METHODS FOR VALUING COUNTRYSIDE AMENITY: AN OVERVIEW

METHODS FOR VALUING COUNTRYSIDE AMENITY 349

METHODS FOR VALUING COUNTRYSIDE AMENITY: AN OVERVIEW Trevor Young and P. Geoffrey Allen+ University of Manchester and University of Massachusetts, Amherstf

The principal methods of valuin ‘non-market’ goods are presented

advantages and disadvantages in measuring the value o the rural environment. As a general rule, when assumptions are f ewer, data requirements are greater but there may also be policy problems for which any one method is inappropriate. In particular, since countryside amenities may offer important intrinsic or non-use values, the contingent valuation technique, despite its weaknesses, may be preferred.

and reviewed in terms of their % asis in economic theory and their

Recently there has been a marked increase in the attention given to issues of environmental quality in rural areas and ‘agriculture and the environment’ has become a particularly popular theme. The topics raised in the debate include questions of whether recreational activity in the countryside should be promoted and whether farmers should be given ‘amenity payments’ for the upkeep of public paths, hedgerows etc. The implication is that society in some way benefits from these proposed changes. Yet it is also apparent that in many cases policymakers have little idea what the appropriate economic evaluation of a change in environmental quality would be. The paper is based on the premise that some quantitative information would be both a necessary and desirable input into the decision-making process in this area. Indeed, it could be argued that benefits which are not measurable may as well not exist, since in the competition for overnment funds, there will be other programmes which

In presenting the principal methods of placing a monetary value+ on ‘non- market goods’, we attempt to demonstrate where the various techniques are placed in terms of economic theory and to indicate their main advantages and disadvantages in measuring the value of the rural environment. The discussion of the probIems of valuing countryside amenity is complicated by the elusive nature of the subject-matter. In particular, although the recreational benefits (e.g., fishing and hunting) which the countryside offers may be readily discernible, the aesthetic benefits, including scenic amenity, are less so. Moreover, members of society who do not directly use countryside amenities may still benefit from their existence. The most important ‘intrinsic’ or ‘non- use’ value is perhaps option value, which refers to an individual’s willingness to

* This aper, in a somewhat altered form, was contributed to the Agricultural Economics Society, 1 9 k Conference.

t Address for correspondence: Department of Agricultural Economics, University of Manchester, Manchester M139PL.

$ Sinden and Worrell (1979) present a number of policy settings in which other indices may be as useful. For example units of time may be used instead of units of money. In other cases an index of relative value may be all that is needed.

offer measurable an % significant results.

350 TREVOR YOUNG AND P. GEOFFREY ALLEN

pay to prevent irreversible changes to environmental resources*. The researcher’s ability to measure these diverse benefits will vary with the quantitative techniques chosen.

1. Those which are based on observed market behaviour (the ‘interdependent demand’ approaches including the travel cost and hedonic pricing methods), and 2. those concerned with contingent or hypothetical valuation (where a measure of willingness to pa or willingness to accept compensation for a

Both categories are presented and criticised in turn. Some indication of their common theoretical foundation is provided but the technical details in terms of duality theory and the concept of equivalent structures are relegated to an Appendix. The various techniques yield measurements at different points in the theoretical structure and under different assumptions. As a general rule, when assumptions are fewer, data requirements are greater but there may also be policy problems for which any one method is inap ropriate. Thus the

examined will often determine the choice of technique.

The methods examined here fall into two main categories:

change in the environment is o r; tained by direct questioning).

availability of data and the types of environmental c g aracteristics to be

1. Interdependent Demand Approaches

In this section we examine methods for obtaining monetary values of changes in environmental quality which re1 on observed market behaviour, and our

the techniques most frequently adopted in this context. However, brief reference is made to a more general hedonic approach which is based on the household production function theory of demand.

main focus is on the travel cost an d hedonic pricing methodst since these are

I . 1

In the TC method, which has been widely used to estimate the demand for recreational facilities, it is assumed that the only decision variable is the number of visits made to a given site, say a fishing lake, and that the quality characteristics of the site are exogenous. The demand equation for the site is given by specifying the number of visits to the (fixed) price of return transportation and other demand shifters, such as income. The underlying utility function would be of the form u = u(v,Z,X), where v denotes the number of visits, Z represents the quality characteristics of the site and X is the set of all other commodities. The return trans rtation expenses are taken to be a proxy of the price of a visit. The estimated rrdinary) demand curve (DI) is illustrated in Figure 1. If water uality of the lake is improved, the curve shifts

The Travel Cost Method (TC)

to D, and. for the same set of 1 ouseholds. the increase in consumer sumlus indicates the willingness to ay for water quality. This will be equivalent td the differences in the value o f t E e transformation function (F) measured at the old

* Weisbrod (1964) first suggested this source of value. It arises when an individual is uncertain regarding his future demand for a good, which has no clear substitutes and which, if destroyed, could not be replaced. See Fisher and Krutilla (1985) for a discussion of the concept in connection with the presentation of wilderness ecosystems, the protection of endangered species etc.

t Hueth and Strong (1984) provide an excellent survey of these approaches when used to measure recreational benefits.

METHODS FOR VALUING COUNTRYSIDE AMENITY 35 1

and new values of utility and characteristic levels (Figure A2 in the Appendix). However the TC method avoids the need to specify explicitly the form of this function.

Price o v i s i t

(E)

Participation rate (v is i tor days)

Figure 1. Illustration of the Use of the TC Method to Value Improvement in Environmental Quality at a Recreation Site.

In addition to the assumptions already noted, the method relies on ‘weak complementarity’.* Thus the marginal value of water quality would be assumed zero for those people who did not use the lake for recreation.

Data Requirements and Empirical Examples

Data are re uired on the number of visits, the fixed price of a visit and income level. a h e r e possible, allowances should be made for the opportunity costs of travel time as well as the direct monetary costs of travel. If time costs are included in the price variable, then ‘full income’, incorporating the value of available time in the income variable, should be used. An. additional complication is that utility may not depend merely on a site visit but also on the journey itself. The effects of utility derived from travel time may however be more difficult to capturet. Finally, quality factors which are considered to

0 = 0. That is to say, when the quantity demandedof a private good is zero, the marginafut&Gor marginal demand price of Z IS zero.

au * A quality variable, Z is weakly complementary to a private good X if 7

t See,forexample, Elson(1973).


influence the level of participation at a particular site may be included in the analysis. *

Most, if not all TC studies attempt to value the ‘recreation experience’, i.e., demand relationships have been derived for hunting deer, small game and waterfowl, for fishing and for eneral outdoor recreation. For example, Gum

areas of Arizona, Shucksmith (1979) examines the demand for angling at a U.K. reservoir, and Hodge and Collins (1984) value consumer benefits from outdoor recreation at an Australian National Park. The common features of these studies are that attention is focused on recreational benefits of rural areas and that demand is being measured at a well-defined recreational site. However, for broader policy questions concerning the value of countryside amenities, the TC technique will undoubtedly prove to be inadequate. For example, if one wishes to measure the benefits of conserving the wetlands, which include saltmarsh, fresh water meadows, eat bo s and drained marshes,t the ap ropriate choice of ‘site’ is not ogvious. Even if interest centres on a spec1 P IC site, sa the Halvergate Marshes, the direct users are likely to be very few in number. Get, judging from the public debate on the subject, concern at the loss of such sites goes far beyond the im act on direct users;

underestimate the value of conservation.

and Martin (1975) deal with a1 f of the above recreational activities in different

there is a substantial intrinsic value. Most certainly the -F C analysis will then

I .2

In a number of settings, individuals can choose the level of consumption of an environmental quality throu h their choice of residential location or their

enviromental uality, and information on the demand for the non-market goods is embe 1 ded in the observed prices and consumption levels of market goods. The hedonic pricing approach has become a popular means of extracting this information.

Typically the demand function for the environmental attribute of interest is estimated through a two-stage procedure:$ (i) Regress ex enditure (E) allotted to relevant market goods on measurable characteristics PZ), including the environmental quality variable of interest. The estimated coefficients and the actual values of the characteristics for the sample are used to compute implicit marginal prices (A) for the characteristics. (ii) Regress the implicit prices on the Characteristics and other variables such as income (M).

However, the interpretation of the resultant function is not as straight- forward as some authors imply. This and other conceptual problems are considered below.

It should be noted that a more general hedonic pricing problem arises when some characteristics are partially controllable by the consumer, since the individual then becomes both the producer and consumer of the non-market good. Pursuing the fishing lake example, the angler may be assumed to * For example, Shucksmith (1979) includes the fish catch rate as an explanatory variable.

However, as noted by Hueth and Strong (1984), this may yield biased arameter estjmates if errors of measurement in the catch rate are correlated with those in the &.pendent vanable.

+ See Bury (1985). $ The ex enditure function E(P,Z) is derived from the minimisation problem: Min. E=PX s.t. Z=f(X). ?he procedure is then as follows: estimate E(P.Z) by regressing E on Z; compute the

Hedonic Pricing Approach (HP)

selection of market goods. B n these cases there is an implicit market in

implicit prices as Ai = ,E ; and regress A on Z and M . d Z.

METHODS FOR VALUTNGCOUJVTRYSIDE AMENJTY 353

produce and consume the fish catch rate. Fishin trips are produced by combining transportation goods and travel time; ash catch is produced by combining purchased fishing equipment and fishing time, given the 'state of technology', including the enwronmental characteristics of the site and the experience of the angler. This will be recognised as an example of the household production funtion (HPF) approach. However, given the data requirements of this method*, little empirical work has been undertaken to date.

Data Requirements and Empirical Examples The HP technique relies on the ability of the researcher to identify a set of

market goods, expenditure on which may be reasonably assumed to embody the value placed on the environmental quality of interest. Hence in a number of studies of public goods and bads (e.g., air pollution and noise), the dependent variable in the first stage regression is housing ex enditure or house prices and

age, heating system etc.) and locational attributes, which would ty ically include a measure of the environmental quality in the resi 1 ential neighbourhood. Whereas property values might be used as data in the study of the demand for some recreation sites, it would seem more appropriate to obtain data on expenditure on the recreational activity itself and to regress this on whatever measureable characteristics of the recreation site which can be found (e.g., catch rates at a fishing lake). Assuming that a relevant expenditure function can be generated in the first stage, the second stage of the procedure requires some data on the socio-economic characteristics of the individuals, and on income level in particular.

The HP method, using roperty values as the dependent variable, has been

the technique to validate their contingent valuation results on the value of air quality. Nelson (1981) claims to have measured the extent to which noise nuisance from six U.S. airports is ca italised in property values. On the other

satisfactory results with the method. An example of the measurement of recreation values using house prices or

rental values is provided by Wilman (1981). One of the very few studies of recreational activities, which use data on recreators' expenditure within a Hp framework, is McConnell(1979).t

For the HP method to be of use in the valuation of countryside amenities, a set of market goods, which might embody the value of environmental quality, must be identified. To some degree conservation of rural amenities may enhance property values; for example the upkeep of woodlands ma provide opportunities for timber production, s ort and recreation. On the ot B er hand,

activities more difficult and so would lower the value of the farm as a production unit. It is unlikely therefore that property values could be used a reliable data base for this purpose. An alternative may be to take expenditure by recreators (hunters, anglers, hikers) as the dependent variable but the drawback here is that, as with the TC method, only the benefits to direct users are being measured. There is no obvious set of market goods which would embody the necessary information to value benefits beyond those enjoyed by recreators. In articular, there is no way that an individual's option value on an

the regressors are the structural characteristics o P the house (number of rooms,

widely adopted in the stu 1 y of non-market goods. Brookshire et a1 (1979) use

hand, Willis and Foster (1983), in t fl eir study of water quality, fail to obtain

the presence of woodlands, ponds an if hedgerows may make general farming

environmenta P good can be expressed in the marketplace. Namely, a cost function for the angler must be estimated.

+ In fact McConnell's work provides an example of the more general HPF approach.


1.3 Criticism of Demand Interdependent Approaches In this section we concentrate on the conceptual difficulties, and in particular the identification problem, which are inherent in the interdependent demand approaches. A number of other criticisms have been raised in the literature (e .g.. , the assumption that individuals can perceive differences in enwonmental quality has been uestioned) but many of these a ply equally to

assumptions can be shown to be untenable, their rejection would vitiate all quantitative analysis. Here we restrict attention to those criticisms which relate specifically to the analysis of non-market goods.

The first step of the HP technique establishes a schedule of marginal implicit prices of characteristics. In fact, it traces out the locus of equilibrium points which are like1 to be the result of the intersection of demand and supply

for a moment, each of the two households shown in Figure 2a is in equiEbrium where the slope of the indifference curve (i.e., the marginal willingness to ay) is equal to the marginal implicit price of the environmental characteristic, i. A regression of expenditures on the levels of characteristic would yield the locus of these points but reveal little about the underlying functions which generate it. Taking derivatives of the households’ indifference curves with respect to the characteristics provides a set of inverse corn ensated demand curves, depicting the relationship between the marginal imptcit price of the characteristic and the consumption of it, at constant utility. These are shown in Figure 2b. However, the identification of these demand curves requires consideration of the supply side. In principle, we can think of aset of firms producing the market oods which embody the characteristic of interest at different locations. These

arms ma have different cost functions, profit levels, managerial ability and so

a locus of equilibrium points which we are observing and it will represent a transformation function only in the unlikely situation where consumers have identical utility functions and income. If there is a distribution of producers and a distribution of consumers, the expenditure-quantity observations trace out tangency points between cost functions and transformation functions. This case requires a carefully specified simultaneous model, if the conditions for identification are to be met.

It should be noted that the device of assuming that supply of a characteristic is perfectly inelastic with respect to price (e.g., Harrison and Rubinfeld (1978)) does not make the problem more tractable. Since equilibrium price must be different at each location in order to generate different observations on the demand function, and since it is unobservable directly, it can only come from some specification of the production technology and so again a simultaneous equation system must be adopted.

Finally, in much of the literature on estimating characteristic demand functions, it appears that considerable effort has been devoted to the estimation of an identity. Brookshire et a1 ex ress some concern about the

which estimates individual hedonic pnces on the basis of individual characteristics demands, and then turns around to estimate demand curves using the same information. This procedure seems somewhat circular . . . ’ (1979, p.12). In fact, it is. No new information can be obtained in the second stage.? An analogy would be to estimate a production function, compute input * Criticism of the approaches appear in Freeman (1979), Harris (1981) and Maler (1974), among

f See Brown and Rosen (1982).

studies of market and non-mar % et goods.* While it may we1 P be that such

forces. The pro r, lem is illustrated in Figures 2a and 2b. Ignoring the sup ly side

forth an dy thus there would exist a set of supply or offer functions, Si. Again, it is

usual two-stage procedure: ‘there is some appre ! ension with respect to the step

others.

METHODS FOR VALUING COUNTRYSIDE AMENTTY

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Figure 2. The Identiflation Problem

356 TREVORYOUNG ANDP.GEOFFREY ALLEN

combinations for a given output, then estimate an isoquant from the constructed input combinations. The is0 uant is already an identity and

information on the production technology is obtained. although it may be ‘estimated’ by means o 9 a simpler function, no additional

2. Contingent Valuation (CV)

With the CV method, the consumer provides direct evaluations of a (small) change in one characteristic (or quality of an activity), where the initial level of utility is maintained and market prices, together with the levels of all other characteristics, are held constant. Thus, it is hoped, direct questioning will provide a measure of contingent willingness to give up income for a change in quality, ceterisparibus.

If M denotes income and Z, the characteristic of interest, the income change necessary to offset a change in environmental quality would be given* as

dM

Alternatively, as different levels of the characteristic are hypothesised, the responses may be interpreted as changes in a transformation function, F(u,Z). The analysis thus provides an indifference curve between income (or all other goods or changes in the value of F) and a selected characteristic. In the literature this indifference surface is also referred to as the bid function (Rosen, 1974), total value curve (Brookshire et af, 1980) and income compensation function (Randall and Stoll, 1980).

-. - dZl

Data Requirements and Empirical Examples CV studies are based on the data rovided by a survey of responses of

economic agents to contingencies put E efore them. The hypothetical market setting must be defined in substantial detail, providing the consumer with information on alternative levels, location and time-dimensions of the characteristics in question, as well as on the institutional arrangements. The respondent is then invited to react to prices posed by the interviewer, indicating whether he would pay the price or go without the good in question; the price is varied iteratively. In addition to the ‘bids’ which are elicited in the various hypothetical situations, a large amount of socio-economic data on the respondent is typically required.

A good indication of the type of em irical work which has been undertaken using the CV method is provided by f chulze et a1 (1981), who review several CV studies. A number of experiments were designed to value the aesthetic benefits of abatement of environmental dama e resulting from coal strip mines, electric-generating plants and geotherma f developments. In addition, CV was used to value recreators’ willingness to pay for ‘encounters’ with various types of wildlife, and Los Angeles residents’ willingness to pay for better air quality.

Figure 3 illustrates the type of information which is forthcoming from these studies. Here, monthly rent on housing is plotted against air quality; if people

refer clean air, rents will rise across a region as air quality improves. Pndividual households with different preferences with respect to air quality will locate at different points along this rent gradient. Two households are depicted * See Brookshire eral, (1979)

METHODSFORVAI.UING COUNTRYSIDE AMENITY 357

here. Household A prefers low rent, oor air quality; household B prefers

willing to pay for an increase in air quality from A, to A2, the answer should be f W per month. However, the rent differential between these households would be fD/month. The difference arises because we are considering a non- marginal change in the environmental uality. The HP approach may then

clean air at a higher rent. If househol 8 B is asked the maximum it would be

over-estimate society’s willingness to pay 9 or this type of change.*

Air Quality

A1 *2

Figure3. The CV and HP Estimates of Willingness to Pay

2. I The direct questioning of economic agents is often criticised as a method of valuing non-market goods because of the biases which may be inherent in the approach. The principal sources of bias are as follows:t

(i) Strategic. If the respondent believes that others may bear the cost of any actual change in environmental quality, willingness to pay for the change may be overstated. On the other hand, if the respondent suspects that he may be taxed by the amount of his stated willingness to pay, then the incentive would be to understate his true preferences. Thus the survey analyst may be confronted with the ‘free rider’ problem.

(ii) Znfornzation. Since contingent valuation is by its nature a hy othetical

knowledge gained through past experience, as well as of observed prices and

Criticisms of the C . V . Approach

exercise, survey responses will ty ically not be based on the same in f ormation as real market activity. Actua P market behaviour takes account of the

* See Brookshire era/ (1 979). t This list follows Schulze er a1 (1981). where further details, including some indication of their

relative importance, may be found.

3% TREVORYOUNG ANDP. GEOFFREY ALLEN

substitution possibilities. The market which is described to the survey respondent may be a poor reflection of the situation if the proposed change in environmental quality were actually to take lace. Moreover, it may not be

(iii) Hypothetical. Related to information bias is hypothetical bias, whereby the interviewer may only elicit hypothetical answers to h pothetical questions.

and judge it to be feasible but also he must believe that his answers will have a bearing on the probability and magnitude of the change in the environment. (iv) Insfrument. The respondent's valuation may depend on the proposed means of payment (the one which offers the reater substitution possibilities

(which may suggest the level of an 'appropriate' bid). There is an additional problem which has only recently been recognised.* It

may be argued that respondents have a mental bud et for non-market goods

possibiy dramatic, environmental change, they may offer their whole 'environment account'. However then they are reminded that there are other environmental goods which they may also value, a different budget allocation may be made. It is then the task of the survey designer to make explicit this kind of budgetary consideration.

In defence of the CV method, Brookshire et al(1979) argue that as a means of valuing non-market goods it may accord more closely with the conditions of economic theory and that the ap roach can also deal with phenomena which lie

will prove useful in cases where it is too costly or difficult to obtain data on actual market behaviour. Moreover, the analysis need not be restricted to direct users of a non-market good and so the technique offers a means. of obtaining some measure of the more elusive, intrinsic values, such as option value. This may be its most important advantage in the analysis of countryside amenities.

Nevertheless, the degree of accuracy of the empirical results is an obvious concern. Bishop and Heberlein (1979) compared survey methods with the results of actual market creation and found a marked divergence.? Moreover, although CV results when compared with hedonic price estimates lie within theoretical bounds,$ this is a very weak test of their accuracy.

Summary The various methods of estimating non-market goods have a common theoretic basis and provide measurements at different points in the consumption technology and under different assumptions. Table 1 summarises the main elements of the methods presented here. As with most quantitative analysis, when assumptions are fewer, data requirements are greater and so the availability of data may determine the choice of techni ue. However, the

will vary in their ability to address particular policy questions. The HP method is most readily suitable where the value of an environmental

quality is likely to be embodied in data on market variables. For example, See Kneese (1 985).

t In a study of goose hunting permit holders, Bishop and Heberlein calculated an average willingness to sell permits of $63. when actual cash offers were made, compared to a value of $101, when hypotheticaloffers were made.

$ Survey responses of willingness to pa in theory will be bounded below by zero and above by rent (expenditure) differentia1sderiveb;rorn the estimated rent gradient.

clear toeither the respondent or interviewer w R at is really being held constant.

To avoid this, the respondent must not only understan dy the proposed change

being preferred) and the starting-point at whic t the bidding process is initiated

including environmental quality. If then they are as f ed to value a particular,

outside historical experience. 1p here are additional virtues. The CV method

nature of the policy setting will also have a bearing on the c 1 oice; the methods

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property,yalues in cities may reflect air quality, proximity to city parks, or noise levels. It is rather less convenient, althou h still quite feasible, to apply the

areas, such as country walks, fishing, shooting etc. In this case, the users of the facilities ‘must be surveyed to obtain the necessary data on expenditures. If some characteristics of the recreational site are under the control of the individual (i.e., endogenous to the system), then the production side of the users’ activities must be taken into account. But in any event, the incorporation of demand and supply factors within a simultaneous system may be required in order to overcome the identification problem. Where consumers are not able to influence the quantity of a characteristic but must treat it as exogenous and where the characteristic can be linked to the expenditure on visiting a specific site, the travel cost method may be used. In this case, an ordinary demand function for users, or sometimes the ‘representative consumer’, is specified and estimated.

We would conclude that for policy questions concerning rural amenities for which an estimate of the value of recreational benefits is required, the HP and TC methods would be appropriate techniques. However, when addressing broader policy issues, such as the conservation of woodlands and wetlands, both methods will be inadequate. This is because they only capture benefits accruing to direct usersof an environment good. If there are significant benefits to members of society who do not directly participate in rural pursuits then both methods would understate the value of the countryside. Furthermore, the interdependent demand methods are based on current or historical market data. They are incapable of valuing a change in environmental quality which may take place at a future date. Thus, where the researcher is dealing with an environmental change which is outside historical experience or which confers considerable indirect benefits, the CV method is more suitable.

It must however be stressed that amongst economists there is controversy over the accuracy and reliability of the contingent valuation method of obtaining monetary estimates of environmental quality. S ecifically, there is

understands the hypothesis and forms the same considered judgement as if faced with phenomenon in reality. The few studies which have been able to compare hypothetical and simulated markets do not promote confidence in this assumption. Unless the CV survey is remarkably well designed, it is likely to produce biased estimates of the value of the countryside. The quantitative exercise can then only be justified if the expected deviation of the estimated valuation is more acceptable than complete ignorance.

technique to the measurement of the bene F its of recreational activities in rural

concern about a key assumption of the analysis, namely t t: at the respondent

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ME’IHODS FOR VALUlNG COUhTRYSIDE AMENfTY 361

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APPENDIX

Duality theory and the concept of equivalent structures for producer or consumer technologies provide a convenient means of illustratin the connections among the methods of valuing non- market goods. Fi ure A I depicts some 0'9 the principal dualit relationships in production and demand theory. 3 e roduction function (0): profit function (T!, and the cost function (C) are the most frequently usefin determinin optimisinp behaviour in production. Here the set of output variables Z command rices denote! by A; the inputs in the production process. X. are associated with aset of prices, P. &e transformation function (G)can be defined as the maximum amount of a commodit Z,, which can be produced given the amounts of the other commodities and the levels of input (& inversion of this function yields the production function. The indirect production function (a), which measures the maximum output produced for a given input price and expenditure is not normally of interest. However. when the analysis concerns a household which is the consumer ofconventional inputs (X) and the producer of item (Z) ielding utility, as in the HPF model, the cost constrained indirect production function is immediate6 applicable.

On the demand side, a set of functions equivalent to 0, C. G and W may be defined. These are the utility function (U). the expenditure function (E), the transformation function (F) and the indirect utility function (V). It is important to note that, whereas U and V are measured in arbitrary units of consumer satisfaction, E and Fare measured on a monetary scale. The latter are therefore appropriate starting points for willingness to pay and consumers' surplus calculations.

Figure A2 takes the diagramatic analysis a stage further by illustrating the derivations of demand and supply functions of various types, as well as the way in which the production and consumption schemes can be inter-connected. Specifically, when the parameters of the consumers' utility function are inte reted as characteristics, the direct and inverse ordina and compensated demand functionsTor they characteristics would be derived from the U, V, gand F functions, as shown.* Similarly. the cost-minimising and profit maximising input demand and output supply functions are denved for the roducer, who creates characteristics, 2. from market commodities, X. However, while commo&y prices, P. are known as data, the characteristics' prices X. are unobservable. This problemt arises in both the HPF approach and in the product differentiation framework (Rosen. 1974). In the latter the marketed good (e.g., a house) consists of a bundle of characteristics ackaged by a roducer and incapable of being repackaged by the consumer. The expenditure-Zobservationskrm the locusof intersection ofeither CorG with either Eor F.

In the CV approach. direct evaluations of the transformation function, F. are made for constant utility and fixed levels of all characteristics exce t the one of interest. The derivative of the transformation function with res ct to the iph characteristic, Zi.is the r i c e dependent compensated demand function for f If this function can be computed it provi es an alternative and indirect method of obtaining the theoretically correct Hicksian measures of consumer welfare.

The demand functions are obtained by differentiation and application of Wold's, Roy's,

t See Deaton and Muellbauer (1980). Hotelling's and Shephard's theorems respectively. See Blackorby cc uf (1 978).

METHODS FOR VALUING COUNTRYSIDE AMENITY 363

Production Fn. I n d i r e c t Production Fn.

W(P,CI

/ Profit Fn.

I

N

I r

Transform a t i o n Fn. C o s t Fn.

DEMAND

u t i l i t y Fn. I n d i r e c t Utility Fn.

Figure A l . Duality Relationsin Productlon and Consumption.


Figure AZ. Connections Among the Methodsot Valuing Non-Market Goods.

METHODS FOR VALUING COUNTRYSIDE AMENITY: AN OVERVIEW

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