZm
(3)
iZm
that is, the change will be justified if the present value of the sum of total additional profits generated from the acquisition of the new technology over the whole of its useful life exceeds the sum of all acquisition and learning costs. Pn The additional profits, iZm Bi , will be generated annually until the useful life of the invention ends in period T. These additional profits should, of course, be discounted using an interest rate, r.4 If the foregoing inequality is expressed over a time continuum, we have: ðT ðn
ðn Bit e
Krt
tZ1 iZm
didtO Cn C
iZm
Api di
(4)
Since Bit and Api are equal in each period (i.e. BitZB and ApiZAp), we may rewrite the expression as follows: ðn ðT ðn B eKrt didtO Cn C Api di (5) tZ1 iZm
Let us consider two further assumptions in order to flesh out the model. The first assumes that the new technology includes an increasing number of innovations in each period. We may call this the speed of the innovation process.5 Thus, innovation increases exponentially, possibly as a result of the positive externalities generated by existing technologies.6 Increasing technical developments will translate into higher productivity, thereby raising the potential profits to be earned in each period. Hence, we may assume that profitability gains due to technological developments are determined by a parameter r. Because the technology is increasingly complex, however, this assumption also implies that it will become more difficult to use, raising learning costs. Let us assume, then, that these costs will rise in proportion to profits depending on the value of r. The second assumption is that the annual profits provided by the adoption of the new technology will decline period by period after its acquisition due to obsolescence and emerging substitute technologies that provide consumers with new alternatives. The erosion of profits in each period of the technology’s life cycle will also be given by r, the parameter that determines the evolution of technological developments. To sum up, the entrepreneur may acquire an increasingly sophisticated technology in each period, which will raise his profits although learning costs will also be higher. The entrepreneur also knows that the annual benefit provided by a new technology will begin to decline from the moment of its acquisition due to obsolescence caused by the speed of innovation. On the basis of these assumptions, the entrepreneur will benefit from acquiring a new technology An in period n if: ðT ðn tZ1 iZm ðT
di0
ri
ðn
B e e e didtO Cn C Ap eri iZm ðn ðn ri KðrCrÞt Be e didtO Cn C Ap eri di
tZ1 iZm
Krt
Krt
iZm
ð6Þ Thus, the entrepreneur will benefit from the technology if the present value of the sum of all additional annual profits generated as a result of acquiring the technology over the whole of its useful life exceeds the sum of acquisition and learning costs, taking into consideration that the technology incorporates further developments in each period providing higher profits, despite the increase in learning costs, and that it is subject to obsolescence. In order to make expression (6) easier to work with, let us express the acquisition and learning costs of the innovation
iZm
P P Note that neither of the sums niZm Bi and niZm Api are discounted. This is because the additional benefits and costs derived from the innovations embedded in the new technology arise in the nth period or thereafter, in which case a discount factor is implicit. 4
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5 This concept is similar to the technology growth rate described in a number of studies, including the eminent paper by Mankiw et al. (1992). 6 Weitzman (1998) analyses how new concepts may be formed from the combination of existing ideas. Stoneman (1995) provides further evidence of the importance of cumulative learning processes for scientific and technical progress.
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in terms of profits: Cn Z l1 B;
Ap Z l2 B
(7)
where liO0 0Ap Z
l2 C ; l1 n
Cn Z
l1 Ap l2
(8)
On the basis of (7), we may rewrite Eq. (6) as follows: ðT ðn ðn B eri eKðrCrÞt didtO l1 B C l2 B eri di (9) tZ1
iZm
the entrepreneur affect incentives to invest in innovation at the time the possibility of purchasing a new technology is raised. This, of course, refers to changes in the parameter m. To this end, it is necessary to find the derivative of G with respect to m
iZm
dG Z dm
h i KrðrCrÞl1 CeKð1CTÞðrCrÞ ðemr Kenr ÞðerCr KeTðrCrÞ Ceð1CTÞðrCrÞ ðrCrÞl2 Þ d ½ rðrCrÞ dm mr
Z
e ½Ke
KrKr
KTðrCrÞ
Ce rCr
Solving expression (9), we find that the entrepreneur will benefit from acquiring a new technology in the market where the net gains obtained from technology investment, G, are greater than zero. This will only be the case if: GZ
GZ
(12)
B½Krðr C rÞl1 C eKð1CTÞðrCrÞ ðemr K enr ÞðerCr K eTðrCrÞ C eð1CTÞðrCrÞ ðr C rÞl2 Þ O0 rðr C rÞ
Since BO0 is a necessary condition for the business to be viable, the entrepreneur will only invest in technology if:
3. Static comparison and design of technological innovation policy This section examines how the net gains obtained from technology investment are affected by changes in the technology uptake periods, in general lifestyles, interest rates, the speed of technological change, and the amount of technology acquisition and learning costs. On this basis, we shall go on to discuss the possible economic policy instruments derived from the model. These effects will be examined assuming that: nOm; mO0; T O0; rO0; rO0; l1 O0; l2 O0 This assumes a period (n) when a given technology that could replace another purchased in an earlier period (m) is acquired; the interest rate (r) is positive; the technology has a useful life (T); technological innovations incorporate ever more developments (r), as a result of which both profits and learning costs increase and inventions become obsolete; and the technology is associated with acquisition costs (l1) and learning costs (l2). All these assumptions fit the model described. (A) In the first place, we shall consider how changes in the period in which the technology currently used by
(10)
The sign of this derivative is indeterminate, depending as it does on the specific values taken by the remaining
½Krðr C rÞl1 C eKð1CTÞðrCrÞ ðemr K enr ÞðerCr K eTðrCrÞ C eð1CTÞðrCrÞ ðr C rÞl2 Þ O0 rðr C rÞ
Furthermore, the entrepreneur will have a greater incentive to invest in the new technology as the value of G increases.
8 9 >O > CðrCrÞl2 < = ! 0 > : > ; Z
(11)
parameters. This is because the increments in the profits that would be obtained by switching technologies will be greater as the time elapsed between technology acquisition periods increases. On the other hand, the learning process required to assimilate the new technology will be more difficult. If learning costs are not too high, it would be logical to suppose that the first of these effects will predominate. Thus, the older the technology currently used by the entrepreneur, the greater the net gains derived from the acquisition of a new technology. (B) Changes in the period in which the new technology is offered, n 8 9 >O > nr KrKr KTðrCrÞ dG e ½Ke Ce C ðr C rÞl2 < = ZK ! 0 > dn r Cr ; : > Z (13) The sign of this derivative is also indeterminate for the reasons given in the preceding point. In this case, however, if learning costs are relatively low, the net gains obtained will be greater if the new technology is acquired. (C) Changes in the length of the technology’s useful life, T 8 > O05 nO m KTðrCrÞ mr nr < dG e ðKe C e Þ (14) Z !05 n! m > dT r : Z 05 n Z m Taking into account the restrictions placed upon the parameters, it will generally be the case that net gains will increase as the useful life of the new technology acquired
G. Gimenez / Technovation 26 (2006) 345–350
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increases, because the present value of future profit flows will In this way, we may establish that the useful life of the be higher. technology (T) has a positive effect on the net gains derived (D) Changes in the speed of the innovation process, r from the acquisition of an innovation, while the interest rate 2 38 9 eKð1CTÞðrCrÞ ðerTCðmCTÞr ðrð1 Cr KmrÞ Crð2 Cr KmrÞÞ CerTCðnCTÞr ðrðK2 CðK1 CnÞrÞ >O > = < > 6 7> dG 1 6 7 rCrCmr Z 2 ðrðK2 Cmr KTrÞ CrðK1 Cmr KTrÞÞ CrðK1 CðK1 CnÞrÞÞ Ce 6 7 ! 0 2 > 5> dr r ðr CrÞ 4 > ; : > Z CerCrCmr ðrð1 Knr CTrÞ Crð2 Knr CTrÞÞ Cðr CrÞ2 ðemr ðK1 CmrÞ Cenr ð1 KnrÞÞl2
The effect is indeterminate and depends on the value of the parameters. This is because of the increasing difficulty of learning to use new technologies due to the incorporation of ever more innovations, even though their application in the production system will raise the profits that can be obtained. Furthermore, the effect of obsolescence results in a decline in the present value of the flow of future profits over the useful life of the technology. (E) Changes in the interest rate, r
(15) (r), the cost of acquisition (l1) and learning costs (l2) have a negative impact. The effects of the remaining factors are indeterminate. In light of the above effects, then, it is possible to design technological innovation policy measures (Fig. 2). Many arguments have been advanced in favour of the application of technological innovation policies with a view to achieving sustained economic growth. As mentioned above, numerous theoretical models attach fundamental
dG eKð1CTÞðrCrÞ ðemr K enr Þ½eTðrCrÞ ð1 C r C rÞ K erCr ð1 C rT C rTÞ Z !0 dr rðr C rÞ2 When interest rates rise, net gains will fall because of the reduction in the present value of future profits. (G) Changes in the amount of technology acquisition costs, l1 dG Z K1 dl1
(17)
Logically, any increase in acquisition costs will translate into a reduction in net gains. (G) Changes in the amount of technology learning costs, l2 dG emr K enr !0 Z dl2 r
(18)
Hence, any increase in the costs incurred in learning to use the new technology will result in a reduction in net gains.7
ð16Þ
importance to technology as a factor that contributes to, even determines, development. Let us assume that a government wishes to provide entrepreneurs with incentives for investment to acquire new technologies. Based on the model described, this would mean seeking to ensure that the net gains derived from the investment in new technology are positive or, in other words, that G is greater than zero. A series of economic policy measures might be proposed to this end. In view of the parameters affecting the decision to invest in technology, the most viable and useful policies would act on interest rates and acquisition and learning costs. These measures are reflected in Chart 2. The useful life of new technologies and the speed of the innovation process, on the other hand, are affected by numerous factors that are not strictly economic.
7
The amount of acquisition and learning costs are fundamental considerations for any entrepreneur in the decision to purchase new technology. The cost of acquisition is, of course, immediately known to the technology user. The entrepreneur will also have some information concerning learning costs, because he already uses technologies of the same kind and this cost is initially assumed to be constant for each periodic innovation. It is, then, an interesting exercise to find the values of l1 and l2 at which the acquisition of a new technology would generate a positive return, assuming a given value for the remaining parameters. These are obtained from expression (11): GO 0 8 ðemr K enr ÞðKeKrKr K eKTðrCrÞ C ðr C rÞl2 Þ > > < l1 ! rðr C rÞ 5 > eKð1CTÞðrCrÞ ½Kðemr K enr ÞðerCr K eTðrCrÞ Þ C eð1CTÞðrCrÞ rðr C rÞl1 > : l2 ! ðemr K enr Þðr C rÞ Fig. 2. Technological innovation policy.
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Finally, technology acquisition periods are a consequence of the policies applied rather than variables related with government intervention. Measures to reduce interest rates (r), acquisition costs (l1) and learning costs (l2) will provide an incentive for the acquisition of new technologies.
4. Conclusions The foregoing discussion presents a model designed to throw light on the economic mechanisms determining the decision to acquire a new technology to replace an existing one. Such acquisitions, of course, involve costs and benefits. The final decision will depend upon whether the investment in the new technology will generate net gains. According to the model, these gains will, in turn, depend on the period in which the technology in use at the time the possibility of acquiring a new one is raised was acquired, as well as the period in which the new technology is offered, its useful life, the speed of the innovation process, interest rates, acquisition costs and learning costs. Benefits will arise from the technology if the present value of the sum of all additional annual profits generated as a result of acquiring the technology over the whole of its useful life exceeds the sum of acquisition and learning costs, taking into consideration that the technology incorporates further developments in each period providing higher profits, despite the increase in learning costs, and that it is subject to obsolescence. The static comparative analysis reveals that of the factors considered only the useful life of the technology, the rate of interest, the cost of acquisition and learning costs have a definite effect on net gains (positive in the first case and negative in the rest) and, therefore, on the investment decision. The discussion of the most appropriate economic policies that a government might adopt to foster investment in the acquisition of new technologies is based on this analysis.
These policies would involve measures to reduce interest rates or to act on acquisition and learning costs.
References Aghion, P., Howitt, P., 1992. A model of growth through creative destruction. Econometrica 60 (2), 323–351. Aghion, P., Howitt, P., 1998. Endogenous Growth Theory. MIT Press, Cambridge, MA. Dosi, G., 1991. The research of innovation diffusion: An assessment. In: Nakicenovic, N., Gru¨bler, A. (Eds.), Diffusion of technologies and social behaviour. Springer, Berlin, pp. 179–208. Dosi, G., Freeman, C., Nelson, R., Silverberg, G., Soete, L. (Eds.), 1988. Technical Change and Economic Theory. Pinter Publishers, London. Freeman, C., 1982. The Economics of Industrial Innovation. Penguin, London. Grossman, G., Helpman, E., 1991. Innovation and Growth in the Global Economy. MIT Press, Cambridge, MA. Mankiw, N., Romer, D., Weil, D., 1992. A contribution to the empirics of economic growth. Quarterly Journal of Economics 107 (2), 407–437. Mansfield, E., 1968. Industrial Research and Technological Innovation: An Econometric Analysis. Norton, New York. Mansfield, E., Schwartz, M., Wagner, S., 1971. Research and Development in the Modern Corporation. Norton, New York. Mansfield, E., Rapoport, J., Romeo, A., Villani, E., Wagner, S., Husic, F., 1977. The Production and Application of new Industrial Technology. Norton, New York. Romer, P., 1990. Endogenous technological change. Journal of Political Economy 98 (5, part 2), S71–S102. Stoneman, P. (Ed.), 1995. Handbook of the Economics of Innovation and Technological Change. Blackwell, Oxford. Weitzman, M.L., 1998. Recombinant growth. Quarterly Journal of Economics 113, 331–360.
Gregorio Gimenez has a degree in Economics (summa cum laude) and a PhD degree from the Faculty of Economics of the University of Zaragoza, where he is currently working as an assistant professor. He has been visiting fellow at several universities in Latin America. His research interests include economic growth, human capital and innovation; topics on which he has several research projects and publications.