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Input prices and material substitution
Input prices and material substitution Choice of methodology for a
disaggregated study
M. J. Holmes
A disaggregated study of the role of input prices in the process of material substitution should involve modelling this role on the basis of incentives given to technological developments which enable firms to substitute away from more expensive materials. An appropriate procedure for empirical investigation should involve the collection of information and data by means of surveying and an analysis on the basis of judgemental techniques. This methodological approach is more appropriate than statistical techniques such as regression analysis and offers the potential to address questions which the more aggregated studies of commodity demand and substitution have left unanswered. The author is a research fellow with the Department of Economics, University of Dundee, Dundee DDl 4HN, UK The following are gratefully acknowledged. Christopher Rogers (University of Dundee), Phillip Crowson and David Humphreys (RTZ Corporation) for help and advice, and the RTZ Corporation for their financial support. The views expressed in this paper are those of the author and should not necessarily be attributed to these sources of assistance.
‘M,.J. Holmes, ‘Input prices and material substitution: the case for a more disaggregated approach’, Materials and Society, forthcoming.
112
Holmes’ argues that our understanding of the role of input prices in the process of material substitution would be greatly enhanced if investigations followed a disaggregated approach. The use of case studies involving specific materials in specific end-uses offers considerable potential in improving our understanding of both the qualitative and quantitative roles played by material prices in material substitution via technological change. This paper discusses the choice of an appropriate methodological approach with which to analyse material substitution so as to acquire this better understanding. It is argued that the role played by input prices should be modelled on the basis of the influence exerted through technological change. Due to consequent data problems, the nature and variety of other influences under examination, and the nature of the relationship between prices and substitution, it is argued that an empirical investigation which obtains data and information through direct contact with industry, and analyses this data and information by means of subjective and judgemental techniques, can be of great use. Indeed, it is argued that this approach has a number of potential advantages over a purely econometric study.
A model of material substitution In broad terms, the desired methodological approach should include two identifiable stages: first, the modelling of the role of input prices in the process of material substitution, which leads to a number of a priori expectations concerning the roles played by input prices and other variables and second, the choice of an appropriate procedure with which to assess these relationships empirically. This section is concerned with the first of these stages and presents a model which explains the role played by input prices in the process of material substitution. The model aims to address questions that the aggregated studies of material demand and substitution have left unanswered. What are the channels
0301-4207/88/020112-09$03.00
0
1988 Butterworth
& Co (Publishers)
Ltd
Input prices and material substitution
through which input prices influence material substitution? What are the roles played by other influences on material substitution? There are two important considerations to be made in constructing this model: the significance of technological change, and the differing characteristics provided by alternative materials. These considerations are now discussed in more detail. The role of technological change
Explicit attention should be paid to the role of technological change and in particular, the influence of input prices on the research and development of, the innovation of, and diffusion of new technologies which imply changes in the material composition of a given product. Case studies by Demler, Tilton and Nappi’ of material substitution in US industry have provided evidence which suggests that input prices have an indirect, long-term influence on material substitution through technological developments which lead to economies in the use of the relatively more expensive factors of production. Hicks’ original statement”
may be of relevance
here:
change in the relative price of the factors of production is itself a spur to invention, and of invention of a particular kind - directed to economising the use of a factor which has become relatively expensive. A
The characteristics of materials
2F.R. Demler, ‘Beverage containers’, in J.E. Tilton, ed, Material Substitution: Lessons ffom Tin-Using Industries, Resources for the future, Washington, DC, 1983; J.E. Tilton, Material Substitution: Lessons from Tin-Using Industries, Resources for the Future, Washington, DC, 1983; and C. Nappi, ‘Metals demand and the American container and packaging industry, 19701990’, Materials and Society, Vol 10, No 3, 1986, pp 455490. 3J. Hicks, Theory of Wages, Macmillan, London, 1932, pp 124-l 25. 4K. Lancaster. Consumer Demand, Columbia University Press, New York, 1971. %.T. Newcomb, ‘Toward a dvnamic theory of substitution and technological change in the materials market,’ Proceedings of the Council of Economics, 98th Meeting of the American Institute of MinMetallurgical and Petroleum ing, Engineers, New York, 1969, pp 168-188.
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Each material is characterized by a combination of physical and chemical properties eg tensile strength, weight, toughness and ductility and so on. Following Lancaster,4 we can argue that a firm’s demand for inputs is a derived demand in the sense that it is these intrinsic characteristics that the firm is ultimately interested in. Newcomb’ has argued that this approach enables production theory to be brought more in line with engineering experience. Variations in input combinations (which may be induced by changes in factor price ratios) can lead to variations in the nature and extent of characteristics and hence the quality of output. Bearing both of those considerations in mind, the model takes the following form. It is assumed that the markets for both a given product and the inputs used in the relevant production activity are both perfectly competitive. In the given production activity, firms produce one unit of characteristics output zO. It is assumed that there are a number of alternative combinations of characteristics which also provide z’; we can therefore construct an isoquant representing the locus of these alternative combinations yielding 2’. Firms maximize the present discounted value (PDV) of profits using a number of material inputs in order to produce z”. More formally, we can write Max I7 (z)
=p.q(p,
z) - wx(w,
z)stz
= z”
(1)
z=Bx
where IYIrepresents the PDV of profits, z represents a vector of characteristics, x represents a vector of present and expected future material inputs, q represents a vector of present and expected future physical output, p and w are vectors of present and expected future output prices and input prices respectively. B is a technology matrix representing the relationships between material inputs and resulting characteristics.
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Input prices and material substitution
Firms face a set of potential factor ratios which are capable of attaining an output level of z”. However, it is assumed that technology is fixed in the short run. Thus, should firms wish to employ a new factor ratio, they must allocate resources towards creating or adopting new technologies which will enable the desired substitution to take place.
=
k{ adoption }
(2)
where adoption refers to the adoption of new technologies which enable firms to substitute materials in order to produce z” with a new combination of material inputs. Let us consider the influence that might play a role in firms’ decision to adopt these new technologies. Input prices
If we assume that an isoquant representing z” is convex in characteristics space, then changes in input prices will alter a firm’s optimal input combination for producing z”. This level of output could now be produced at lower cost with a new factor ratio which economizes on the factor which has become relatively more expensive. Firms will have an interest in both the behaviour of current and future input prices. Uncertainty. Uncertainty has been a characteristic of the non-ferrous metal markets manifesting itself in both price and quantity uncertainty. Such uncertainty has been the result of factors ranging from cartels, political instability and nationalizations in producer countries, to the nature of demand and speculation. Blair and Turnovsky, in theoretical studies6 have attempted to apply economic theories of uncertainty to the theory of the firm and the firm’s demand for inputs when price or quantity uncertainty exists. It has been shown that subject to a number of assumptions, a risk averse firm will demand less of a particular input if its associated uncertainty increases. Furthermore, Blair’ has shown that the conventional estimates of elasticities of substitution (a measure of the responsiveness of factor ratios to changes in factor price ratios) which do not take account of uncertainty, are both biased and inconsistent.
Consumer preferences and product differentiation. Typically, firms employing non-ferrous metals as inputs are in competition to sell their output. Changing consumer tastes and preferences may give firms the desire to respond to consumer needs. On the other hand, firms may differentiate their products in the face of constant preferences in order to gain an advantage over their competitors. This too can lead to an ‘%.D. Blair, ‘Random input prices and the alteration in the material composition of output. The roles of consumer theorv of the firm’. Economic inuuiw, Vol 12, 1974, pp 214-225; R.D. Blair,.‘Estimapreferences and product differentiation are considered together in this tion of the elasticity of substttution when discussion because there may exist a number of interrelationships input prices are random’, Southern Economaterial substitution and the between competitive considerations, mic Journal, Vol 41, 1974, pp 141-144; S.J. Turnovsky, ‘The behaviourof a comquality of output. The nature of these interrelationships impinge on the petitive firm with uncertainty in factor mardesirability of undertaking material substitution. In the cases of both the kets’, New Zealand Economic Papers, Vol in the face 3, 1969, pp 52-58; and S.J. Turnovsky, ‘changing consumer preferences’ and ‘product differentiation ‘The theory of production under conditions of constant preferences’ arguments, firms seek to increase their sales by of stochastic input supply’, Mefroeconomivarying the quality of their output; this in turn requires an adjustment in ca, Vol 23, 1971, pp 51-65. factor ratios in order to achieve a new combination of characteristics. ‘Blair, ‘Random input prices’, ibid.
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Input prices and material substitution
Government. We can view government policy and regulation as influencing substitution and technological change both directly and indirectly. In a direct sense, concern over security of supply might lead to resources being devoted to undertaking research and development into ways in which less reliance can be placed on the factor concerned. In an indirect sense, we have environmental issues (eg lead in petrol) and standards (vis-d-vis the quality of goods) which may have an impact on the choice of material inputs. More generally, resources allocated to scientific research may result in more or less of particular materials being used.
Price of output. Binswanger and Ruttan’ have analysed the ways which the price of output can influence a firm’s total amount of research and the bias of technical change. In their cost-benefit approach to modelling a firm’s decision to undertake innovative activity, movements in the price of output can influence the profit made before and after research. The expected discounted output price enters as a weight in determining the expected net benefits of any research plan. It is then argued that in the case of a firm which faces an (infinitely) elastic demand for its output and has an infinitely elastic input supply, increases in the expected discounted output price will lead to an increase in the total amount of research; but the effect on the bias of technical change cannot be predicted since we need to take into account research possibilities and factor costs. Cost of technology. An important consideration might concern the (monetary) costs associated with installing and operating new technologies. The costs associated with installation may dampen the effects of changes in input prices. Even if a firm finds it economically viable to install new technology, the running costs of that technology might still outweight any potential advantages.
*H.P. Binswanger and V.W. Ruttan, Induced Innovation, Johns Hopkins, London, 1978, pp 108-l 13. ‘A. Bieber, with P. Dubarle, Problems Involved in Introducing New Materials in the Transport Industries, OECD, Directorate for Science, Technology and Industr;y, DSTI/SPR/87.3, 1987.
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New materials. Beiber,’ in a discussion of the problems involved with introducing new materials in the transport industries, has pointed to a number of considerations which concern ‘entrepreneurs’ motivations, to their positioning strategies in a free competition world and to the way in which they decide for an ‘innovation strategy’ and an R&D policy that takes into account the behaviour of their competitors and their regulatory environment’. Beiber indicates that in the transport industries, a shift towards materials that are more expensive but are easier to work and are of better quality has been a recent major trend. It is argued that the ease with which new materials can be worked with has been influenced by the development of computer-assisted design and computer-integrated manufacturing, new industrial partnerships between the diverse interests who design components using new materials, increasing internationalization where chemical and industrial knowhow is concentrated in the hands of a smaller number of multinationals, the rapidly escalating requirements for scientific expertise and escalating R and D costs, and workforce attitudes to the introduction of new technologies.
Changes in the level of output. Higher levels of output may be associated with increased profits and size of operations and hence the resources required for adopting new technologies.
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Input prices and material substitution
Significance of materials in total costs. Evidence presented in Demler” suggests that the relationship between price and material substitution is influenced by the significance of materials within total costs. A rise in the price, or a rise in the price uncertainty of a material may have little or no effect on its use if that material constitutes a small proportion of total costs and the final price paid by consumers. Modelling the influences The functional form for the firm’s decision to adopt such technologies is thus assumed to take the following form: adoption
= 1 {w, UNC, PDCP, Govt, Mix}
(3)
where w represents the price of materials, UNC represents price and quantity uncertainty associated with material inputs, PDCP represents product differentiation and consumer preferences of characteristics, Govt represents the role of government in influencing the material composition of products and Mist represents the remaining arguments discussed above. The set of factor ratios which the firm can adopt depends on the extent of innovative activity ie those new technologies which are commercially available. Innovations which have direct implications for material substitution can be derived from a number of sources: firms who are producers of the product concerned, associations representing the producers and fabricators of materials, the government, academic institutions, and other research establishments. In each case, the extent of innovative activity depends on the amount of expenditure on research and development, and a range of considerations which make any subsequent invention commercially available. We can write innovation a,b,c,d,f=
m{R&D,Q}
(4)
where R&D represents expenditure on research and development and Q represents those influences which make any subsequent invention commercially viable. Innovators are assumed to be influenced by the costs associated with producing the innovation, and their perception of how the arguments discussed earlier will influence the product manufacturers’ demand for new technologies. Superscripts a, b, c, A, f identity the origin of the innovation: a refers to firms themselves, b refers to associations which represent producers and fabricators of materials, c represents the government, d refers to academic institutions and f represents other research establishments. We can define a series of formulations which determine the amount of R&D undertaken: R&D’- b*‘%d.f = n {w, UNC, PDCP, Govt, Mix}
“‘Demler,op tit, Ref 2.
116
(5)
A number of points must be made. First, the qualitative role played by input prices may differ between agents who undertake R and D. It has been argued that the firm has an incentive to research into ways of economizing on the use of more expensive materials. Associations which represent producers and fabricators of the more expensive materials may search for ways of increasing that material usage by altering the characteristics that can be derived eg providing greater strength. Second, there is a high element of uncertainty which concerns future results from research and, in particular, how successful research will be in providing an invention with the desired adjustment in factor
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input prices and material substitution
ratios and whether such an invention will constitute a commercially viable product. This uncertainty can have an important bearing on expenditure. We can draw parallels with the cost of technology above. The researcher will be concerned with the expected costs of installation and operation that manufacturers of the product might need to incur. It will be necessary to include this argument in Misc. Third, not all of these agents will necessarily be involved in a given case of material substitution. Equations (l)-(5) constitute a model with the aim of explaining the role played by input prices in the process of material substitution. The model pays explicit attention to the significance of technological change in the process of material substitution. Input prices exert an influence on material substitution through the incentives given to the creation and adoption of new technologies which economize on the use of the more expensive materials. Indeed, in order to understand this role, we need to take into account the stages of technological change as well as the other influences which might be of significance. We can compare this model with the econometric models of Slade, Mathur and Clark, and Valdes” which have analysed material substitution at disaggregated levels. These studies have specified a production function explaining the relationship between material inputs and output (eg Cobb-Douglas, CES), obtained cost minimization or profit maximization conditions, and then derived an estimating equation explaining input ratios where input price ratios are the key independent variable. Estimated parameters include elasticities of substitution. The role of input prices is not incorporated in a satisfactory manner since technological change is incorporated by utilizing a lag structure for input prices and this constitutes a worrying misspecification problem. In addition, the estimating equations may be further misspecified because they omit the other influences on material substitution eg uncertainty over material price and supply, consumer preferences and product differentiation, legislative factors etc. innovaBinswanger and Ruttan’” model firms’ decision to undertake tive activity on the basis of a cost-benefit approach. Firms are assumed to evaluate the PDV of net benefits associated with particular innovative activity eg with the aim of economizing on the use of a particular input.. Although quantitative arguments such as input prices and output prices are included in such a computation, little is said about the other important influences on the decision to substitute materials which have been discussed above.
Empirical investigation “M.E. Slade, ‘Prices changes and metals markets: modelling short- and long-run copper-aluminium substitution’, Materials and Society, Vol 4, No 4, 1980, pp 397411; SC. Mathur and PC. Joel, ‘An econometric analysis of substitution between aluminium and copper in the electrical conductor industry’, Materials and Society, Vol 7, No 1, 1983, pp 115-124; and R.M. Valdes, ‘Substitution in the insulated cable market: a study of copperaluminium materials substitution’, Materials and Society, Vol 11, No 3, 1987, pp 259-277. “@I tit, Ref 8.
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In order to estimate the relationships set out earlier and so provide a qualitative and quantitative assessment of the role played by input prices in the process of material substitution, we must select an appropriate technique of empirical investigation. It is argued that an appropriate technique is one which collects data and information by means of surveying, and analyses the data and information by means of subjective and judgemental procedures. Surveying might be characterized by presenting manufacturers of the chosen products and those agents responsible for technological advancements which permit material substitution with questions which concern the relationships preSented in the model. These questions might be posed in the form of a formal questionnaire together with the use of personal interviews in
Inputprices and material substitution order to clarify unclear questions and answers. The nature of the data and information received will be varied. In order to reach overall qualitative and quantitative statements of the relationships presented in the model, we can form the necessary judgements by weighing up the variety of data and information on the basis of the ‘significance’ and ‘relevance’ of each respondent both to the model and the aims of the study. It is shown that this procedure for empirical investigation is preferable to the use of regression analysis which would involve the estimation of the above equations by regression techniques. The choice of technique rests on a number of considerations such as the nature and extent of data requirements and availability, the nature of the qualitative influences included in the model, and the nature of the relationship between material prices and substitution. These considerations are discussed in more detail. Data requirements
and availability
Holmes13 discusses the types of data and information requirements that this study generates and shows how limited official sources are. A range of disaggregated data is required which includes the consumption of materials, output, prices and costs, the technological change (resources allocated to the research of, innovation of, and diffusion of new technologies which have implications for the material composition of products, the nature of these projects, the scientific and engineering issues associated with material substitution and hence the implications for the quality of output). Official data sources in the UK fail to meet these requirements in a satisfactory manner. Surveying can be used to obtain the types of information and data that official sources do not reveal. A judgemental analysis based on data and information obtained by surveying may place fewer demands on data resources than regression analysis. The data requirements of regression analysis place considerable demands on the availability of UK disaggregated data. Regression analysis requires long runs of consistent data in order to provide estimated coefficients which are of a reasonable standard. Since these requirements are not satisfied, there is no guarantee that the estimated coefficients will be unbiased and efficient. The nature of variables under consideration An inspection of the model outlined earlier shows that both quantitative and qualitative influences are included. If regression analysis was employed as a means of estimating the model, attempting to incorporate the qualitative influences would mean using a number of proxies such as dummy variables; this in turn would raise questions concerning the specification of the regression equations. By relying on surveying as a means of collecting data and information, and judgemental techniques as a basis for analysis, we can address the questions concerning the influences of the qualitative influences on material substitution in a more direct manner with the possibility of avoiding the use of questionable proxies.
13M J Holmes, ‘An investigation of the role of input prices in the process of material substitution: data requirements and availability’, Dept of Economics, University of Dundee, mimeo, 1988.
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The nature of the relationship between material prices and substitution Standard microeconomic theory implies a number of strong presumptions concerning the relationship between material price and substitution. These presumptions are that the functional relationship between
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Input prices and material substitution
price and substitution is both reversible and continuous. argued that these are very strong presumptions to make. 0
0
The functional relationship between price and substitution is not necessarily reversible ie we will not necessarily find a symmetrical response by substitution to price changes. A reversible and symmetrical relationship might be present in the short run if current technology permits the substitution of materials with relative ease ie with little cost or disruption. However, it has been argued that material substitution does take place with some cost or disruption with the desired degree of adjustment occurring in the longer run through resources being allocated towards research into technical advances which will economize on the use of the material whose price has risen. However, for that material to regain its lost market, any subsequent price fall may have to considerably outweigh the initial price rise in order to compensate for the resources allocated towards the initial technological developments. Another consideration concerns a firm’s perception of the permanence of a given price change. A firm may need to be reasonably secure in the knowledge that a price realignment is going to remain long enough to justify any subsequent investment in new technologies which will affect the material composition of its product. For a given price movement, these long-term expectations may differ between upward and downward realignments. The functional relationship between demand and price is not necessarily continuous. Typically, microeconomic theory assumes that there are an infinite number of alternative input combinations which can be used for producing a given level of output. Substitution will thus occur as a response to changes in price no matter how small these changes in price are. It is more likely the case that both short- and long-run demand exhibit discrete jumps as prices vary. A firm may face a limited number of alternative input combinations. Consequently, the relative price of a material may rise with (little or) no effect on its demand, but as a ‘threshold’ is passed it may become desirable to adopt an alternative input combination. The demand for the material may thus drop sharply as it is substituted by other materials.
This suggests that we should try to avoid obtaining strict parametric values such as elasticities of substitution which are unqualified (ie do not take account of the more technical aspects of the relationship between price and substitution). This suggests that regression analysis may not be the most appropriate analytical technique. Furthermore, the estimated coefficients obtained from regression analysis presume that the relationship between price and substitution is constant over time, which is too strong a presumption to make. Following Tilton,14 it can be argued that a constant relationship would require a constant relationship between relative input prices and the number of induced innovations, and the number of induced innovations and their cumulative effects on input ratios. There are reasons to doubt that such stable relationships exist. The relationship between prices and the number of induced innovations is complex and many other determining factors need to be taken into account. The relationship between the number of induced innovations and their cumulative effects on input ratios is not necessarily a stable one as each innovation tends to have differing
‘%p tit, Ref 2.
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Input prices and material substitution
implications for the material composition of a given product. An empirical approach based on surveying should enable us to acknowledge, by way of its directness, the important facets of the relationship between material price and substitution. The above discussion suggests that there are problems associated with using regression analysis to estimate the relationships in the model. These problems are the large demands placed on data availability, the nature of the variables under consideration, and the strong presumptions concerning the relationship between input prices and material substitution. An empirical technique which consists of surveying as a means to collect information and data, and judgemental techniques as a means of analysis, offers the potential to be less constrained by data problems and take a more realistic view of the relationships that exist between material prices and material substitution. Despite these advantages, there are a number of problems with this technique of empirical investigation. In the case of surveying there is much scope for ambiguity in the questions posed and answers received. In the case of analysing, a high degree of personal judgement is required. Indeed, this form of analysis is not as rigorous as regression analysis in terms of evaluating the quality of the results obtained.
Summary An appropriate methodological approach for investigating the role of input prices in the process of material substitution in selected case studies is one which models the role of input prices on the basis of the influence exerted through technological change. The appropriate method of empirical investigation should utilize surveying as a means of collecting data and information, and judgemental techniques as the basis for an empirical analysis. The benefits of using this approach are that lesser demands are placed on data availability, qualitative influences can be examined in a more satisfactory manner, and we can avoid making strong presumptions on the relationship between input prices and substitution, It now remains for case studies to proceed along these lines. We will then be in a position to address the questions that the aggregated studies of commodity demand and substitution have left unanswered. We will be able to identify the channels through which input prices influence material substitution and provide a more detailed account of the role of technological change.
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disaggregated study
M. J. Holmes
A disaggregated study of the role of input prices in the process of material substitution should involve modelling this role on the basis of incentives given to technological developments which enable firms to substitute away from more expensive materials. An appropriate procedure for empirical investigation should involve the collection of information and data by means of surveying and an analysis on the basis of judgemental techniques. This methodological approach is more appropriate than statistical techniques such as regression analysis and offers the potential to address questions which the more aggregated studies of commodity demand and substitution have left unanswered. The author is a research fellow with the Department of Economics, University of Dundee, Dundee DDl 4HN, UK The following are gratefully acknowledged. Christopher Rogers (University of Dundee), Phillip Crowson and David Humphreys (RTZ Corporation) for help and advice, and the RTZ Corporation for their financial support. The views expressed in this paper are those of the author and should not necessarily be attributed to these sources of assistance.
‘M,.J. Holmes, ‘Input prices and material substitution: the case for a more disaggregated approach’, Materials and Society, forthcoming.
112
Holmes’ argues that our understanding of the role of input prices in the process of material substitution would be greatly enhanced if investigations followed a disaggregated approach. The use of case studies involving specific materials in specific end-uses offers considerable potential in improving our understanding of both the qualitative and quantitative roles played by material prices in material substitution via technological change. This paper discusses the choice of an appropriate methodological approach with which to analyse material substitution so as to acquire this better understanding. It is argued that the role played by input prices should be modelled on the basis of the influence exerted through technological change. Due to consequent data problems, the nature and variety of other influences under examination, and the nature of the relationship between prices and substitution, it is argued that an empirical investigation which obtains data and information through direct contact with industry, and analyses this data and information by means of subjective and judgemental techniques, can be of great use. Indeed, it is argued that this approach has a number of potential advantages over a purely econometric study.
A model of material substitution In broad terms, the desired methodological approach should include two identifiable stages: first, the modelling of the role of input prices in the process of material substitution, which leads to a number of a priori expectations concerning the roles played by input prices and other variables and second, the choice of an appropriate procedure with which to assess these relationships empirically. This section is concerned with the first of these stages and presents a model which explains the role played by input prices in the process of material substitution. The model aims to address questions that the aggregated studies of material demand and substitution have left unanswered. What are the channels
0301-4207/88/020112-09$03.00
0
1988 Butterworth
& Co (Publishers)
Ltd
Input prices and material substitution
through which input prices influence material substitution? What are the roles played by other influences on material substitution? There are two important considerations to be made in constructing this model: the significance of technological change, and the differing characteristics provided by alternative materials. These considerations are now discussed in more detail. The role of technological change
Explicit attention should be paid to the role of technological change and in particular, the influence of input prices on the research and development of, the innovation of, and diffusion of new technologies which imply changes in the material composition of a given product. Case studies by Demler, Tilton and Nappi’ of material substitution in US industry have provided evidence which suggests that input prices have an indirect, long-term influence on material substitution through technological developments which lead to economies in the use of the relatively more expensive factors of production. Hicks’ original statement”
may be of relevance
here:
change in the relative price of the factors of production is itself a spur to invention, and of invention of a particular kind - directed to economising the use of a factor which has become relatively expensive. A
The characteristics of materials
2F.R. Demler, ‘Beverage containers’, in J.E. Tilton, ed, Material Substitution: Lessons ffom Tin-Using Industries, Resources for the future, Washington, DC, 1983; J.E. Tilton, Material Substitution: Lessons from Tin-Using Industries, Resources for the Future, Washington, DC, 1983; and C. Nappi, ‘Metals demand and the American container and packaging industry, 19701990’, Materials and Society, Vol 10, No 3, 1986, pp 455490. 3J. Hicks, Theory of Wages, Macmillan, London, 1932, pp 124-l 25. 4K. Lancaster. Consumer Demand, Columbia University Press, New York, 1971. %.T. Newcomb, ‘Toward a dvnamic theory of substitution and technological change in the materials market,’ Proceedings of the Council of Economics, 98th Meeting of the American Institute of MinMetallurgical and Petroleum ing, Engineers, New York, 1969, pp 168-188.
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Each material is characterized by a combination of physical and chemical properties eg tensile strength, weight, toughness and ductility and so on. Following Lancaster,4 we can argue that a firm’s demand for inputs is a derived demand in the sense that it is these intrinsic characteristics that the firm is ultimately interested in. Newcomb’ has argued that this approach enables production theory to be brought more in line with engineering experience. Variations in input combinations (which may be induced by changes in factor price ratios) can lead to variations in the nature and extent of characteristics and hence the quality of output. Bearing both of those considerations in mind, the model takes the following form. It is assumed that the markets for both a given product and the inputs used in the relevant production activity are both perfectly competitive. In the given production activity, firms produce one unit of characteristics output zO. It is assumed that there are a number of alternative combinations of characteristics which also provide z’; we can therefore construct an isoquant representing the locus of these alternative combinations yielding 2’. Firms maximize the present discounted value (PDV) of profits using a number of material inputs in order to produce z”. More formally, we can write Max I7 (z)
=p.q(p,
z) - wx(w,
z)stz
= z”
(1)
z=Bx
where IYIrepresents the PDV of profits, z represents a vector of characteristics, x represents a vector of present and expected future material inputs, q represents a vector of present and expected future physical output, p and w are vectors of present and expected future output prices and input prices respectively. B is a technology matrix representing the relationships between material inputs and resulting characteristics.
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Input prices and material substitution
Firms face a set of potential factor ratios which are capable of attaining an output level of z”. However, it is assumed that technology is fixed in the short run. Thus, should firms wish to employ a new factor ratio, they must allocate resources towards creating or adopting new technologies which will enable the desired substitution to take place.
=
k{ adoption }
(2)
where adoption refers to the adoption of new technologies which enable firms to substitute materials in order to produce z” with a new combination of material inputs. Let us consider the influence that might play a role in firms’ decision to adopt these new technologies. Input prices
If we assume that an isoquant representing z” is convex in characteristics space, then changes in input prices will alter a firm’s optimal input combination for producing z”. This level of output could now be produced at lower cost with a new factor ratio which economizes on the factor which has become relatively more expensive. Firms will have an interest in both the behaviour of current and future input prices. Uncertainty. Uncertainty has been a characteristic of the non-ferrous metal markets manifesting itself in both price and quantity uncertainty. Such uncertainty has been the result of factors ranging from cartels, political instability and nationalizations in producer countries, to the nature of demand and speculation. Blair and Turnovsky, in theoretical studies6 have attempted to apply economic theories of uncertainty to the theory of the firm and the firm’s demand for inputs when price or quantity uncertainty exists. It has been shown that subject to a number of assumptions, a risk averse firm will demand less of a particular input if its associated uncertainty increases. Furthermore, Blair’ has shown that the conventional estimates of elasticities of substitution (a measure of the responsiveness of factor ratios to changes in factor price ratios) which do not take account of uncertainty, are both biased and inconsistent.
Consumer preferences and product differentiation. Typically, firms employing non-ferrous metals as inputs are in competition to sell their output. Changing consumer tastes and preferences may give firms the desire to respond to consumer needs. On the other hand, firms may differentiate their products in the face of constant preferences in order to gain an advantage over their competitors. This too can lead to an ‘%.D. Blair, ‘Random input prices and the alteration in the material composition of output. The roles of consumer theorv of the firm’. Economic inuuiw, Vol 12, 1974, pp 214-225; R.D. Blair,.‘Estimapreferences and product differentiation are considered together in this tion of the elasticity of substttution when discussion because there may exist a number of interrelationships input prices are random’, Southern Economaterial substitution and the between competitive considerations, mic Journal, Vol 41, 1974, pp 141-144; S.J. Turnovsky, ‘The behaviourof a comquality of output. The nature of these interrelationships impinge on the petitive firm with uncertainty in factor mardesirability of undertaking material substitution. In the cases of both the kets’, New Zealand Economic Papers, Vol in the face 3, 1969, pp 52-58; and S.J. Turnovsky, ‘changing consumer preferences’ and ‘product differentiation ‘The theory of production under conditions of constant preferences’ arguments, firms seek to increase their sales by of stochastic input supply’, Mefroeconomivarying the quality of their output; this in turn requires an adjustment in ca, Vol 23, 1971, pp 51-65. factor ratios in order to achieve a new combination of characteristics. ‘Blair, ‘Random input prices’, ibid.
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Government. We can view government policy and regulation as influencing substitution and technological change both directly and indirectly. In a direct sense, concern over security of supply might lead to resources being devoted to undertaking research and development into ways in which less reliance can be placed on the factor concerned. In an indirect sense, we have environmental issues (eg lead in petrol) and standards (vis-d-vis the quality of goods) which may have an impact on the choice of material inputs. More generally, resources allocated to scientific research may result in more or less of particular materials being used.
Price of output. Binswanger and Ruttan’ have analysed the ways which the price of output can influence a firm’s total amount of research and the bias of technical change. In their cost-benefit approach to modelling a firm’s decision to undertake innovative activity, movements in the price of output can influence the profit made before and after research. The expected discounted output price enters as a weight in determining the expected net benefits of any research plan. It is then argued that in the case of a firm which faces an (infinitely) elastic demand for its output and has an infinitely elastic input supply, increases in the expected discounted output price will lead to an increase in the total amount of research; but the effect on the bias of technical change cannot be predicted since we need to take into account research possibilities and factor costs. Cost of technology. An important consideration might concern the (monetary) costs associated with installing and operating new technologies. The costs associated with installation may dampen the effects of changes in input prices. Even if a firm finds it economically viable to install new technology, the running costs of that technology might still outweight any potential advantages.
*H.P. Binswanger and V.W. Ruttan, Induced Innovation, Johns Hopkins, London, 1978, pp 108-l 13. ‘A. Bieber, with P. Dubarle, Problems Involved in Introducing New Materials in the Transport Industries, OECD, Directorate for Science, Technology and Industr;y, DSTI/SPR/87.3, 1987.
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New materials. Beiber,’ in a discussion of the problems involved with introducing new materials in the transport industries, has pointed to a number of considerations which concern ‘entrepreneurs’ motivations, to their positioning strategies in a free competition world and to the way in which they decide for an ‘innovation strategy’ and an R&D policy that takes into account the behaviour of their competitors and their regulatory environment’. Beiber indicates that in the transport industries, a shift towards materials that are more expensive but are easier to work and are of better quality has been a recent major trend. It is argued that the ease with which new materials can be worked with has been influenced by the development of computer-assisted design and computer-integrated manufacturing, new industrial partnerships between the diverse interests who design components using new materials, increasing internationalization where chemical and industrial knowhow is concentrated in the hands of a smaller number of multinationals, the rapidly escalating requirements for scientific expertise and escalating R and D costs, and workforce attitudes to the introduction of new technologies.
Changes in the level of output. Higher levels of output may be associated with increased profits and size of operations and hence the resources required for adopting new technologies.
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Significance of materials in total costs. Evidence presented in Demler” suggests that the relationship between price and material substitution is influenced by the significance of materials within total costs. A rise in the price, or a rise in the price uncertainty of a material may have little or no effect on its use if that material constitutes a small proportion of total costs and the final price paid by consumers. Modelling the influences The functional form for the firm’s decision to adopt such technologies is thus assumed to take the following form: adoption
= 1 {w, UNC, PDCP, Govt, Mix}
(3)
where w represents the price of materials, UNC represents price and quantity uncertainty associated with material inputs, PDCP represents product differentiation and consumer preferences of characteristics, Govt represents the role of government in influencing the material composition of products and Mist represents the remaining arguments discussed above. The set of factor ratios which the firm can adopt depends on the extent of innovative activity ie those new technologies which are commercially available. Innovations which have direct implications for material substitution can be derived from a number of sources: firms who are producers of the product concerned, associations representing the producers and fabricators of materials, the government, academic institutions, and other research establishments. In each case, the extent of innovative activity depends on the amount of expenditure on research and development, and a range of considerations which make any subsequent invention commercially available. We can write innovation a,b,c,d,f=
m{R&D,Q}
(4)
where R&D represents expenditure on research and development and Q represents those influences which make any subsequent invention commercially viable. Innovators are assumed to be influenced by the costs associated with producing the innovation, and their perception of how the arguments discussed earlier will influence the product manufacturers’ demand for new technologies. Superscripts a, b, c, A, f identity the origin of the innovation: a refers to firms themselves, b refers to associations which represent producers and fabricators of materials, c represents the government, d refers to academic institutions and f represents other research establishments. We can define a series of formulations which determine the amount of R&D undertaken: R&D’- b*‘%d.f = n {w, UNC, PDCP, Govt, Mix}
“‘Demler,op tit, Ref 2.
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(5)
A number of points must be made. First, the qualitative role played by input prices may differ between agents who undertake R and D. It has been argued that the firm has an incentive to research into ways of economizing on the use of more expensive materials. Associations which represent producers and fabricators of the more expensive materials may search for ways of increasing that material usage by altering the characteristics that can be derived eg providing greater strength. Second, there is a high element of uncertainty which concerns future results from research and, in particular, how successful research will be in providing an invention with the desired adjustment in factor
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ratios and whether such an invention will constitute a commercially viable product. This uncertainty can have an important bearing on expenditure. We can draw parallels with the cost of technology above. The researcher will be concerned with the expected costs of installation and operation that manufacturers of the product might need to incur. It will be necessary to include this argument in Misc. Third, not all of these agents will necessarily be involved in a given case of material substitution. Equations (l)-(5) constitute a model with the aim of explaining the role played by input prices in the process of material substitution. The model pays explicit attention to the significance of technological change in the process of material substitution. Input prices exert an influence on material substitution through the incentives given to the creation and adoption of new technologies which economize on the use of the more expensive materials. Indeed, in order to understand this role, we need to take into account the stages of technological change as well as the other influences which might be of significance. We can compare this model with the econometric models of Slade, Mathur and Clark, and Valdes” which have analysed material substitution at disaggregated levels. These studies have specified a production function explaining the relationship between material inputs and output (eg Cobb-Douglas, CES), obtained cost minimization or profit maximization conditions, and then derived an estimating equation explaining input ratios where input price ratios are the key independent variable. Estimated parameters include elasticities of substitution. The role of input prices is not incorporated in a satisfactory manner since technological change is incorporated by utilizing a lag structure for input prices and this constitutes a worrying misspecification problem. In addition, the estimating equations may be further misspecified because they omit the other influences on material substitution eg uncertainty over material price and supply, consumer preferences and product differentiation, legislative factors etc. innovaBinswanger and Ruttan’” model firms’ decision to undertake tive activity on the basis of a cost-benefit approach. Firms are assumed to evaluate the PDV of net benefits associated with particular innovative activity eg with the aim of economizing on the use of a particular input.. Although quantitative arguments such as input prices and output prices are included in such a computation, little is said about the other important influences on the decision to substitute materials which have been discussed above.
Empirical investigation “M.E. Slade, ‘Prices changes and metals markets: modelling short- and long-run copper-aluminium substitution’, Materials and Society, Vol 4, No 4, 1980, pp 397411; SC. Mathur and PC. Joel, ‘An econometric analysis of substitution between aluminium and copper in the electrical conductor industry’, Materials and Society, Vol 7, No 1, 1983, pp 115-124; and R.M. Valdes, ‘Substitution in the insulated cable market: a study of copperaluminium materials substitution’, Materials and Society, Vol 11, No 3, 1987, pp 259-277. “@I tit, Ref 8.
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In order to estimate the relationships set out earlier and so provide a qualitative and quantitative assessment of the role played by input prices in the process of material substitution, we must select an appropriate technique of empirical investigation. It is argued that an appropriate technique is one which collects data and information by means of surveying, and analyses the data and information by means of subjective and judgemental procedures. Surveying might be characterized by presenting manufacturers of the chosen products and those agents responsible for technological advancements which permit material substitution with questions which concern the relationships preSented in the model. These questions might be posed in the form of a formal questionnaire together with the use of personal interviews in
Inputprices and material substitution order to clarify unclear questions and answers. The nature of the data and information received will be varied. In order to reach overall qualitative and quantitative statements of the relationships presented in the model, we can form the necessary judgements by weighing up the variety of data and information on the basis of the ‘significance’ and ‘relevance’ of each respondent both to the model and the aims of the study. It is shown that this procedure for empirical investigation is preferable to the use of regression analysis which would involve the estimation of the above equations by regression techniques. The choice of technique rests on a number of considerations such as the nature and extent of data requirements and availability, the nature of the qualitative influences included in the model, and the nature of the relationship between material prices and substitution. These considerations are discussed in more detail. Data requirements
and availability
Holmes13 discusses the types of data and information requirements that this study generates and shows how limited official sources are. A range of disaggregated data is required which includes the consumption of materials, output, prices and costs, the technological change (resources allocated to the research of, innovation of, and diffusion of new technologies which have implications for the material composition of products, the nature of these projects, the scientific and engineering issues associated with material substitution and hence the implications for the quality of output). Official data sources in the UK fail to meet these requirements in a satisfactory manner. Surveying can be used to obtain the types of information and data that official sources do not reveal. A judgemental analysis based on data and information obtained by surveying may place fewer demands on data resources than regression analysis. The data requirements of regression analysis place considerable demands on the availability of UK disaggregated data. Regression analysis requires long runs of consistent data in order to provide estimated coefficients which are of a reasonable standard. Since these requirements are not satisfied, there is no guarantee that the estimated coefficients will be unbiased and efficient. The nature of variables under consideration An inspection of the model outlined earlier shows that both quantitative and qualitative influences are included. If regression analysis was employed as a means of estimating the model, attempting to incorporate the qualitative influences would mean using a number of proxies such as dummy variables; this in turn would raise questions concerning the specification of the regression equations. By relying on surveying as a means of collecting data and information, and judgemental techniques as a basis for analysis, we can address the questions concerning the influences of the qualitative influences on material substitution in a more direct manner with the possibility of avoiding the use of questionable proxies.
13M J Holmes, ‘An investigation of the role of input prices in the process of material substitution: data requirements and availability’, Dept of Economics, University of Dundee, mimeo, 1988.
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The nature of the relationship between material prices and substitution Standard microeconomic theory implies a number of strong presumptions concerning the relationship between material price and substitution. These presumptions are that the functional relationship between
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price and substitution is both reversible and continuous. argued that these are very strong presumptions to make. 0
0
The functional relationship between price and substitution is not necessarily reversible ie we will not necessarily find a symmetrical response by substitution to price changes. A reversible and symmetrical relationship might be present in the short run if current technology permits the substitution of materials with relative ease ie with little cost or disruption. However, it has been argued that material substitution does take place with some cost or disruption with the desired degree of adjustment occurring in the longer run through resources being allocated towards research into technical advances which will economize on the use of the material whose price has risen. However, for that material to regain its lost market, any subsequent price fall may have to considerably outweigh the initial price rise in order to compensate for the resources allocated towards the initial technological developments. Another consideration concerns a firm’s perception of the permanence of a given price change. A firm may need to be reasonably secure in the knowledge that a price realignment is going to remain long enough to justify any subsequent investment in new technologies which will affect the material composition of its product. For a given price movement, these long-term expectations may differ between upward and downward realignments. The functional relationship between demand and price is not necessarily continuous. Typically, microeconomic theory assumes that there are an infinite number of alternative input combinations which can be used for producing a given level of output. Substitution will thus occur as a response to changes in price no matter how small these changes in price are. It is more likely the case that both short- and long-run demand exhibit discrete jumps as prices vary. A firm may face a limited number of alternative input combinations. Consequently, the relative price of a material may rise with (little or) no effect on its demand, but as a ‘threshold’ is passed it may become desirable to adopt an alternative input combination. The demand for the material may thus drop sharply as it is substituted by other materials.
This suggests that we should try to avoid obtaining strict parametric values such as elasticities of substitution which are unqualified (ie do not take account of the more technical aspects of the relationship between price and substitution). This suggests that regression analysis may not be the most appropriate analytical technique. Furthermore, the estimated coefficients obtained from regression analysis presume that the relationship between price and substitution is constant over time, which is too strong a presumption to make. Following Tilton,14 it can be argued that a constant relationship would require a constant relationship between relative input prices and the number of induced innovations, and the number of induced innovations and their cumulative effects on input ratios. There are reasons to doubt that such stable relationships exist. The relationship between prices and the number of induced innovations is complex and many other determining factors need to be taken into account. The relationship between the number of induced innovations and their cumulative effects on input ratios is not necessarily a stable one as each innovation tends to have differing
‘%p tit, Ref 2.
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implications for the material composition of a given product. An empirical approach based on surveying should enable us to acknowledge, by way of its directness, the important facets of the relationship between material price and substitution. The above discussion suggests that there are problems associated with using regression analysis to estimate the relationships in the model. These problems are the large demands placed on data availability, the nature of the variables under consideration, and the strong presumptions concerning the relationship between input prices and material substitution. An empirical technique which consists of surveying as a means to collect information and data, and judgemental techniques as a means of analysis, offers the potential to be less constrained by data problems and take a more realistic view of the relationships that exist between material prices and material substitution. Despite these advantages, there are a number of problems with this technique of empirical investigation. In the case of surveying there is much scope for ambiguity in the questions posed and answers received. In the case of analysing, a high degree of personal judgement is required. Indeed, this form of analysis is not as rigorous as regression analysis in terms of evaluating the quality of the results obtained.
Summary An appropriate methodological approach for investigating the role of input prices in the process of material substitution in selected case studies is one which models the role of input prices on the basis of the influence exerted through technological change. The appropriate method of empirical investigation should utilize surveying as a means of collecting data and information, and judgemental techniques as the basis for an empirical analysis. The benefits of using this approach are that lesser demands are placed on data availability, qualitative influences can be examined in a more satisfactory manner, and we can avoid making strong presumptions on the relationship between input prices and substitution, It now remains for case studies to proceed along these lines. We will then be in a position to address the questions that the aggregated studies of commodity demand and substitution have left unanswered. We will be able to identify the channels through which input prices influence material substitution and provide a more detailed account of the role of technological change.
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