textabare - a model for assessing the benefits of wool ...data.daff.gov.au/brs/data/warehouse/pe_abarebrs99000240/rr92.6_textabare.pdf · preferred supply, demand and substitution

A model for assessing the benefits of wool textile research :&&;g$&$&;$;;*&&<y;f; & .$ .r; 3

Vivek Tulpule, Brian Johnston and Max Foster

ABARE RESEARCH REPORT 92.6 E ABARE

0 Commonwealth of Australia 1992

This work is copyright. The Copyright Act 1968 permits fair dealing for study, research, news reporting, criticism or review. Selected passages, tables or diagrams may be reproduced for such purposes provided acknowledgment of the source is included. Major extracts or the entire document may not be reproduced by any process without the written permission of the Executive Director, ABARE.

ISSN 1037-8286 ISBN 0 642 17453 9

Australian Bureau of Agricultural and Resource Economics GPO Box 1563 Canberra 2601

Telephone (06) 272 2000 Facsimile (06) 272 2001 Telex AGEC AA61667

ABARE is a professionally independent research organisation attached to the Department of Primary Industries and Energy. I

Foreword

The application of benefit-cost analysis to the outcomes of research work can provide a guide to help in the allocation of limited funds among alternative projects. This paper contains a description of a model, known as Textabare, which can be used to estimate the benefits from research in wool textile production and processing.

The results of the first application of the model, in the evaluation of the returns to the CSIRO research leading to the development of the Sirospun process for spinning wool, are reported in Research Report 92.5, The Economic Gains from Sirosputz Technology.

It is envisaged that Textabare will provide a 'user-friendly' tool to assist project managers to estimate benefit-cost ratios for alternative research proposals.

BRIAN FISHER Executive Director, ABARE

April 1992

Acknowledgments

The structure and contents of this paper have been improved greatly following helpful comments by Chris Vlastuin, Ken Brewer, Gil Rodrigues and Edward Wheeler.

Contents

Summary

1 Introduction

2 Modelling the benefits from wool textile research 2.1 Simplifying assumptions 2.2 Qualitative analysis 2.3 The mathematical framework

3 The treatment of parameter uncertainty

4 Sensitivities to parameter values

5 Conclusions

Appendixes A Mathematical background to the model B Discounting procedure C Generation of Monte Carlo parameter values

Box Model supply and demand equations

Figures A Key linkages between processing stages, as modelled B Initial impact of a process innovation C Changes to prices and quantities resulting from

a process innovation D Benefits from a process innovation E Profile of annual costs and benefits from an innovation F Dependence of calculated benefits from Sirospun

on assumed wool supply elasticity G Triangular probability density function for the value

of a model parameter

Tables I Elasticities used in the Sirospun analysis 2 Elasticities of sensitivity of benefits to Australian

wool growers

Summary

It has long been acknowledged that the introduction of a cost saving innovation at one point in a multistage production chain can benefit producers of raw commodities further up the processing chain. Recognition of this possibility has encouraged wool growers to invest funds in research in wool textile processing.

The aim in this paper is to describe a partial equilibrium, world level, linear model of the wool production and processing chain which can be used to estimate the benefits of research results which lower production costs at different stages of the chain. It is envisaged that the model, known as Textabare, will provide a useful tool to assist in decisions about the allocation of research funds over alternative research projects in wool processing.

The stages represented include top, yarn, fabric and garment production. Because Textabare thus incorporates each of the important stages in the wool production and processing chain, it enables consistent evaluation of research projects on a variety of different aspects of wool processing. Substitution possibilities between products of different fibre composition and between fibre and non-fibre inputs are also incorporated.

Since there is some uncertainty associated with the model parameters used in Textabare, and the extent of future cost savings likely to be generated by any given innovation, Monte Carlo analysis can be carried out using ranges of possible parameter values. This enables users to generate probability distributions for outcomes. For example, the results obtained using the model are sensitive to the set of

Innovations in wool processing,

a multistage production

process

Modelling the economic effects of innovation in

the wool chain

Substitution possibilities

between inputs an important feature

Uncertainty about model parameters

needs to be catered for

Benefits of wool textile research 1

preferred supply, demand and substitution elasticities used.

Future work on In particular, the extent of benefits to Australian linkages between wool growers from research is found to depend elements in the crucially on the responsiveness of the supply of wool chain would Australian greasy wool to the price obtained, and be of value also to the extent to which substitution can occur

between fibre and processing inputs in pure wool textile and garment production. (There is a trade-off between processing costs and loss of material.) While there is already a substantial amount of information available on Australian greasy wool supply responsiveness, there is very little quantitative information available about the degree of substitutability between fibre and other inputs (for example, the extent to which wool yarn use is increased, at constant output, in response to a rise in the price of non-fibre inputs in weaving, and vice versa). Future work in this area to provide better estimates for these parameters would help to improve the accuracy of model results.

2 ABARE research report 92.6

Introduction

The transformation of greasy wool into pure wool and wool blend garments involves many intermediate stages, including the production of wool top, yarn and fabric. Technical innovation which reduces production costs at any of these stages can lead to greater demand for greasy wool, thereby increasing its price and improving the profitability of its production. Recognition of this possibility has led the wool growing industry in Australia and overseas to allocate significant funds to research and development in wool textile manufacturing processes.

One of the difficulties associated with allocating limited research funds between alternative projects in this industry lies in the need to make comparisons between innovations affecting different stages of the wool processing chain, and having different expected patterns of adoption over time. An economic evaluation of any research project requires an assessment of both its costs and its potential benefits. The expected costs of conducting a project may be determined using relatively straightforward accounting techniques. In contrast, consistent calculation of the benefits from different types of innovations requires an economic model which can be used to estimate the effects of an innovation on prices and output levels throughout the wool production and processing chain.

The aim in this paper is to describe an economic model, known as Textabare, which can be used to estimate benefit-cost ratios for a range of wool textile and wool production research projects. It is envisaged that Textabare will provide those interested in the allocation of research funds with a 'user-friendly' tool, first to help assess the payoff from past research projects in the wool production and processing chain, and then to estimate the expected payoffs from alternative future projects.

A description of the wool production and processing chain and a discussion of some of the issues associated with modelling research benefits in multistage production chains are provided in chapter 2. The treatment of parameter uncertainty and its implications for ex ante comparative evaluation of different research projects are considered in chapter 3, and the sensitivities of model results to changes in parameter values are evaluated in the particular case of the modelling of a spinning innovation, Sirospun, in chapter 4.


research

The production of final products from raw farm commodities often involves a number of intermediate production stages, each coordinated by different decision makers. Freebairn, Davis and Edwards (1982), using a multi-stage supply and demand model, showed that research which reduces off-farm costs can lead to increased demand for raw farm products, thereby benefiting farm enterprises as well as downstream producers. Mullen, Alston and Wohlgenant (1989) and Mullen and Alston (1989) extended the framework developed by Freebairn, Davis and Edwards to model the effects of, and benefits from, the introduction of cost saving innovations in wool top and greasy wool production. Mullen et al. (1989) also suggested a method for modelling the further stages of wool processing.

Like the work referred to above. that described here relates specifically to cost saving process i~inovations. I t does not relate, explicitly, to product innovations. Trajtenberg (1989) highlights the difficulties associated with the econornic analysis of the effects of new products. In particular, the exercise can be very data intensive. As it happens, the first application of Textabare has been to the technique termed Sirospu~i, the products of which have some degree of novelty and are being marketed partly on that basis. In Textabare, however, to simplify the modelling procedure the innovations represented are not assumed to lead either to the introduction of new consumer goods or to any qualitative change in variable inputs (as can be required by new producer goods). At this stage, the model is confined to innovations which provide the adopting producers with a means of combining existing variable inputs in a more efficient manner'. Formally, the introduction of a process innovation is equivalent to providing an adopting producer with an alternative production or cost function for an established output or input.

The important linkages between the different elements of the wool production and processing chain are illustrated in figure A. Greasy wool is an input into the production of wool top, wool top is an input into wool and wool blend yarns, and these yarns are inputs into fabrics which, in

I However, preliminary work indicates that with some adjustments it might be possible also to account for the effects o f some types o f product innovations.

4 ABARE r.c~sc~ar.c,h 1.~7701.t 92.6

'---KG linkages between processing stages, as modelled I A Australian

e g r e a s y wool

I

C ABARE Rest-of-world

@ greasy wool

$. @+ Wool top @ Non-wool top

I I I

r i c h @ Wool-poor @ Non:wool fabrrc fabrlc

I PI. Proce\vng lnput a Averaging 70 per cent wool by we~ght b Averagtng 30 pcr ccnl wool by weight I -__A

turn, enter into production of the garments which are the final consumption goods. The processing inputs into the production of each commodity include labour, capital equipment, transport services and in some cases promotion and advertising. Apart from the vertical linkages between production stages, there are also horizontal linkages between commodities at the same production stage. Such linkages can result from substitution possibilities, in both input and consumption, between products of different fibre composition. For a more detailed description of the wool production and processing chain, see Department of Primary Industries and Energy (1989).

Given the extent of linkages within and between production stages evident from figure A, innovations which affect production decisions at one point in the wool chain are likely to affect demand and price conditions for other commodities in the chain, In turn, these price changes could affect both the profits at each production stage and the welfare of final consumers. For example, as has been mentioned, benefits may flow to wool growers from a cost saving innovation at an intermediate wool processing stage.

Benefits of woo1 textile research 5

The magnitude of these benefits will depend on the extent to which cost reductions in wool processing increase the demand for wool products generally, and on how this rise in demand feeds back to raise the price of greasy wool.

In order to determine the extent of price and quantity changes following the introduction of an innovation at different stages of textile production and the effect of these changes on producer profits and consumer welfare, an economic model of the wool production and processing chain known as Textabare has been developed. Textabare is a partial equilibrium, linear, world level model of the wool production and processing chain (as depicted in figure A). The model can be used to calculate the net benefits from a cost saving innovation (which may be adopted in one or more of the industries in the wool chain) to all the participants in the chain, including Australian wool growers and final consumers.

The calculation of the size of the net benefits generated by an innovation involves modelling the following process:

A cost saving innovation with applications in one or Inore of the industries in the wool chain is introduced.

The innovation is initially adopted to some extent, and over time the proportion of the output of the adopting industries produced using the innovation increases until some maximum (ceiling) adoption level is reached.

The cost saving afforded by the innovation in each period following its introduction encourages the adopting firms to increase their output supplies and input demands above those which would have prevailed in the absence of the innovation.

As a result, the cost saving provided by the innovation generates temporary supply and demand imbalances in the markets for the goods produced by the adopting industries and for their inputs. These imbalances are transmitted, at least to some degree, to all markets in the chain.

In each period following the initial adoption of the innovation, the prices and quantities of all commodities in the wool chain adjust so as to bring the markets to a new equilibrium.

The price and quantity changes in each period also lead to changes in the annual profits of both adopting and non-adopting firms and in the welfare of final consumers (relative to what the profit and welfare levels would have been i i the absence of the innovation).

These relative changes to annual profits and welfare, in each period following the adoption of the innovation, are discounted and summed to yield the present value of gross benefits from the innovation. The present value of the costs of development of the innovation, discounted likewise, is subtracted from the present value of the gross benefits to obtain the net present value of the innovation. This is done both in aggregate and from the standpoints of different groups of agents in the wool chain.

2.1 Simplifying assumptions Modelling the process described above involves specifying the economic linkages between the different commodities in the wool chain, and the degrees to which producers and consumers adjust their demands in response to cost changes resulting from an innovation. To render the model tractable in terms of both computational and data requirements, a number of simplifying assumptions have been made.

The adoption decision The decision as to when, if ever, to adopt an innovation is typically a complex one, involving the formation of price expectations. In particular, rational agents will consider adopting an innovation only if it will be profitable to do so at the rationally expected post-innovation prices. In turn, however, post-innovation price levels will depend on the extent of adoption.

The modelling of such a process could be expected to be fairly involved, and therefore, to simplify the procedure, adoption levels are imposed exogenously; that is, they are determined outside the model. This involves specifying an adoption level for each period following the introduction of the innovation, including a maximum adoption level. The assumed adoption levels may be based on expert information or on extrapolation from existing adoption levels, or on a combination of the two. Projection of the path of adoption over time may be linear, or may employ some more complex functional form, where the data support it (for example, sigmoid or S-shaped adoption curves).

Benefits o f wool textile research 7

The shift in supply curves due to an innovation

As has been noted, the measured benefits rest on production cost reductions leading to shifts in both supply and demand schedules. Lindner and Jarrett (1978) noted that the extent and distribution of benefits from an innovation depend crucially on the assumed shape of the supply and demand curves for different commodities in the production chain and the way in which the introduction of an innovation shifts those curves. They demonstrated that an industry adopting a cost reducing innovation could nevertheless incur losses as a result, if the industry's supply curve were nonlinear and if the shift in that supply curve due to the innovation were non-parallel.

Rose (1980) pointed out that, typically, it is not possible to judge the nature of the shift in supply curves caused by an innovation (even after it has occurred) because information about the way in which an innovation affects production possibilities or industry cost functions is generally too limited for this purpose. He suggested that the only realistic strategy is to assume that shifts in supply are parallel; that is, that unit cost savings from an innovation are the same at all levels of output. The difficulties referred to by Rose do in fact arise in relation to innovations in wool processing technologies, and Textabare therefore incorporates the assumption that shifts in supply immediately following the introduction of an innovation are parallel. It is also assumed - again following Rose - that the industry supply curves are linear.

The treatment of time The modelling approach does not take into account the possibility that the adoption of the innovation to some given extent in a given period will have effects in subsequent periods - that is, that there will be observable lags in adjustment of supply and demand to the given usage of the technique. Also, no account is taken of the effect of past or expected prices on current decisions; that is, decision makers are assumed to be myopic. This approach is consistent with those adopted in most studies of the benefits from innovations, including the analysis by Mullen, Alston and Wohlgenant (1989) of the benefits from cost saving innovations in the wool top and raw wool industries.

The decision to model the wool processing chain in a static framework has some advantages. The principal advantage is that it reduces problems of data availability. A dynamic model of the wool production and processing


chain would require knowledge about the way in which price expectations are formed in each of the industries, and their dynamic responses to past and expected future price shocks. There is very little information available on such dynamic interactions for the commodities concerned. In addition, where econometric analyses of dynamic price responses for relevant industries are available (for example, see Ball, Beare and Harris 1989) the commodity groups chosen do not always correspond to those of interest here.

The extent of aggregation The wool production and processing chain includes a very large number of commodities. However, because of the difficulties of obtaining price and quantity data on each of these, a number of commodities have been aggregated into categories. Strictly, such aggregation rests on the assumption that all the products within a given category are perfectly substitutable, either as inputs or consumption goods. At least in some cases, this is clearly untrue. Additional work could be done to disaggregate these groups; however, at this stage of model development, it was felt that such disaggregation would not be justified by the likely improvement in the results. The main examples of aggregation include the following:

All greasy wool in the 17-24 micron range - that is, all 'fine wool' - has been aggregated, and other wool is omitted from the model.

All wool top produced from greasy wool in the 17-24 micron range has likewise been aggregated, regardless of the fibre diameter or length of the wool used in its production.

The 'non-wool top' category (see figure A) comprises all worsted fibres not containing wool. These consist mainly of synthetic fibres, and have been aggregated regardless of the fact that different types of synthetic fibres have different properties.

Yarns, fabrics and garments of the same general class of fibre composition (pure wool, non-wool, wool-rich and wool-poor) have also been aggregated into single groups. For example, men's suits of a particular fibre composition have been aggregated with women's skirts of the same fibre composition in the same homogeneous category.

Because of the difficulties of obtaining information on the costs of individual processing inputs (all inputs other than fibres), such inputs

I Benefi'ts of wool textile research 9 ~

have been aggregated to form a single 'processing input' category for each type of output. This simplification was also adopted by Mullen et al. (1989).

Finally, all commodities other than greasy wool (tops, yarns, fabrics and garments) are aggregated at the world level, and thus are not distinguished according to the country of their production or consumption.

The partial equilibrium nature of the model Textabare is a partial equilibrium model, in which no allowance is made for the effect of innovations in fine wool processing on the prices of commodities outside the production chain shown in figure A. such as wheat and coarse wool. In most cases, the errors that arise from ignoring such effects - for example, the effect of changes in wool markets on world wheat prices - are likely to be cmall. However. although specific non-fibre commodities are not included in the model, account is taken of the fact that producers move between fine wool production and other activities in general in response to changes in the price of fine wool.

Supply elasticities for processing inputs The supplies of all processing inputs (including labour, capital, and services such as transport and advertising) are assumed to be perfectly elastic in relation to the demands of the wool industries. This assumption is justified because the industries in the wool chain tend to be small in the markets for the processing inputs. This means that producers of these inputs would be prepared to supply any quantity likely to be demanded by industries in the wool chain without changing their prices.

2.2 Qualitative analysis

Demand and supply effects The following examples illustrate some features of the modelling approach used. A detailed mathematical description of the model is provided in appendix A, and is summarised in the next section.

117itiul c;f(~ct.~

Consider a cost saving innovation at the wool top production stage. In production of wool top, three inputs may be distinguished for present

10 ABARE ~.eseui.c.lr report 92 .h

purposes: greasy wool of Australian origin, greasy wool of overseas origin, and a 'processing input' which includes labour, capital equipment and transport services. The initial impact of adoption on these inputs is depicted in figure B. The industry total cost function for wool top prior to the introduction of an innovation is Co in panel a , and the associated supply curve (marginal cost) is So in panel b.

The adoption of the innovation in wool top production is assumed to lead to a reduction in unit production costs. Following Rose (1980), the reduction in unit costs is assumed to be the same at all output levels. The total cost function for wool top production shifts from Co to C, and the supply function for wool top shifts in a parallel fashion to S,. The extent of this shift at any given date will depend, positively, on the extent of adoption at that date.

Assume that initially prices do not change. The desired output of wool top then increases to Q, (panel h), with an increase in the desired usage of greasy wool and processing inputs reflected by a rightward shift in the demand functions for greasy wool and the processing input, as in panel c. If the prices of wool top and greasy wool remain unchanged, adoption of the innovation leads to an excess supply of wool top and an excess demand for greasy wool.

Because the processing input is (by assumption) in perfectly elastic supply to the wool processing industry, its equilibrium market price will not change. The other markets come to equilibrium subsequently, as the prices of fibre inputs and outputs change to equalise supply and demand. Equilibrium in all markets in the wool chain will require the mutual adjustment of all the prices for products in the production chain, including the final products.

Adjustment to equilibrium In the above account of the initial disequilibrium effects, it was convenient to consider an innovation at an early stage in the production chain. The initial effects of an innovation at a later stage are qualitatively analogous, md are of greater interest in connection with the first application of Textabare, which was to an innovation in pure wool yam spinning. The process of reaching a final equilibrium will therefore be described using that example.

The effects, within any one period, of the introduction and adoption of a cost saving innovation in pure wool yam production can conveniently be


I B Initial impact of a process innovation

I j a) wool top, total cost l ABARE i

Output b) Wool top, marginal cost

I Qo 1 c) Greasy wool

- -

Quantity

Australian greasy wool Overseas greasy wool Processing input C C

I

I

I QO QO Qo Quantity , 12 ABARE research report 92.6

separated into first round and second round. The initial first round effect (see figure C) is a downward shift in the wool yarn supply curve (from So to SI in panel c). At the same time, the increase in wool yarn supply requires a rightward shift in the demand curve for wool top, from Do to Dl, and hence an increase in the price of wool top from Po to PI , in panel b.

Output in the wool top industry expands to meet this increased demand from the wool yam industry, and as a result the wool top producers' demand for greasy wool must also expand: Do shifts to Dl in panel a. The increased demand for greasy wool raises its price (from Po to PI in panel a).

The expansion in the output of wool yarn resulting from the innovation leads to a fall in its price, initially from Po to PI in panel c. This price fall induces an expansion in wool fabric supply (from So to Sl in panel d) and the price of wool fabric falls to P,. In turn, the fall in the price of wool fabric leads to a fall in the price of wool garments (from Po to PI panel e) . At the end of the first round, the level of output in each industry has expanded from Qo to Ql and prices have moved from Po to PI .

Second round demand and supply effects occur as a result of interactions between pure wool, wool blend and non-wool items. For example, the increase in the price of wool top leads to an increase in the prices of wool blend garments. (It is assumed that the innovation is applicable in the spinning of pure wool only, and thus generates cost savings in wool processing but not in blend processing.) This leads consumers to substitute out of wool blend items into pure wool items (the shift from Do to D, in panel e), thereby generating a further increase in demand for all pure wool inputs including greasy wool. The demand curves for pure wool fabric and yarn (panels d and c) shift to Dl and the demands for wool top and greasy wool shift from Dl to D,. In the final equilibrium the prices for each product are P, and output levels are Q2.

In the model, market equilibrium is restored within each period, including the second round effects. The periods differ only in the assumed extent of adoption of the innovation.

Benefits and costs In general, benefits may accrue to wool growers, processers and consumers. It can be shown that producers are able to obtain benefits from the innovation if there are some fixed factors in production, and hence


Changes to prices and quantities resulting from a process innovation

a) Greasy wool

I QO Ql Q2 Quantity QO Q I Q Z Quantity 1

C) Pure wool yarn d) Pure wool fabric

I I ' - - QO Q I Q2 Quantity

e) Pure wool garments

I I L 1 -- - Qo Ql Q2 Quantity

1 1 I _ _ _ - - * QoQlQ2 Quantity


decreasing returns to scale. The model allows for the possibility that this is the case in all the industries represented. However, in the analysis of Sirospun technology conducted by Johnston et al. (1992), it is assumed that fixed factors in the processing industries are negligible. Such industries will not be able to gain from the introduction of an innovation. (More realistically, there are likely to be short term advantages of innovation which are competed away and which are not represented in a standard partial equilibrium type model.) In that case, producer benefits are confined to greasy wool production, where there is at least one fixed input, namely land.

The gross benefits obtained from the innovation are then as illustrated in figure D, which is derived from figure C. In panel a , greasy wool producers gain additional profits (rents on fixed factors of production) equal to the shaded area P2ABPil. Consumers gain an addition to their consumer surplus of P,,CEFGP2 (panel b) in the consumption of pure wool garments, but lose P,HIP,, in the consumption of wool blend garments, the price of which has increased from P,, to P , (panel c).

The sum of the increase in economic rents to greasy wool producers and the net gain in consumer surplus for final consumers constitutes the economic benefit generated by the innovation. The representation here is for a single period (year), characterised by some given extent of adoption of the technology. The total net present value of gross benefits from the innovation may be evaluated by discounting future benefits from the innovation in each period following initial adoption.

Typical profiles for the gross benefits from an innovation and for its development costs are represented in figure E. Annual project research and development costs are shown as the line CNC'. Costs are likely to continue to be incurred even after the date of initial adoption.

The gross annual benefits from a project shown as the upper line BB'B'. Such benefits begin to accrue at the date of initial adoption and increase over time. This is because, over time, the proportion of yarn being produced using the innovation increases, until some maximum adoption level is reached. The first period in which the innovation is employed is to, and the maximum adoption level is reached at date t,. Adoption is here shown as proceeding in a linear fashion; however, alternative adoption profiles may be used. After the date of maximum adoption, the gross annual benefits continue to be obtained in perpetuity. The economic

Benefits o f~ lool tex-tile rrsear-ch 15

-

Benefits from a process innovation

Price a) Greasy wool producers 4

C

Quantity b) Purchasers: pure wool garments

Price

Price C) Purchasers: wool blend garments

f

-- Quantity


Annual costs/benefits

t

advance provided by an innovation does not disappear after its replacement by later technology. Subsequent technology must build on the welfare level provided by the original innovation if it is to yield net benefits.

The net annual benefits from the innovation are given by the line CNN'Nf'B'B'. This line coincides with the line CC' until benefits begin to accrue, then with N'N" (the summation of NC' and BN") and then with BB'B' once development costs cease to be incurred.

To obtain the net present value of benefits from, and costs of, the innovation, their values are discounted to present value terms. The estimated level of benefits will depend on the discount rate used to value the stream of welfare from the innovation. Discounted benefits will in any case be greater if they are acquired sooner rather than later in time. The discounting and compounding procedures used to calculate the net present value of gross benefits from an innovation and project costs are discussed in appendix B.

I 1 Benefits of wool textile research 17

2.3 The mathematical framework

The approach described above diagrammatically is put into operation within Textabare by specifying mathematical relationships for the supply and demand of each commodity in the wool chain; these are presented in the box. (A detailed mathematical description of the model, with the derivations of these equations, is given in appendix A.) The equations are solved simultaneously to generate the percentage changes in price and quantity needed to restore market equilibrium in each period following the introduction of an innovation. In turn, these price and quantity changes are used to calculate the resulting changes in annual profits and consumer welfare.

Model supply and demand equations

The following supply and demand equations for each product in the wool chain are solved for each period (year) from the date of introduction of the innovation. The adoption of the innovation is treated as a supply shock in the adopting industry and in those it supplies, and as a demand shock in its input supplying industries. The extent of adoption changes from year to year. The equations are solved simultaneously (once for each period) to yield the percentage change in the prices and output levels of commodities in the wool chain. Note that all the percentage changes referred to are relative to the levels in the absence of the innovation.

I Supply porn i n d u s t ~ k

Price determination for the processing input to indusfly k

Aggregate demand for input i (any product in the wool chain other than garments)

18 ABARE researclz report 92.6

Demand for garments of each type of material

where: q'k is the percentage change in annual output supply; p'k is the percentage change in p k , the price of output k ; w ; is the percentage change in the price of input i; wtrk is the price of the processing input of industry k; x'i is the percentage change in annual aggregate demand for input i; x'id is the percentage change in annual demand for the ith consumer product; p:, is the percentage change in the price of consumer product g; &(,k is the own- price output supply elasticity, and &ik is the elasticity of output supply with respect to the price of input i; q j j k is the cross elasticity of demand for input i with respect to input price j and qjpk is the elasticity of demand for input i with respect to the output price of industry k; v;,~ is the cross elasticity of demand between final products i and g; j'k is the proportion of output produced using the innovation (in the given period); Mi is the number of industries using input i; N k is the number of inputs used to produce the kth output; jlk is the change in the firm's unit costs produced by the innovation; Bk(w) is a function which represents how the cost function shifts in response to changes in the input price vector w; and ai~, is the proportion of the total demand for input i in industry k.

It should be noted that because the model equations for percentage changes are specified as linear, the price and quantity changes generated are approximations to the actual changes which would take place. The approximation errors associated with the use of a linear model increase as the size of the supply and demand shocks (in this case, the size of the cost saving generated by an innovation) increases. However, Mullen and Alston (1989) have found in simulation experiments that the size of such errors is not likely to be very large for at least certain types of innovations in the wool industries.

The demand equations (3 and 4) explicitly incorporate the possibilities for substitution between products of different fibre composition. Such substitution is possible at the garment consumption stage, where consumers can substitute between pure wool, wool-rich, wool-poor and non-wool garments. There are also input substitution possibilities at the wool yarn production stage, where producers of wool-rich and wool-poor yarns may substitute between the use of wool top and other fibre tops, at the margin. Substitution between fibre inputs and non-fibre (processing) inputs is also allowed for.


As has been noted, the modelling of supply equations for each industry allows for the possibility that processing industries might face decreasing returns to scale in aggregate (that is, have upward sloping aggregate supply curves, as will be the case if there are fixed factors in production). This feature of the model makes it possible to test the sensitivity of the results obtained to the contrary assumption, which is often preferred in modelling work of this kind, that the supply curves for intermediate industries are horizontal. Also, if information about the extent of fixed factors in different processing industries could be obtained, it would be possible to alter the own-price elasticities of supply in the model to account for such new information.

20 ABA R E r.eseur.ch r.clpor.r 92.6

The treatment of parameter uncertainty

The results obtained using Textabare depend on the values of the elasticities used to define the supply and demand curves in the model. As a result, because there is a degree of uncertainty associated with those parameters, there is also some uncertainty in the outcomes generated by the model. To acknowledge the uncertainties associated with the parameters in the model. stochastic (or Monte Carlo) analysis has been incorporated into Textabare. This enables users to obtain a probability distribution for the benefit-cost ratio of a project, based on probability distributions for parameters used in the model. Effectively, Monte Carlo analysis enables measures of uncertainty associated with parameter values to be translated into measures of uncertainty in the model outcomes.

The first step in the stochastic procedure is to specify, for each parameter, a probability distribution which is representative of the uncertainty as to the parameter's true value. The model is then run repeatedly, each run having different values for the parameters drawn at random from their respective probability distributions. The benefit-cost results from these runs are aggregated in the form of a probability distribution.

In the Monte Carlo analysis used in Textabare, random parameter values are drawn, independently, from a triangular distribution for each parameter,

I specified by a lower bound, a most likely value and an upper bound. The

I method for obtaining such parameter values is described in appendix C.

The number of runs in the model in a stochastic simulation experiment needs to be large enough so that the results reach a steady state - that is, so that the results from additional runs of the model make acceptably small differences to the summary statistics based on all the runs. A more complete description of the procedure of stochastic simulation is contained in Taha (1982).

By the use of Monte Carlo analysis, lower bounds can be placed on values for benefit-cost ratios, and it is possible to ascertain the probability that the benefit-cost ratio for a research project exceeds unity, given the degrees of uncertainty surrounding the parameters used. For the results of

Benefits of wool textile research

the Monte Carlo ailalysis on the Sirospun technology, see Johnston, TulpulC, Foster and Gilmour (1 992).

Monte Carlo analysis is of value both ex ante and ex post (that is, both prior to the research and after its application). Even for technologies that are well established, there are uncertainties in measurement of the benefits. But it is particularly useful ex ante, when there is also uncertainty as to the direct cost savings likely to be achieved.

To apply the stochastic method to this uncertainty, estimates of the minimum, most likely and maximum cost savings from an innovation are required. The minimum cost saving from an innovation can be taken to be zero, representing the eventuality that the research project fails to produce a commercially viable innovation. The most likely and maximum cost savings from the proposed innovation would need to be estimated by scientists and engineers in the industry at which the innovation is targeted. Given these three figures, Textabare could be used to estimate, for example, the probability that the benefit-cost ratio from an innovation having uncertain cost advantages for the adopting industries will exceed unity - that is, the break-even point.


Sensitivities to parameter values

The stochastic procedure described in the previous chapter gives a measure of the uncertainty in the results due to the uncertainties in the values of all the model parameters taken together. It is also important to evaluate the sensitivities of the results to individual parameters. Such sensitivity analysis is useful for two reasons. First, it can be used in the process of model validation. If, for example, the sign on one of the sensitivity parameters does not intuitively appear to be correct, this might indicate a flaw in the model. Second, given the relative influence of each of the model parameters on the results, it becomes evident which of them could most usefully be measured more accurately.

In this section, the sensitivities of the model results to assumptions about the elasticities used are discussed in the particular case of the evaluation of Sirospun, an innovation which has reduced the unit cost of producing pure wool yams by 25 per cent, at the same time increasing the processing costs of producing wool fabric by about 1 per cent. The expected maximum adoption level for the innovation is 20 per cent of spinning capacity for pure long staple fine wool. A generalised account of the market effects of a cost saving in spinning was given in section 2.2.

Using Textabare it can be shown that, with a discount rate of 5 per cent and under the stated assumptions and 'most likely' parameter values, the annual benefit to Australian wool growers from Sirospun, once the expected maximum extent of adoption is reached, is $A43.3 million, and that the benefit-cost ratio for Australian wool growers is about 123:l (Johnston et al. 1992).

The approach to testing the sensitivity of such results to the chosen values of different parameters in the model follows that developed by Pagan and Shannon (1984). The values of each of the independent parameters in the model, in turn, are increased by one per cent and the resulting percentage change in the calculated annual benefits to Australian wool growers at maximum adoption is calculated. In this way, an 'elasticity of sensitivity' or 'sensitivity parameter' is generated for each of the independent parameters in the model.


The elasticities used in modelling the effects of Sirospun technology are listed in table 1 (for a discussion of these values, see Johnston et al. 1992). The results of the sensitivity analysis in relation to benefits to Australian wool growers in a year following maximum adoption of Sirospun are presented in table 2. The annual benefits from Sirospun prove to be most sensitive to the elasticity of supply of Australian greasy wool and to the elasticity of substitution between pure wool yam and processing inputs into pure wool fabric. While there is a large amount of information about the elasticity of supply for Australian greasy wool, there is very little hard information about the substitution elasticities between processing inputs and fibre inputs. More accurate estimation of such elasticities would therefore appear to be a fruitful course of research, from the standpoint of improving the results obtained using Textabare.

As has been mentioned, the signs on the sensitivity parameters to some extent help establish the validity of the model results. In this case, all the sensitivity parameters have the expected signs. For example, the sensitivity with respect to the supply elasticity for Australian greasy wool is negative, indicating that an increase in that elasticity would lead to a fall in annual benefits to Australian greasy wool producers. This result would be expected, because the higher the supply elasticity of an industry, the lower the increase in price received for any given increase in output, and - in this case - the greater the share of benefits from Sirospun that flow to other participants in the wool chain. The variation of the calculated annual benefits from Sirospun to Australian wool growers with assumed supply elasticity of Australian greasy wool is shown in figure F.

r------------------------------------------------------ ! F Dependence of benefits from Sirospun on assumed wool supply I

I elasticity a ! I

I r--------- -- - - - - --- - -- - - - - - i

8 1 I I 0.0 0.5 1 .0 1.5 2.0 2.5 1

Elasticity of supply of Australian greasy wool I

24 ABARE r-esearclz report 92.6

1 Elasticities used in the Sirospun analysis

Own-price supply elasticities

Australian greasy wool (17-21 microns) Overseas greasy wool ( 17-2 1 microns) Wool top Non-wool top Pure wool yarn Wool-rich yarn Wool-poor yam Non-wool yam Pure wool fabric Wool-rich fabric Wool-poor fabric Non-wool fabric Pure wool garments Wool-rich garments Wool-poor garments Non-wool garments

Cross-price demand elasticities (Demand for first commodity with respect to the price of the second commodity with output held constant) a

Australian greasy woolloverseas greacy wool Australian greasy wool processing input into wool top processing Wool toplnon-wool top Wool top/processing input into pure wool yarn Wool toplprocessing input into wool-rich yarn Wool topiprocessing input into wool-poor yarn Non-wool top/processing input into wool-rich yarn Non-wool top/processing input into wool-poor yarn Non-wool toplprocessing input into non-wool yarn Pure wool yarniprocessing input into pure wool fabric Wool-rich yarnlprocessing input into wool-rich fabric Wool-poor yarnlprocessing input into wool-poor fabric Non-wool yarnlprocessing input into non-wool fabric Pure wool fabriclprocessing input into pure wool garments Wool-rich fabriclprocessing input into wool-rich garments Wool-poor fabric/processing input into wool-poor garments Non-wool fabriclprocessing input into non-wool garments

Consumer demand elasticities for garments

Pure wool garments Wool-rich garments Wool-poor garments Non-wool garments

Own-price elasticity Income elasticity -1 .O 0.8 -1.5 0.7 -1.5 0.6

b 0.5

a 'Processing input into' any product means all inputs other than raw material that arc used in its production. b Determined by homogeneity and symmetry rcstrictions.

I Benefits oJ"wool textile re.seurch 25

2 Elasticities of sensitivity of benefits to Australian wool growers

Parameter Sensitivity a

Own-price supply r/asric.iri~s Australian greasy wool -0.47 Overseas greasy wool -0.12

C ~ ~ o s s e1u.stic.itie.s of' denlaild (ar c.oirsrai~r orrt,r,rrti Australian greasy wool/overseas greasy wool Australian greasy woollprocessing input into wool top Wool toplnon-wool top Wool top/processing input into pure wool yarn Wool toplprocessing input into wool-rich yarn Wool top/processing input into wool-poor yarn Non-wool top/processing input into wool-rich yarn Non-wool toplprocessing input into wool-poor yarn Non-wool top/processing input into non-wool yarn Pure wool yarnlprocessing input into pure wool fabric Wool-rich yarnlprocessing input into wool-rich fabric Wool-poor yarn/processing input into wool-rich fubric Non-wool yarnlprocessing input into non-wool fabric Pure wool fiibric/processing input into pure wool garuiients Wool-rich fabric/processing input into wool-rich pnrnients Wool-poor f:ibric/processing input into wool-rich garments Non-wool hbric/processing input into non-wool garments

O~c*rr-[u'ic,r c/o~roirtl cltr.stic~itic.\ Pure wool garments 0.18 Wool-rich garments -0.0 1 Wool-poor garments 4 . 0 1

Iirc~oirrcJ clci.tfic,iticr,r c!f' tlc~nrrrirrl Pure wool garments Wool-rich garments 0 Wool-poor garments 0 Non-wool garments 0

Noro: Where cla\licil~c\ appro;ich infinity, the clasticitics of scnsit~vity oblained are negligible. a 1'crccnl;lgc i~lcrcn.;c in csritrlatcd annual bcncfits. a f~cr 'ceiling' :Idoption of Sirospun. given a I per cent incrcosc in the absolute n~ngni~utlc of the indicntcd clastlcity, with all other indcpendenLly dcrcrrrlirlctl pnrnnlcters unc1r;lrlgcd.

The sensitivity parameter for the elasticity of supply of overseas greasy wool is also negative. The greater the supply elasticity of overseas greasy wool, the greater the expansion of the overseas industry in response to an increase in the use of greasy wool; thus, the smaller the share of the

26 ABA R E i.c.cc,cri.c,h r.c,por.t (12.6

increase in use drawn from Australia, and the lower the returns from the innovation to Australian producers.

The sensitivity parameter for elasticity of substitution between wool top and non-wool top is also negative, though small (-0.04). As has been noted, one effect of the innovation is to increase the price of wool top, due to increased demand from pure wool yarn producers (see section 2.2). This price increase disadvantages producers of wool-rich and wool-poor yarns (who are not themselves able to employ the innovation) and as a result they increase the proportion of non-wool top in their yarn blends at the expense of wool. By definition, an increase in the substitution elasticity between wool top and non-wool top increases the extent of such substitution by wool blend yarn producers, thereby damping the rise in demand for wool top and greasy wool. As a result, the benefit to wool growers from the innovation is reduced.

The sensitivity parameters for elasticity of substitution between Australian greasy wool and the processing input into wool top production, and for elasticity of substitution between wool top production and processing input into pure wool yarn production, are both negative. Again, the reason for this is that the prices of wool top and greasy wool increase as a result of Sirospun technology; processing inputs, in contrast, are highly elastic in supply, and no appreciable change in their prices results. Again by definition, increases in the substitution elasticities between pure wool inputs and non-fibre inputs increase the substitution out of the fibre inputs into non-fibre inputs in response to an increase in wool price. As a result, the increase in demand for wool products is lessened and the benefits to wool growers from Sirospun technology are reduced.

In contrast, the sensitivity parameters for the elasticities of substitution between pure wool products beyond the tops stage and the corresponding non-fibre inputs - that is, between wool products and the processing inputs into pure wool fabric and garment production - are positive. The reason for this is that, in the model, the prices of pure wool yarns and fabrics fall due to the Sirospun technology (see section 2.2). There will be a tendency for the wool products to substitute for non-fibre inputs. The larger the cross elasticity, the greater this substitution, and hence the greater the demand for wool and the benefits to wool growers.

The results obtained are also sensitive to the demand elasticity for pure wool garments. The sensitivity parameter for this elasticity is positive

Benefits of ~ loo l textile re~earch

(that is, the larger the absolute value of the demand elasticity, the greater the benefits to wool growers). In the model, the fall in the price of pure wool garments resulting from the innovation increases their sales. An increase in the absolute size of the demand elasticity increases the extent of this rise in demand, and hence the benefits to wool growers. (The apparent sensitivity to income elasticity of wool garment demand is in fact a general measure of sensitivity to price elasticities, to which income elasticities are linked by assumption: see equation A.13, appendix A.)

Above, it has been assumed that the processing industries have virtually flat supply schedules, with output supply elasticities approaching infinity; as a result they cannot, as modelled, retain any of the benefits from an innovation - all such benefits are passed to greasy wool producers and final consumers. To test the effect of very significant departures from this assumption, the supply elasticities for processed fibre products were reduced from 1 000 000 to 10. This very dramatic reduction in supply elasticities had a negligible effect on annual benefits to greasy wool producers, indicating that key model results are not highly sensitive to the assumptions adopted concerning returns to scale in the processing industries.


Conclusions

The use of Textabare provides a framework for consistently estimating the benefits from research leading to innovations in different stages of the wool production and processing chain. The approach explicitly acknowledges the uncertainties associated with the parameters used in the model in two ways: first, through the incorporation of a Monte Carlo analysis which converts the uncertainties associated with the parameters, taken together, into measures of probability attached to the results; and second, by gauging the sensitivity of model results to changes in individual parameters.

The Monte Carlo analysis enables project managers to estimate, for example, the probability that an innovation with uncertain future cost advantages will exceed unity. The sensitivity analysis provides some clues as to which of the elasticities employed need closer empirical attention with a view to improving the model results obtained. In particular, the sensitivity analysis suggests that more work needs to be done to obtain information on elasticities of substitution between fibre and non-fibre processing inputs.

Benej7ts of wool textile reseurch

Appendix

Mathematical background to the model

To formalise the diagrammatic approach of section 2.2 of the main text, it is necessary to specify the nature of the supply and demand relationships which make up Textabare and to identify the way in which the introduction of an innovation affects those demand and supply relations.

A. 1 Cost, supply and demand functions The output supply and input demand functions for the commodities in the wool chain are based on the cost functions applying in each industry. In each period, these cost functions are assumed to have the following form for a representative price-taking firm producing output k using Nh inputs.

where w is an Nh dimensional vector of the inpul prices faced by the firm; Qh is the output of commodity k; Bk(w) is a quasi-concave, twice continuously differentiable function which accounts for changes in production costs as input prices, w, change; and Ak is a constant parameter. The parameter is the effect of innovation on the unit costs of the firm. If the adoption of the innovation reduces costs, is negative, whereas it is positive if costs are increased.

The supply curve generated by the assumed cost function is linear in the output price, and the shift caused by the introduction of the innovation is parallel. That is, if the output price pk is set equal to marginal cost, dCidQ,

(A. 2 ) Q ~ ( w , P ~ , , u ~ ) = P ~ I B k ( w ) - ( P ,

d The input demand functions Q, ( w , pk,,Llk) are not necessarily linear: their shape depends on the functional form of Bk(u1). The following form may be obtained for the input demand functions by applying Shephard's lemma to equation (A .1 ) (see Varian 1984, p. 54), substituting Qj(w ,px , p k ) for Qk using equation (A.2):

30 ABARE r- search report 92.6

In the model, the supply and input demand equations are in log-difference form, so that percentage changes in demand and supply are written as functions of the percentage changes in input and output prices and the shift in the innovation parameter.

Supply fivm each industiy The aggregate supply curve for industry k may be converted into log- difference form by totally differentiating the supply equation (A.2) for industry k and dividing the expression so obtained by total output ( Q k ) ,

which yields the following expression:

where q; is the percentage change in output supply, pi is the percentage change in the price of output k, w; is the percentage change in the price of input i , E , , ~ is the own-price output supply elasticity, .cik is the elasticity of output supply with respect to the price of input i, and px is the proportion of output produced using the innovation.

The single non-fibre 'processing' input at each stage - which may be thought of as an amalgam of labour and capital - is assumed to be in perfectly elastic supply. As a result, the prices of each processing input, I . , are assumed to remain constant and the supply function, in log- difference form, may be represented by

where w;,: is the price of the processing input in industry k.

Demand for each input Using the same procedure described above for obtaining the output supply change equation, it is also possible to obtain a linear equation for percentage change in aggregate demand for input i:

Beneji'rs of wool textile research 31

where xJ is the percentage change in demand for input i, qijk is the cross elasticity of demand for input i with respect to input price j and qipk is the elasticity of demand for input j with respect to the output price, pk, Mi is the number of industries using input i and a ik is the proportion of the total demand for input i in industry k.

Consumer demand for final products To complete the set of model equations, it is necessary to specify the final demand equations for each of the four types of garment. The demand for each of these products may be expressed in log-difference terms as follows.

4 (A.7) . x i = x q . 1,ipk i = k - ,a,..., k

g =l

where x:is the percentage change in demand for the ith consumer product, qg is the cross elasticity of demand between final products i and g , and ph is the percentage change in the price of consumer product g. The equation may be obtained by totally differentiating an arbitrary consumer demand function and dividing the expression so obtained by total demand. Note that, the model being a partial equilibrium one, income levels are assumed to be exogenously fixed. It is also assumed that demand for garments is not affected by changes in the prices of other goods.

A.2 Restrictions on elasticities A large number of elasticities are needed to define the equations underlying Textabare. Because consistent estimates of these may not always be available in the literature, symmetry and homogeneity restrictions have been applied to reduce the number of elasticities which need to be assumed.

The first set of restrictions, relating to output supply and input demand elasticities, follow from the zero price homogeneity of input demand and output supply equations (see Varian 1984, p. 46) and the symmetry of price effects (see Varian 1984, p. 56).

Homogeneity restrictions:

In equations (A.4) and (A.6) respectively,


Symmetry restrictions:

(A. 10) c. ~k q . . ljk = c . jk qjik

(A. 11) Qk q i p k = Epk

(A. 12) q . . jlk = q. . ~ j / & + 'kEik

where Cik represents the share of total cost accounted for by the ith factor in industry k; rik is the total cost of employing the ith factor as a share of revenue in industry k, qqlG is the parlial cross elasticity of demand for input i with respect to input j with output held constant, rk is the ratio of total variable cost to revenue in industry k and the other parameters are again as defined in equations (A.4) and (A.6). (Note that restriction (A.lO) is often stated in terms of the equality between Allen substitution elasticities.)

To derive restriction (A.12) first note that the cost function (1) may be written in the following form:

(A. 12.1) C(w, Qo ) = B(w)f (Qo

where f(.) is a polynomial function. (The subscript k has been dropped for the sake of notational convenience.) As a result, the demand function for input j has the following form:

Differentiating (A.12.2) with respect to wi and multiplying the resulting expression by wilxj yields the following expression:

where Qo is the pre-innovation equilibrium level of output.

I Benefits ofwool textile research

Multiplying the above expression by [B(wlf(Qo)/B(wlf(eo)], and appropriate cancellation, yields restriction (A. 12).

Restrictions on consumer demand elasticities follow from the assumed zero homogeneity in prices and income and symmetry of cross-price effects of consumer demand equations (see Varian 1984, p. 133), and are as follows:

4

(A. 13) C r7ig + V l y = 0 g=1

where Tiy is the income demand elasticity for garment i, and si is the share of consumption of garment i in total consumption.

A.3 Evaluation of the cost saving term The calculation of the term ~ l k Bk (w)/pk in equation (A.4) is required in order to be able to determine the extent of shifts in demand and supply. In general, the value of this expression will not be directly observable; its value may nevertheless be estimated using information on the extent of unit cost savings following the introduction of the innovation. Such information may be derived from data obtained in commercial trials of an innovation or, in advance of such trials, from the calculations of the researchers concerned. On the other hand it may be evaluated using tools such as the Tankard model of wool production and processing (International Wool Secretariat 1990).

If the percentage reduction in unit costs from adoption of an innovation in industry k is found to be fk, then the value of Bk (w)/pk is

(A. 15) p k B k ( ~ ) / P k = f k I r k

where rk is the total cost of production as a share of revenue. This follows from the fact that the percentage reduction in unit costs, fk, is Clk Bk(w)QIC(Q).


A.4 Calculating benefits from an innovation

The change in annual profits and consumer welfare resulting from the introduction of an innovation may be calculated, for each period, from the price and quantity changes which follow the introduction of the innovation. The formulas used to calculate such benefits rely on the assumption that industry supply curves are linear.

Using an appropriate discount rate (see appendix B), the single-period benefits obtained using the formulas outlined in this section may be aggregated to obtain an estimate of the gross present value of benefits from the innovation. This estimate may be compared with the costs of running the research project to obtain a net present value and benefit-cost ratio.

Producer benefits If - as in the Textabare model - supply curves are assumed to be linear, it can be shown that producer surplus (or alternatively, profit) in industry k in any one period is given by the following expression:

(A. 16) 0 if E~~ > 1

or 0 0 0.5R [ 1 ( ~ ~ 1 ) * ] / & ~ if

where RO is industry revenue and E : ~ is the own-price elasticity of supply at the particular price and quantity prevailing. The superscripts are added to denote the situation prior to the introduction of an innovation. Similarly, in the post-innovation equilibrium, single-period profit or producer surplus is:

(A. 17) 0.5 R' / EL if EL 2 1

1 or 0 . 5 ~ ' (1 - (E;, - I)'] / if€,, t 1

where R1 is industry revenue in a given period after the introduction of the innovation and is the post-innovation own-price elasticity of supply.

pk. Of the post-innovation parameters in equation (A. 17), R I may be calculated using the following formula:


(A. 18) R' = R'(I+ p')(l + q')

where p' and q' are the proportional changes in the price and quantity respectively, in industry k, in the period under consideration, relative to the situation in the absence of the innovation. (The periods differ in the extent of adoption of the innovation.) The elasticity of supply is also likely to change following the introduction of the innovation, and it may be approximated using the following formula:

N ,

(A. 19)

where w) is the change in the price of input j in the period under consideration (relative to the absence of the innovation) and ci is the pre- innovation cost share of input i in the total costs of the industry under consideration.

The single-period gain (or loss) resulting from the innovation is given by the profit calculated using equation (A.17) less profit calculated using equation (A. 16).

Consumer benefits The change in single-period consumer welfare is measured by approximating the change in the consumer indirect utility function due to a change in prices brought about by the innovation (see Varian 1984, p. 116, for a description of the indirect utility function).

The post-innovation indirect utility function has the general form:

where P' is the vector of post-innovation garment prices and Y is consumer income. A second order Taylor expansion of equation (A.20) around the pre-innovation consumer price vector yields the following (see Varian 1984, p. 313):


where k and j both signify garments of one of the four fabrics considered.

Dividing equation (A.21) by the marginal utility of income, a money metric measure of the change in utility resulting from the innovation is obtained is obtained (see Deaton and Muellbauer 1980, p. 184, for a discussion of this approach). Application of Roy's identity (see Varian 1984, p. 93) then yields an expression in terms of elasticities, observed variables and variables generated using the model. The money metric change in utility may be written as follows:

0 where P: = P, (1 + p; ) .

Appendix

Discounting procedure

To be able to obtain a single measure of the benefits from a project with a varied pattern of net benefits over time, it is necessary to choose a base reference period and calculate the value of the stream of future and past net benefits at that reference period. To be able to do this, it is necessary to establish a discount rate, here denoted i. The discount rate effectively provides a measure of the exchange rate between the values of future and present consumption. Here, for simplicity, benefits alone are referred to, but the same procedure applies also to costs.

The value at reference date t* of benefits, D, obtained at date t' is given by :

Therefore, the total 'present' value of the benefits from a project at the reference date, denoted by NPV(t*), is:

where t' = 1 is the starting date for the project (not necessarily the same as the reference date - see below) and T is some final date. Within Textabare, T is set at infinity.

Choice of reference year An important issue in benefit-cost analysis is what the reference time should be, since the choice of reference date for discounting will affect the valuation obtained. Some authors argue that in an ex ante analysis of a project, it is often appropriate to use the date when work on the project would begin. However, this would not necessarily be the best date to use if a number of different projects with different inception dates were being compared. If there is some date on which a decision must be made among projects, that would be a natural reference date. In ex post uses of Textabare, 1990 has been chosen as the reference year.


Choice of discount rate

The results of a benefit-cost analysis can be very sensitive to the discount rate used. A higher discount rate results in a lower present value for future benefits, relative to present or past benefits, than does a lower discount rate. In relation to investments, where costs precede benefits, the higher the discount rate, the less will be the estimated present value of the benefits relative to the present value of the costs.

It has been suggested that the appropriate discount rate should correspond to the actual market valuation of future consumption relative to present consumption. Such a discount rate is given by the interest rate which market participants adopt for investments and loans which entail no risk. For a number of years, the real interest rate on Australian government bonds has been about 5 per cent. This might provide a lower bound to the range of possible discount rates appropriate for use in this analysis. It has also been argued that the discount rate should incorporate a premium to account for risk; however, the extent of this risk premium is difficult to measure. Acknowledging these arguments, the Department of Finance has suggested that a discount rate of 5-10 per cent should be used in benefit- cost analysis (see Department of Finance 1991, chapter 5) .

In applications of Textabare, 5 per cent has been used as the discount rate, with a sensitivity test on the effect of using 10 per cent. The need to include a risk premium does not arise, since uncertainties can be taken into account by stochastic modelling.


Generation of Monte Carlo parameter values

The use of Monte Carlo simulation enables model outcomes to be presented as probability distributions rather than point estimates. The Monte Carlo procedure involves repeatedly running the model, each time using different parameter values for all, or a selection of, parameters, the value for each parameter being in the present instance drawn from a triangular distribution. If the Monte Carlo simulation experiment involves n runs of the model, then n random samplings from the probability distribution for each model parameter are required. Note that it is assumed here that the parameters are independently distributed.

In figure G, 81, Om and 6, are respectively the lower bound, most likely and upper bound values for the parameter under consideration. For the Monte Carlo simulations it is necessary to obtain values of 6 such that the value of the density function at 8, , f(On ), is as shown (b). This is achieved as follows.

The area of the triangle ABuI3/ is taken as unity. At the nth run, a random number U , in the uniformly distributed range [0,1] is generated. The corresponding value for the coefficient 13, is that for which the area of the triangle B&61 is U,. Below, the expression for obtaining 6, from U , is derived.

Triangular probability density function for the value of a model G - parameter ------- --

.I----- I

I f i e )

Value o f e


Since the area of the triangle ABu81 is equal to one by definition, the value of the density function at the most likely value 8,, a, is

It can be seen that

where h is the value of the density function at 8,. Substituting ((2.1) into ((2.2) for a , the following expression is obtained for h:

Above, 8,, is defined by the equality of U,, with the area of the triangle B8,,8/. Hence

(C.4) U,, = 0.5(8,, - 8, )b

By substituting (C.3) into (C.4) and rearranging, it can be shown that

This formula is applicable for values of U,, less than the area of the triangle A&,@ For values between that area and unity, the same procedure is used to obtain a slightly different formula. If U , 2 (8 , - 8 1 ) / (8 , - 8,),

References

Ball, K., Beare, S. and Harris, D. (1989), The dynamics of fibre substitution in the raw fibre market : a partial adjustment translog model. ABARE paper presented at the Conference of Economists, Economic Society of Australia, University of Adelaide, 10-1 3 July.

Deaton, A. and Muellbauer, J. (1980), Economics and Consumer Behaviour, Cambridge University Press, Cambridge.

Department of Finance (1991), Hand Book of Benefit Cost Analysis, AGPS, Canberra.

Department of Primary Industries and Energy (1989), Prospects for Further Processing of Wool in Australia, AGPS, Canberra.

Freebairn, J.W., Davis, J.S. and Edwards, G.W. (1982), 'Distribution of research gains in multistage production systems', American Journal of Agricultural Economics 64(1), 39-46.

International Wool Secretariat (1990), Wool Yarn Technologies, Textile Technology Technical Information Bulletin MP-31, Ilkley, United Kingdom.

Johnston, B., Tulpule, V., Foster, M. and Gilmour, K. (1992), The Economic Gains from Sirospun Technology, ABARE Discussion Paper 92.5, Canberra.

Lindner, R.K. and Jarrett, F.G. (1978), 'Supply shifts and the size of research benefits', American Journal ofAgricultura1 Economics 60(2), 48-58.

Mullen, J.D. and Alston, J.M. (1989), The Returns to the Australian Wool Industry fiom Investment in Research and Development, Rural and Resource Economics Report 8, New South Wales Department of Agriculture and Fisheries, Division of Rural and Resource Economics, Sydney.

-, - and Wohlgenant (1989), 'The impact of farm and processing research on the Australian wool industry', Australian Journal of Agricultural Economics 33(1), 3 2 4 7 .

Pagan, A.R. and Shannon, J.M. (1984), 'Sensitivity analysis for linearised computable general equilibrium models', in Piggott, J. and Whalley, J. (eds), New Developments in Applied General Equilibrium Modelling, Cambridge University Press, Cambridge, pp. 104-18.

Rose, R. (1980), 'Supply shifts and research benefits: comment', American Journal of Agricultural Economics 62(4), 834-7.

42 ABARE reseurch report 92.6

Taha, H.A. (1982), Operations Research: An Introduction, 3rd edn, Macmillan, New York.

Trajtenberg, M. (1989), 'The welfare analysis of product innovations, with an application to computerised tomography scanners', Journal of Political Economy 97(2), 444-79.

Varian, H.R. (1984), Micl.oeconomic Analysis, 2nd edn, Norton and Co., New York and London.

Benejits of ~ ' o o l tex-tile research 43

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