Expansion in French total agricultural output over the last four decades has been accompanied by an equally, if not more, significant increase in France's trade for agri-food products. Thus, the volume of French agri-food exports increased more thart six-fold between 1961 and 1990 (Monceau, 1995). France which was a net irnporter of food products in the sixties became a net exporter in 1970. This net exporting position in agri-food products was steadily consolidated over the 70's and 80's so that France is now the second world exporter of agri- food products behind the USA and before Netherlands.

Although French imports of agri-food products did not experience the same expansion as agri- tbod exports during the same period, they have steadily increased to reach in value terms 150 billion french francs in 1994, among which 213 represented irnport shipments of processed tbod products. Such a pattern is not surprising and is associated with a gradual integration of the EU agri-food sectors, and the development of intra-trade in this kind of products (Chevassus- Lozzaand Gallezot, 1993;[START_REF] De Frahan | Le commerce intra-branche dans I'industrie agrorlimentaire européenne: une nouvelle forme de globalisation[END_REF]. French imports of agri-food products originating from the rest of the EU are now representing about 70o of the total. Given this situation, it is interesting to know how the various competing import supplies of a given agri- food product interact between each other but also with the production of home-produced agri- food products.

The objective of this paper is to explain the patterns of imports and home-produced supplies for raw and processed agricultural products, using a differentiated product model. For this purpose, we propose a generalization of the Armington model based on an homogenous, indirect and implicitly additive structure of consumer preferences from which demand for imported and home-produced products are derived. Its empirical implementation is facilitated by the use of an homogenous 'Constant Difference of Elasticities' (CDE) functional form developed by [START_REF] Hanoch | Production and demand models with direct or indirect implict additivity[END_REF]. Relative to the Annington model, this proposed differentiated product model offers the advantage of computing varying elasticities of substitution among sources of import and domestic supplies. rilhen estimated econometrically, the CDE functionai form must satisfu certain conditions (in the form of inequality restrictions on its parameters) to be globally or locally valid over its regularity donrain. If conventional econometric estimation techniques were used, these conditions are not imposed and are usually tested "ex-post". On the other hand, in order to I ensure that the estimated parameters of the CDE function are globally or locally valid, constrained estimation techniques similar to those developped by Shumway et al. (1990) or Hlazilla and Kopp (1986) for flexible functional forms could have been applierl. We did not follow this route in estimating the CDE functions but rather leant towarcls an another alternative bayesian-like approach developed by Geweke (1988, 1989). In fact, imposing inequality constraints on parameters can be viewed as supplying prior information before we proceed to the econometric estimation of the functional form with a data sample, and then to infer the posterior distribution of the parameters. Such an estimation strategy which has been employed recently by Chalfant et al. (1991), Hayes et at. (1990), and Tifiin and Moxey (Igg2) for input and consumer demand and output supply systems derived form flexible functional forms has never been applied to agricultural trade modelling. It is also our intent to fill this gap by adapting the Geweke's procedure to the estimation of CDE demand functions.

The rest of the paper is structured in the following manner. The next section develops the conceptual model used to explain the imports and home supplies of goods. The estimable version of this model is also presented in this section. This is then followed in section 3 by a presentation and explanation of the bayesian estimation procedure employed in this study. In section 4, we report and discuss econometric results for twenty six agri-food products consumed in France, using annual data fronr 1977 to 1994. Concluding remarks are provided in the last section.

-Conceptual and empirical models

The proposed differentiated product model framework retains two essential characteristics from the Armington specification. First, we distinguish commodities that are differentiated by kind as "goods" and "goods" that are differentiated by origin as "products". Second, we assume that the utility function is homogenously and weakly separable. This proposed framework is however more general than the Armington model in the sense that we allow for imperfect substitution between various import and domestic sources of a given commodity but we also make the following additional asumptions: (i) varying elasticities between any two products of a good in a given market; (ii) distinct elasticities of substitution between any two pairs of products in a given market; and (iii) imports and domestic production are viewed as final good supplies entering the decision process of the consumers.

Given these assumptions, it is then possible to define a direct, homogenously and weakly separable consumer preference structure where each good qi for i: 1,2...,n canbe supplied by a set of m geographically differentiated products 4;,, from ,r: I.2,. ... m. The products Qi, can be ordered into a set of n separable and mutually-exclusive groups. The utility function corresponding to this separable structure is homogenously weakly separable and is defined as follows:

Utql : U [vr(q,,,8]2,...c|tu), tz(Q2t,822,'..Qzr),..., ttn(4nt,Qn2,...Qr)J tl ] where v,(.) are viewed as homogenous sub-utility functions which depend upon a set of geographically differentiated products qir. Linear homogeneity of the sub-utility functions also implies that q, = vi(.) . (lt.l and v,(.) satisfy the usual conditions of monotonicity, quasi- concavity and differentiability. Due to the linear homogeneity of the sub-utility functions v,(.) ' it is possible to derive subgroup conditional demands of the form, for all s belonging to group q,,1 8, : g,[ P,,J 'for s = ]' ' m and i =l' "'tt l2l

The optimizationprocedure behind the utility function [ ] may be viewed as occuring in two stages. The consumer determines first the product aggregates of each good I subject to an income constraint and then allocates them among competing suppliers. Because the utility function is homogenously separable, we can define aggregate price indices p; which depend upon eachp;" through an explicit price function. In the Armington model, these price functions are represented by CES price aggregators of all import source prices.

The proposed differentiated product model expresses these prices functions (indices) in an implicitly additive fashion through the use of a CDE functional form. Hence implicit CDE price functions are defined and expressed as: iï,,(p,,,p)=f B,,r,,'u =l t3 l .r=l s= I where each I1;" is approximated by a cDE functional form, 21" is the product price pi* normalized bythe aggregate price of good i. In [3.], ^Bi, is called the distribution parameter. ô;s or dir=l-b,, arethe price parameters.a,, is also called the substitution parameter. The CDE price function is globally valid if 4, t 0, b,, .1, and either 4, < 0 for all s or 0 tb," tl for all s (Hanoch, Lg75, p all). Weaker conditions can be obtained and consist of (i) one b,, > | ancl (ii) some.B,, and ô;, being of different signs. By applying Roy's identity, we derive the CDE demands for various (import and domestic) supplies: The subscript i is now omitted for reasons of convenience.

Allen elasticities of substitution can be derived using the following expression:

.,st: d.,,* o,-tso ao -6.,,L k=t S" tsl where ô", is the Kroenecker sign equal to I for s : / and 0 elsewhere.

From expressions [4.] and [5.] it can be seen that the Armington model characterized by a constant elasticity of substitution o can be derived by setting all the â., equal to a constant â. The elasticity of substition o is then equal to a = lb .

The system of demand share equations formed by expression [3.] and with stochastic residuals /-r5 could be estimated by an appropriate systern estimation technique such as iterative seemingly unrelated estimation (ITSUR) or maximum lilkelihood (N/L) approach, which takes into account the adding up conditions associated with the budget shares ( S, ). However, due to the highly nonlinear structure of the CDE demand equations, it is probable that non convergent and/or local optimum estimation solutions will occur. Furtherrnore, the existence of a right hand side endogenous variable implies a simultaneous estimation bias problem that needs to be taken into consideration. One way to overcome the nonlinearity of the CDE dernand equations is to linearize and transform all of them in a log-ratio fonnr. Then, iterative three stage least squares estimation is applied to this new sytem of linearized CDE dernand equations in order to ensure that, first, the estimated parameters are invariant with respect to the share equation dropped, and second, that the simultaneity bias problenr is taken into account.

As it will be explained later, the above estirnation procedure is not feasible in our study because the bayesian estimation procedure that we are using requires all the explanatory variables in'the CDE share equation system to be exogenous. As a result. we adopt a two-step approach to estimate the parameters of the CDE demand equations. First, the system of log- linearized CDE demand equations is transformed in first differences. Therefore, the explanatory variables are expressed in a rate of variation form. We approximate the rate of variation of the price aggregator p by a Stone's geometric price index of all import and domestic sources. This transformation is justified through a total differentiation and a rearrangement of the implicit CDE price function. To show this, let us differentiate expression [3.] and express dp/p as a function of all thep". 'fhe rate of change dptp is then given by: I This transformation which was first suggested b1, Theil to estinlate nultinomial logit model and then used by Rossi for system of cost share equations eusures that the estinrated shares are ahval,s positive and smaller tlmn one. Consequently, the utonotonicity conditions are aulonraticalh, satisfied, Froln an econonretric estimation perspective. it means that the stoclnstic residual p,.' follou's a logistic distribulion. 16l P'

Then, substituting dp/p in the first-difference, log-linearized CDE equations yields the final estimable econometric model specification (which we designate LA-CDEH): t' =b,dp' -b*fu+(b^-b,Ni,t,*>+e, fors= 1,' "m-1 U l !' -P' "-P' s=l Pt where dy I y = (dS, / S',) -(dS^ I S^); d(.) designates the symbol "first-difference"; and e, is a vector of stochastic residuals which follows a multivariate normal distribution with zero means and a variance/covariance matrix E . Note that in expressing the CDE demand share equations in first difference, the parameters .8, vanish and are not identifiable. It is also worth pointing that this two-stage estimation of the CDEH demand equations is somewhat similar in spirit to the estimation procedure of the LA-AIDS model within which the aggregate translog price index (common to all AIDS share equations) is replaced by a Stone's geometric price index. It differs however from the LA-AIDS approach in the sense that the CDE demand equations are expressed in first differences2.

-Econometric imPlementation

Given the proposed empirical model, the objective is to obtain bayesian estimates of the parameters à, incorporating (global or local) vailidity conditions. This section describes the bayesian estimation procedure used to estimate the coefficients â, and explains a practical method to generate posterior distributions that satisfy the validity conditions of the CDE function.

-Bayesian approach

Bayesian estimation consists of combining prior information (prior density functions) with sample information (sample likelihood function) to obtain a posterior density of the parameters. prior information that can be used for the parameters can be either informative (based on existing data or knowledge of the phenomen under study by the investigator) or non- informative or diffuse. In the former case, a prior density function can be well defined and incorporated into the bayesian approach. In the latter, diffuse priors are characteized by a flat 2 This link with the LA-AIDS approach justifies the use of the acronym LA-CDEH for the above estimable density function approximated by a constant. In this study, we assume that prior information is diffirse, consisting of validity conditions imposed on the LA-CDE model. This means that in either cases -local or global validity conditions3 -the vector of parameters (â) will satis$ the inequality constraints defined earlier. We also consider that this prior information on the parameters à is known with certainty, so that a prior density function can be defined by a single Its implementation is only feasible in simple cases where the number of parameters is scant (in general no more than three). Beyond this, it is impossible to integrate expression [0.]

analytically, and we must have recourse to Monte Carlo integration procedures.

3,2 Monte Carlo integration with importance sanryling At first glance, the most logical way to use Monte Carlo integration to approximate expression [0.] is to draw a large number of random drawings from the posterior distribution and then take the sample means as a "proxy" for E(b). To find a posterior distribution of à consistent 3 It should be reminded that there is no need to worry about monotonicity conditions since they are built in the empirical CDEH specification.

a It should be pointed out that several estimates ofâ can be fonned, depending upon the investigator's objective function (see Chalfant et al., 1991, p. 479).In our case. the adoption of the means of the posterior distribution implicitly implies that the loss function is quadratic. Then. the mean of the posterior distribution for ô minimizes the expectec loss.

with the (global or local) validity conditions, we would only retain the replications for which such conditions are satisifed and then compute the means of the parameters ô. In so doing, these "restricted" means approximate the truncated posterior density function defined by expression [0.].

In cases where random numbers cannot be easily generated from the posterior distribution, it is possible to use Monte Carlo integration techniques with importance sampling. This alternative procedure involves drawing from a density function known as the importance function and then taking weighted averages across draws. Put more formally, consider g(à) to be the importance function, from which random numbers are generated. Assume that the à1 is the ith random draw from 3(à) and w, = f (b,ly) I s@,). Then, the weighted means can be shown to approximate the integral appearing in expression [10.]: b=E(b)=luab r^ (blv) gR (blyydb

s^ (blv) ë, f ^(!,iD L"(k) fR çrrrrll) l.f o (h,r,lv) È, { çn r'" [11 ]
where f R and gR arethetruncated posterior density functions, ô1p, is a draw of parameter à for which the validity conditions hold, and n is the number of draws for which the validity conditions hold.

At the same time as the means is generated, it is possible to compute other relevant indicators'

The frrst one is the probability that the validity conditions are satisfied. This probability is given by the following expression:

7R lt rrrll) u2l
where .ôrr is the total number of draws. Another useful indicator is the variance (and then the standard deviation) of the posterior distribution which is obtained by taking the estimated variance of the posterior distribution. The latter is computed taking into account the importance density function.

,. yR lbrrrll) ?='rre,r',lrl i,(n,r,-îf ## Finally, to check whether the selected importance density function behaves well, the numerical standard error (nse) proposed by Geweke (1989) can be used for the indicators previously defined. The numerical standard error is given by the following formula.

t/2 f=,'o'o' -n)'( f (brr g@G)t) ,2,rffi, lv) 2 ) nse(b) = ll4 l a
In our case of estimating the LA-CDEH, the method of Monte Carlo integration with importance sampling is welljustified because the posterior distribution of the parameters à has a complex form, thus hindering to generate a well behaved truncated density function through simulation. To show this, the results obtained by Zellner for a set of regression equations is applied to the parameters ô of the LA-CDEH. Assuming diffuse priors for ô and X, the resulting posterior density function for h is given by: .f (r'lù nltl-''' tl5 l where ae denotes "is proportional to", Z is the number of observations and A is a matrix of size m-l by n-l formed by the following elements: aii =feiçb)'e,(b)J where e,(â) is the vector of residuals for the tth CDEH equation Although the above posterior density function is "unfamiliar", it is much easier to work with than the corresponding posterior probability distribution associated with an estimable CDEH model expressed in levels. In this latter case, the CDE demand equations include a right hand side (RHS) endogenous variable (i.e. the price aggregator p) which should be accounted for.

To incorporate this RHS variable in the bayesian estimation of the parameters of the CDE model specification expressed in level form would have required to undertake a full system analysis of the CDE model including the demand equations and the CDE implicit price function given by expression[3.], This would have resulted in a highly nonlinear model structure from which it would have been impossible to generate a posterior distribution of the parameters.

Furthermore, a review of the literature on bayesian econometrics reveals that, apart from Zellner's study of systems of linear simultaneous equations which derives the posterior distributions of the parameters5, no work has been conducted over the last two decades on the bayesian estimation of nonlinear simultaneous equations. Given this situation, we had side- stepped this simultaneity bias problem by exogenizing the price aggregator and then by expressing the CDE demand functions in first difference form'

-Estimalion strategt

To implement Monte Carlo integration with importance sampling for the parameters of the LA-CDEH model, we follow closely the multi-step procedure proposed by Chaffant et al (1991). First the system of LA-CDEH demand equations given by expression [7.] and estimated by ITSUR estimation method produces estimates 6 and its variance/covariance matrix V(b) . Then, the random draws for the parameters ô are generated with the importance density function which is assumed to follow a multivariate Student-l distribution. The random number generator used for the Êdistribution is based on random drawings from the multivariate normal distribution which are then adjusted to the Êdistribution using the various relationships existing between the normal, chi-squared and Student Êdistributions. This procedure suggested by Van Dijk and [START_REF] Van Dijk | Further experience in Bayesian analysis using Monte Carlo integration[END_REF] included several steps which are easily implementable. To expand the number of drawings and also to improve convergence (Geweke, 1988), antithetic replications are also obtained and included into the bayesian estimation procedure. Once the random drawings for the parameters b have been generated, the corresponding values of the posterior density functions fl) are computed using expression [1.]. The third step of the estimation procedure consists of checking whether each replication satisfies the global or local validity conditions. Then, the means and the variance of the posterior distributions and the assoicated probability distributions for which validity conditions hold are estimated using expressions [12.] and [13.]. Finally,n.s.e. of the estimated parameters 6are derived to check the accuracy and the stability of the econometric results.

-Application to France

The generalized Armingon model developed in the previous section is estimated for import and home produced supplies of agri-food goods in France. For each of the goods considered, 5 Even in Zellner's case, the posterior distribution frtnction of tlte stnrcutural parameters is even more "unfamiliar" than the one found for a set of regressiotl equatiotts.

we distinguish three sources of competing supplies, namely imports fiom the Rest of the EU (.rl) and from the Rest of the World (RoW) (.r:2) and consumption of home-produced products (t-3). A time trend is also incorporated to capture non-price effects. The empirical CDEH demand specification (expressed in first differences) that will be used with the French data has the following form: t,_o, where l" is a constant term standing for the autonomous effect of the trend variable. Data for all the dependent and explanatory variables are available on an annual basis over the period 1977-1994 and are all expressed in rate of variation. The rate of change for the Stone's 6 There are respectively 30 and 50 raw agricultural and food processed products in tlre NAP 600 nomenclature. l0 geometric price index was computed using an arithmetic average of current and past year budget shares.

-Econometrùc results

Table I reports results on the structure of consumer preferences, including results obtained with the conventional econometric approach on the one hand, and those based on the bayesian approach on the other hand. Tables 2 and3 give the associated parameter estimates of the generalized Armington model under the three assumptions: the unrestricted case, the global validity case, and the local validity case. With the traditional econometric (unrestricted) estimation, global validity conditions are satisfied for only three products, and local validity conditions for eight products (column (2) of Table l). For the other products, estimated parameters should not lead to any interpretation, due to the non-validity of the demand equations. This can be seen through the signs of Allen partial elasticities of substitution (columns (3) to ( 5) of Table l).

(insert Table I)

(insert Tables 2 and3)

These difficulties to interpret substituability and complementarity relationships among the various import and home-produced sources can be overcome by using results of the bayesian approach, which imposes local or global validity conditions on the parameters. First, it can be seen (column (6)) that the posterior probability for the global validity is frequently small, except for products such as "flowers and plants" (16%), "milk industry by-products" (23oÂ), "baby food and dietetic foods" (15%), "brandies" (63Yo), "wine aperitives" (15%), and "fruit and vegetable juices" (21%). Nevertheless, it can be noticed that the posterior probability for global or local validity is greater than 30o for about two-thirds of the set of agri-food products (this probability is greater than 20o for 85% of the products). Moreover, the standard deviations computed for these posterior probabilities are always very smallT, and such a finding ensures the robustness and the stability of derived results.

The examination of posterior probabilities on the signs of Allen elasticities of substitution under the global validity restriction (columns (7) to (l l) of Table 1) gives the following information on the substituability relationships among sources:

7 These stândard deviations are not reported in Table I dtle 1o lack ofspace. ll -The posterior probability that there exists at least one complementarity relationship between two sources is generally small (see cotumn (8) of Table l). Cases where the posterior probability that all Allen elasticities are positive is greater than 50oÂ, are the most common (see column ( 7) of Table l). Exceptions are for "canned vegetables", "prepared feed", "coffee, tea and other herbs", "soup mixes", and "brandies". In all these cases, the complementarity occurs between French products and imports from the Rest of the EU.

Conditionnally upon the existence of at least one complementarity relationship among sources (columns (9) to (l l) of Table 1), this complementarity can be characterized as follows:

-The elasticity of substitution is negative with a high posterior probability, between imports from the Rest of the EU and imports from the RoW for all raw agricultural products, except:

"fresh vegetables" and "dried vegetables", and for all processed food products, except: "canned fruit and jam" and "fruit and vegetable juices".

-The elasticity of substitution is never negative, with a significant posterior probability, between imports from the Rest of EU and home-produced products, for any product.

-The elasticity of substitution is significantly negative between imports from the RoW and home-produced products for only one product among processed food products ("fruit and vegetable juices").

As a result, imposing global validity conditions on the CDEH demand equations in the case where at least one complementarity relationship occurs, allows us to conclude to a high tendency to complementarity between the two kinds of imports (from the Rest of the EU and from the RoW) for a very large majority of goods. Otherwise, substituability is the rule between French products and imports from the Rest of the EU on the one hand, and between

French products and imports from the RoW on the other hand. Such a result clearly runs counter the "preference communautaire "s.

The objectives of this paper are two-fold. First, we develop an alternative product differentiation model which is more general than the Armington specification. econd, we propose the use of bayesian estimation procedures in agricultural trade modelling. The application to this Generalized Arminton model to French trade in agri-food products yields mixed results which are however superior to those obtained with a conventional estimation procedure.

These mixed econometric results may lead readers to question the usefulness of bayesian estimation methods to agricultural trade modelling. We do not think so and opt for a more optimistic outlook in suggesting that this first attempt in applying bayesian mehtods can be improved in several respects. First, the adoption of an homogenous consumer preference structure is too restrictive and should be relaxed towards more general non-homogenous structures. Second, the use of of Monte Carlo integration with importance sampling is one procedure among a set of simulation methods to generate random numbers. Hence, there have been some recent applications of Monte Carlo method based on the use of Markov chains to econometric modelling [START_REF] Gordon | Echantillonnage de Gibbs et autres applications économétriques des chaînes markoviennes[END_REF]. We could perhaps employ this latter approach in estimating the Generalized Armington model developed in this paper. Finally, a third direction to improve the econometric performance of this trade model would be to select other bayesian estimation procedures which are not necessarily based on the approximation of integrals of posterior distributions. In this vein, we are especially thinking of bayesian bootstrap analysis of systems of equations similar to the one proposed by Heckelei and Mittelhammer (1ee6).

  the region of the parameter space for which global or local validity conditions are satisfied. Then, through the Bayes rule, we obtain a posterior density function.l(.) expressed as:.f (bl),) = p(b) L(r'lù Ie l wherey is the sample data set and Z(.) is the likelihood function based on observed data. As the prior density function is a simple(unitary) indicator function, the posterior probability distribution is no more than a truncated density function generated from the sample likelihood function in expression [9.]. A point estimate of the parameters à which does not violate the regularity conditions is then obtained by taking the mean of the posterior distibution over the the domain D, that isa:E(b) = [o*h f (bly)db tlo ]Expression [10.] is the conceptual tool that serves to derive point estimates of the parameter b.

  4.1 -Data Data used to estimate the system of CDEH demand equations stem from two reference sources. Import data by origin were obtained from the French Custorns trade data base while the prices and quantity consumed of home-produced goods are aggregates from the French national accounts developed by the Institut National des Statistiques et des Etudes Economiques(INSEE). Before we proceeded with the bayesian estimation, both data sources had to be harmonized to generate comparable price and quantity aggregates on the various supplies of agri-food products. Such a task is difficult, if not impossible, to perform at the aggregate level (3 SITC digit levels for instance). On the other hand. it is possible to obtain satisfactory and comparable data if we develop all these quantity and price aggregates at a more detailed and disaggregated level. For this purpose, we used the "NAP 600" level of the French National Accounts nomenclature (about 700 products) and matched it with the corresponding nomenclature of the French Customs data base. There are about 80 agri-food products6 at the NAP 600 level but we only retain the ones for which each of the three import and home-produced supplies represent at least lo of the total consumption. This selection resulted in a set of 26 (7 agricultural and 19 processed food) products, the consumption of which represents over 300 billion FF in 1994. Imports of the retained products represent 600/o of total imports of French agri-food products on average(1990-94).

Table 2 :

 2 Parameter estimates of the generalized Armington model

	Agricultural raw products
	bl	b2	b.	al	ù2

This result must be qualified when only weak conditions are imposed on parameters (local validity). Recall that these conditions are associated with a posterior probabilit-v which is largely greater than the one of the global conditons.In this case of local validity, complementârity between French products and imports from the Rest of the EU can be observed for several raw agricultural products and for some processed food products. But in the case of local validity, complementaril-v betrveen French products and imports frorn the RoW remains the exception for raw agricultural products, but can be encountered n,ith a significant posterior probability for a few processed food products (see columns (9) to (l l) ofTable l). t2


Documentation Économie

Rurale Rennes
email: dvenners@roazhon.inra.fr

Optimal Land Use and Manure Management: an Application to the French Case

Keywords: nitrate pollution, intensive rearing, tradable polluting rights, French environmental regulation

The problem of pollution originating from intensive rearing is analysed through a general welfare economics model. The policy option chosen to avoid this situation relies chiefly on command and control measures, with a Iimited amount of Iivestock manure which can be applied to the land (170 kg of nitrogen in the 1991 EC directive). When the standards are defined, the producers will maximise their profit under this constraint. This leads to develop a market of manure spreading rights, between farmers having land available for spreading manure, and farmers having a high disposai rate per unit of land. An empirical illustration conceming Brittany is presented.

As a matter of fact the eut in priee support for cereals led to lower feed costs.

Consequently, priees of livestock products, mainly pork and poultrymeat have decreased. These commodities becoming more competitive, there is an expansion effect at the expense of beef. Using a simplified world trade model which allows the simulation of the consequences of the CAP reform, it has been demonstrated that pork and poultrymeat would increase in France by 8.5 per cent from 1993 to 1995 [START_REF] Léon | Réforme de la PAC : un faible impact sur la répartition régionale des valeurs ajoutées[END_REF]. The figures confirm the results of the model since, during this period, the priee decrease of feed compounds reached 8.7 per cent, whilst the production of pork and poultry meat increased by 9.3 per cent.

Simultaneously in these regions arable and permanent cropland has increased at the expense of permanent grassland, leading to a more important use of fertilizers. Consequently, not only manure and minerai surpluses appear to be causing nitrate deterioration of drinking water, but they are also the cause of the disruption of ecosystems due to eutrophication, and the emission of ammonia into the atmosphere. The presence of pathogens in slurry is another source of contamination of water facilities.

Controlling increasing pollution from agriculture becomes a major challenge for water protection and also for the protection of ecosystems. But, the management of manure represents a specifie problem in intensive rearing regions since the volume of this by-product is increasing and many farmers want to dispose of their larger quantities as cheaply as possible, Le. waste application on their land, or in the close vicinity. Their motivation is not the effective use of the nutrients, according to the uptake by crops, but the disposai of manure within the limits of crop tolerance.

Subsidiarily, the high level of tolerance of the maize explains the development of this crop. ln countries where this problem is acute, such as The Netherlands, researches have been conducted to determine the costs of reducing emissions from pig farming according to the situation of the farms and the type of measures [START_REF] Leneman | Costs of reducing nitrogen and phosphorus emissions on pig farms in The Netherlands[END_REF]. The impact of environmental regulations on dairy farms has been carried out in the UK [START_REF] Rigby | European environ mental regulations to reduce wtaer pollution: an analysis of their impact on UK dairy farms[END_REF][START_REF] Rigby | European Community guidelines to reduce water pollution by nitrates from agriculture: an analysis of their impact on UK dairy farms[END_REF]. These studies are useful since they permit a better targeting of environmental policies, but they only concern the relationship between policy makers and producers. If we intend to define a Pareto optimum, we have to take into account explicitly the consumer with his level of utility determined by his set of preference orderings.

The second section of the paper proposes a model of public economy where consumers' preferences are represented by a collective utility function ; farmers produce jointly animal and plant outputs along with organic nitrogen. This nitrogen contributes, on the one hand, to soil fertilisation; on the other hand, it contributes to a pollution which is proportional to the spreading intensity per hectare. After characterising the Pareto optimum of this economy, we remind that a «Iaissezfaire» situation inevitably strays from il. The proposed internalisation solution considers the creation of two markets: one between consumers and producers; the other between producers who, depending on the level of animal wastes, trade amounts of organic nitrogen or spreading rights. We then evaluate to what extent French regulations are inspired trom this normative solution.

The third section develops this model by formalising a market of manure spreading rights. A first empirical illustration is also provided, revealing the implicit overvalue related to the land because of the slow and progressive implementation of the nitrate regulation. The fourth section is the conèlusion.

2. SOCIAL OPTIMUM: FROM THEORY TO POLICY IMPLEMENTATION ln a first sub-section, we present a model where effluents are produced by farmers and where consumers bear the negative extemalities originating from intensive rearing. The co-production of organic nitrogen leads at the same time to a negative externality towards consumers and to an externality which is mutually positive among producers. Therefore, the internalisation solution requires the creation of two markets. The second sub-section analyses the extent to which current policies of nitrate surplus management follow the recommendations of this modal.

The microeconomic model

Simplistically, a basic geographical unit is considered, such as a watershed

where there are problems related to slurry excess. The fertilizing value of animal rejections and the assimilative capacity of the soil are thus taken into account. The polluting emission e integrates the spreading load per hectare and per farm j :

1 J n
e=-I-..:L J j=1 Zj [START_REF]Production négociée du droit des pollutions agricoles[END_REF] According to this formula. the contribution of each farm j to the overail pollution only depends on the amounts spread per hectare. The model can include, without any additional effort, a more accurate weighting function where the a j parameter would depend on the farm technology, on other inputs k j , on the location in the watershed.... At first sight, equation [START_REF]Production négociée du droit des pollutions agricoles[END_REF] only represents some kind of smoothing of organic nitrogen among farms, smoothing that could reduce the level of pollution felt by consumers.

The uO utility function is supposed to be differentiable. strictly quasi-concave, increasing in X.,x, and decreasing in e. Similarly, !j(Yja'Yj"n'i'Zj,kj)=O,j= 1, ... Jis difterentiable and concave. Land allocations Zj being assumed to be quasi-fixed, the Pareto optimum of this economy results from the following program:

MaxV(xu,x"e) S.t 1 J n,. e=-L.-' J j=1 Zj J J cjY ju = L.n;r ; n'j = L.nn j = 1, ... J )=1 /=1
J J X u :0; L.YjU ; x, :0; L.Yj, (p) j=1 j=1 [2] At the optimum, technological (a) and resources (p) constraints are saturated, which leads to the following Lagrangian :

L(.) = V(x u ,x"e) + L.aJj(Yju' Yj"n,) ,Zj,kj) + j [3]
From this expression, we can derive the first order necessary conditions that allow to characterise the Pareto optimum in the following way:

Vu fju

[f r " 1 V,] -=-+C• ----V j,/=I, ...J V, fj, J f r , ]zr V,

. av {)fj

Wlth: Vu =ax ,fju = .:J.•. "" u VY,.

[4] ln other terms, the classical equality of substitution marginal rates between consumers and producers is corrected here because of the extemality provided by the co-production of organic nitrogen. The latter leads to two contradictory effects:

i) a positive effect: the supply of organic nitrogen by fann j contributes to the fertilisation of plant productions of fann j' .

ii) a negative effect: it affects the consumer's utility.

The resolution if this system of equations provides, theoretically, the optimal pollution level e•. Classically, in the absence of public intervention, the competitive equilibrium of this economy with an extemal effect is not Pareto-optimal [START_REF] Baumol | The theory of environmental policy[END_REF]. In fact, it is clear that the various producers do not take into account, in their optimisation process, the effects of the amounts spread on the consumer's utility. But these extemalities can be seen as resulting from a lack of property rights concerning the environment. When a system of strict liability exists and under which a source is financially responsible for damages, then the paretian efficiency can be restored. [START_REF] Dales | Pollution, property and priees[END_REF] initially proposed the set up of a market of polluting rights in order to restore social efficiency. In our case, the extemality is revealed through the relation between two factors: land and organic nitrogen. Il has two effects: a negative effect on the consumer; a mutually positive effect among producers; some of them must get rid of a slurry excess, while the others benefit from fertilising elements. This leads to the creation of two different markets: one market between producers and consumers that contributes ta the search for e'; the other between producers who have or do not have an excess of slurry.

Let's assume that the aggregated consumer can offer an amount of polluting rights e' with a unit price of P, and has an exogenous income R ; P. is the price of crop output while Pa = 1 (the animal output is the numeraire). The consumer behaviour can be written as :

Max U(x a ,x•. e') s.t x a + P.x. -p,e' = R [5]
Noting À the Lagrange multiplier related to the budget constraint we obtain the following first order conditions:

U =À a U, = Àp, U, =-Àp, [6]
Concerning producers, the spreading of organic nitrogen now depends on the purchase of spreading rights for a quantity e d (with a weighting factor ~), which leads them to buy or sell organic nitrogen at unit price W" The program of producer j can then be written as :

Max yja + P,YP' -P,e1 + w,(cjYja -n'J) S.t JAYja'Yi',n'i,zj,kj)=O (a) e d =5.L (f3) J iz.

J

where ex and f3 are the Lagrange multipliers. Thus :

[7]

-P, + f3 =0 [8]
This new competitive equilibrium is also characterised by the equality between supply and demand on the various markets:

X a =LYja j eS =Le:

j x, = LYj, j LCjYia = Ln zJ j j
Alter removal of the multipliers, expressions [6] and [8]lead to:

[9]
which is equivalent to expression [4] that characterises the paretian optimality as soon as the corrective factor due to externality does not depend on j. On the other hand, [9] clearly shows that the equilibrium price, W" may be positive or negative depending on whether the fertilising contribution of organic nitrogen is more important than its harmful effects. Therefore, depending on the cases, the farmer offers either an amount of organic nitrogen or a spreading area. This latter case will be formalised in the following section by an illustration. Furthermore, there is no market where polluting emissions are traded between farmers and consumers. This market is implicit through the definition of standards concerning the disposai rate per unit of land. These standards are supposed to take into account the interests of the consumers as weil as the interests of the producers. It is to this issue that we tum next.

Second best policy instruments: the French regu/ation system

The set up of the internalisation scheme previously described through the creation of a market of rights would come up, in practice, against many difficulties: non-convexity of agricultural technologies, non point characteristic of nitrogen pollution, ... Moreover, it is impossible to set up a market of pollution rights between consumers and producers who are more or less victims of, or responsible for the pollution harmful effects.

In effect, and in a second order approach, the determination of an environmental policy is taken to be a two-step process : first, the policy maker sets standards in the form of maximum nitrogen units which can be spread per hectare; otherwise a standard e that substitutes to the e' which would result from the equilibrium set by the first market of rights. In a second stage, a regulatory system is designed to achieve the standard. As mentioned by Cropper and Oates (1992, p.685) this is often the way environmental decision making proceeds; it is the so-called «command and control approach ». However, this system may prove not to be neutral, as it is often the result of the state of the various existing forces and is in fact a compromise, which explains some perverse or non expected effects. The current French system of internalisation of animal related pollution highlights this situation.

The French system, a very complex one, combines regulation and economic tools. In terms of texts, the two most important on es are the law on c1assified

facilities and the European Directive on nitrates originating from agriculture.

The 1976 law on « classified facilities» is a general framework for the integrated management of polluting installations, whatever their activity. However, for agriculture, only rearing is concerned. An activity coming under this Act has to be « classified », i.e listed in a nomenclature. This applies only to installations of a certain size for enumerated species. The law defines two types of installations: those which have a reduced impact on the environment, and for which a mere notification to the « Prefet» is enough, and those which have serious harmful effects or are dangerous, and which require the «Prefet »'s permission. For the latter, an environmental impact assessment is needed, to detail the impact that the project may have on the environment, whether it is neighbourhood unrest, effects on the landscape or on water quality. In order to protect the water, and especially groundwaters, the farmer must plan large enough slurry storage capacities and spreading areas. ln order to enlorce the « Directive nitrates ", France has delined vulnerable areas where agriculture contributes to the degradation 01 water quality and to the eutrophication 01 groundwaters. In these areas, which make up 46% 01 the used agricultural acreage (<< Echo des Nitrates", 1997 n0113), the amount 01 animal effluents spread must not contain more than 170 kg 01 nitrogen par hectare, starting in 1999. France has not used the possible derogation that allows to go up to 210 kg per hectare between 1996 and 1999.

The enlorcement 01 these obligations is insured by the law, but also by using the Polluter-Payer Principle (PPP), together with an aid system. Originally, agriculture was one 01 the activities likely to pay taxes, however it was not until 1992 that an official agreement was reached between the ministries 01 agriculture and environment on the one hand, and prolessionals on the other hand. In exchange for their entry into the PPP system, farmers obtained a financial aid that allowed them to regularise their obligations with respect to the «classilied lacilities" law and the « nitrates" Directive. This system constitutes the «Agricultural pollution Control

Program " (APCP). This only concems intensive rearing, arable crops and minerai lertilisers are therelore excluded.

A November 1993 decision delines the technical and linancial decisions that allow to set up the APCP. For eligible farms, an environmental audit allows to determine the work required for rearing buildings and effluent storage capacities to comply to the various norms. This audit is completely paid for by the govemment and the water agencies. A contract is then passed with the farmer to take charge 01 the work deemed necessary to comply with the various norms, given the fact that only one third of the financial amount is under the farmer's responsibility. A progressive integration of eligible farms, according to their size, has been selected, knowing that there are about 70,000 such farms.

For farms which are part of the APCP, the polluting tax is estimated in a twostep process. The first step corresponds to the estimation of the gross tax. The latter depends on the dumping of suspended matter, organic matter, reduced nitrogen and phosphorus. However, since farmers have agreed to invest in order to pollute less, even if they already enjoy public aids, their gross tax benefits from an allowance under the form of a purification premium. The amount of the latter is such that the amount of the net tax becomes very small. This premium represents a very strong incentive to use spreading rather than slurry treatment, ail the more since the latter is still today two to three times more costly.

To summarise, the French system of intemalisation of animal related pollution shows a number of deficiencies for the consumer as weil as for the producer. At the consumption level, this system negotiated between the govemment and farmers integrates very poorly the utility function of consumers who must pay more for their drinking water. This system is not efficient, since well-known polluters are rarely prosecuted. The limited number of people sued for damaging the environment shows that the liability principle is not strictly enforced, and therefore that this principle does not allow to intemalise damages to the environment due to agriculture. At the production level, in order to prompt farmers to go by the rules, economic incentives are used under the form of aids with the APCP and, for farmers not complying with the standards the incentives are in the form of polluting charges (Doussan, 1997).

The latter are only used to compensate for the lack of efficiency of regulation and police measures. Resorting to a single standard of 170 kg of nitrogen per hectare does not allow to take into account local conditions and is another cause of inefficiency. The stress put on spreading, and the indirect incentive to produce caused by financial aids granted to comply to the various standards, put even more pressure on the land market. Under such conditions, it is only logical to see the emergence of an implicit market of spreading rights.

disposable. These assumptions ensure the existence of the production function describing the technically efficient production plans.

As long as the Nitrate Directive is not enforced, the farmer is close to maximising the profit given the quasi-fixed inputs level Zj:

where p and q indicate the respective price vectors for Y j and x j ' The previous assumptions related to T ensure a solution for program [10] and the existence of the restricted profit function ITRj(p,q,zJ ln a partial equilibrium framework the term "restricted" recalls that the optimisation has been only operated upon a subset of T;

it concerns other dual expressions of the technology such as the cost function CRj(y,q,f j ) intermediary of [10] in a step-by-step optimisation and that we shall use subsequently:

[11]

The enforcement of the Nitrate Directive can be formalised as a new constraint for the technological choices of the farmer and corresponds in a second-best approach to the potential altainment of the optimal level of pollution e' defined by equation [4] :

[12]

e is the guideline regulating the quantity of nitrogen from animal waste that may be spread per hectare of farmland (170 kg per hectare). As previously Yj" represents the quantity of animal products whereas cjYja in,dicates the organic nitrogen byproduct issued from animal breeding. The scalar Zj is the acreage of the farm which is available for spreading. Linked with the land constraint Zj =f j , expression [12] can be or not saturated at the optimum according to the Iivestock size and the total acreage of the farm. However, it can be more easily relaxed than Zj = Zj since the farmers are able to lease spare land in the neighbourhood in order to spread their surplus of animal waste. In other words, the land input provides two services : one for farming and the other one for spreading. Furthermore, they can be linked insofar as sorne crops allow more or Jess organic nitrogen. In the hypothetic market for manure spreading services, the producers will be buyers or sellers depending on whether expression [12] is initially saturated or not.

Let us note Zj' the net demand of manure spreading services for the farm j. In the present instance, manure spreading services are costless or the above limit e is not respected and that would imply a positive latent demand Zj, > O. Hence, the program for the producer can be written as :

M,~P"Yj -CRj(Yj.q,Zj) 0 < CjYja <-

S.t _

e zfr + Zj [13] whereas the possibility of a manure spreading market with a unit price I.ll, leads to the following behaviour :

S.t [14]

The prescribed constraint applies on the overail agricultural surfaces, i.e:

j = 1••.. J
However it remains a potential moral hazard : overspreading, multiple spreading supply of the same area, ... Let us now consider the positivity constraint 0:0; cjY ja . It is saturated for a zero livestock production: Y ja =O. In that Zj' + Zj case, the fanner potentially supplies the whole surface for a manure spreading service. Furthennore some crops such as vegetables do not tolerate manure which involves : Zj' > -zr This last inequality is also true in the case where the positivity constraint is not saturated at the optimum. Then we may deduce the expression of the lagrangian related to [14] : [15] with the following first-order conditions:

[16]

Eliminating the multiplier .:l we obtain the total demand of manure spreading service for the fann j : Z;,(p,q,w"Zj'Cj.e) and y~(p,q,w"zj,cj,e) being the solutions of [14]. Resolving this program also allows us to define the restricted profit function :

The competitive market equilibrium for manure spreading rights is characterised bya rentai price w;, solution of the following equation : J L,z;,(p,q, w, ,Zj,C j ,ë) =0 j=l

A tirst empirical illustration [18]

The previous model has been the object of an application using the results obtained through a direct survey in Brittany. This region has experienced a large growth in livestock farming in the last three decades. In particular, the number of pigs and poultry has strongly increased, representing respectively 55 per cent and 45 per cent of the total French production (SCEES, 1996). Moreover, Brittany is the first region for milk production. As a result, it has the highest disposai rate per unit of land relative to other French regions. Because of its geological features, Brittany has 80 per cent of total disposable water coming from water streams and reservoirs. In consequence, the region is vulnerable to nitrate and phosphate pollution and 60 per cent of water resources are threatened in the near future [START_REF] Sraep | Schéma régional d'alimentation en eau potable[END_REF]. In some places, the use of aquifers had to be abandoned and water treatment supplemented with denitrification. Nowadays, about 60 000 persons are fed with a drinking water exceeding the maximum allowable concentration whereas 850 000 people are occasionally exposed to drinking water with concentrations over 50 mg/!.

The overail results of Brittany farms that depend on the APCP allow to characterise the farms which need large spreading areas and, on the contrary, those which are likely to receive animal effluents. This highlights the fact that intensive farms with rearing installations specialised mainly in pig production or in pig and bovine production need between 10 and 40 hectares of spreading land outside the farm. On the contrary, less intensive farms with rearing installations specialised in bovine production have 5 to 15 hectares of unused spreading capacities.

The previous model has been applied to two samples of French intensive livestock farms located in Brittany and whose rearing installations are specialised mainly in pig production and in pig and bovine production. Table 1 provides some statistics about them. The various outputs (vegetables and livestock) are indexed by m, m =l,... M with Yj = (Yjp ... Yjm""YjM)' The objective function that we intend to maximise expresses the producer's rationale behaviour. Given the availability of data this function is defined from the gross margins per activity GM jm which can be written as : [19] where Pm and q represent output and input priees, !4im the output quantities and the quasi-fixed factors. We calculate the total gross margin as the sum of the margins per activity4 :

GMj(p, Yj,q'zj) =L,GM jm =L,PmYjm -CRjm(Yjm,q,Zj) m m
whose maximisation corresponds to the restricted profit function defined by [10] :

[20] The prescribed constraint linked to the Nitrate Directive can be considered also as a quasi-fixity. It first leads to define the shadow priee w j , issued from the restricted profit function IlRj(p,q,Zj"Zj,Cj.e)SUCh as :

[22]

The farmer compares this last value with w; solution of [18]. As an illustration, if w j , > w; there is a marginal gain to rent land for spreading. Following Fâre and Primont (1995 p.56) the estimated values w j , have been calibrated by W; which is the average priee for hired land. For W; = FF 1,000 (corresponding to the observed priee of the rent in Brittany), resolution of [21] and [22]leads to higher shadow priees for spreading services from FF 1,170 to FF 1,300 in the case of pig farms.

Moreover, the resolution in Zj, of:

[23] provides z;, (p,q, W"zj,cj,e) One could expect to obtain a more important equilibrium price w; in the case of farms specialized in pig production because of a lesser average land availability (cf table 1). However, in the two study cases, the equilibrium price is similar and varies between FF 1250 and FF 1300. That can be explained by the Act on classified facilities : the application was stricter for land-independent husbandry, especially for storage capacities. Thus. cattle breeders are penalised through lack of storage capacities and require subsequently more acreage for spreading.

The use of land off the holding for waste spreading will be limited by the cost of transportation. For pig manure such cost reaches FF 0.77 per ton and per km [START_REF] Poux | Etude sur l'insertion optimale des procédés de traitement dans les cantons en excédebt structurel[END_REF].

CONCLUSION

The model developed shows that the intemalisation of animal related pollution requires the creation of two markets of rights to pollute. The first market between producers and consumers is impossible to install. The regulation means used instead are not very efficient, since these regulations are the result of a negotiation between the administration and the professionals. Consumers are not in any of the two parties' mind. The only progress is the unofficial set up of an exchange market dealing with rights to pollute between producers who, by exceeding the standard of 170 kg of nitrogen per hectare need additional spreading areas, and farmers who use less intensive production systems, and can, therefore, receive some slurry.

The way this market between producers operates is detailed in a generic model that takes into account the fertilising value of slurry. For the sake of simplification, this model does not integrate the cost of transport of slurry, which Iimits its practical use. However, a preliminary application shows shadow prices of spreading areas that are higher than the usual land rentai cost. It is therefore obvious that the use of this parallel market of spreading rights is the answer of producers to regulations when they are located in areas with a high animal density.

ln the current price context, it is possible to extrapolate the effects of an increase of the production density on the shadow land prices. At a certain level, it is not in the producers' interest to look for new spreading areas. Rather than exporting their slurry at an increasing cost, either because lands are too expensive or because transport costs are too high, they must use other solutions.

The first solution is to use animal food which is less rich in proteins, which allows to decrease the nitrogen content of the effluents. At first, it is possible to decrease noticeably the nitrogen content, by about 25% for pigs [START_REF] Dourmad | Réduction des rejets azotés des porcs par la voie alimentaire: évaluation économique et influence des changements de la Politique Agricole Commune[END_REF]. Above that value, the cost increases drastically and the rearing becomes much more difficult. It may then become more interesting to consider manure processing. There again regulations may play a role. In areas of structural excess, the limitation of spreading areas per producer would right away make the processes of slurry treatment more attractive.

As a last resort, when the marginal cost 01 the excess nitrogen unit becomes too high, the solution may be to decrease the production levaI. The only way to internalise pollution 01 larming origin is to play with this parameter.

  characterised by a high agricultural employment per sq km have known an intensive animal husbandry development. This development has been encouraged by the Mc Sharry reform of the Common Agricultural Policy.

  The 1992 translation into French law of the Directive on nitrates originating from agriculture widens the field of application of the law on classifies facilities. For example, dairy cows, which were not concemed by the 1976 nomenclature, appeared in the 1992 version. Rearings of 40 to 80 cattle heads come under the simple declaration regime, while those of over 80 cattle heads are subject to the permission regime. Let's remind that the overail objective of this Directive is to «prevent and reduce the pollution by nitrates from agriculture source». The Directive addresses the earlier Directive on the quality 01 drinking water delining the Maximum Allowable Concentration 01 nitrates (50 mg per litre).

  optimisation is constrained by some quasi-fixities on inputs and outputs. They can be expressed as linear constraints related to land availabilityS, family labour, milk quotas, cultural rotations, size of rearing installations... The resolution of [21] is obtained using S.A.S.lO.R procedures which provides : rr~(value of the objective function for each farm), ~m (optimal quantities per éIIIR activity) and _ _ J • This last term represents the marginal increase of the restricted éfi jk profit provided by a marginal increase of the quantity Zjk' It is still defined as the shadow priee w jk related to Zjk which is equal to the unit priee W k of the input Zk where the maximisation states upon the whole input space.

  the net demand of manure spreading services for the farm j. In fact, equation [23] is just another way of writing one of the first order necessary conditions of the program [14]. According to the two studied samples, these values are represented in figures 1 and 2 which also indicate the equilibrium priee w; , solution in w, of [18].

Figure

  Figure one: Market equilibrium for intensÎve pig rearings Supplyand demand of SprcadiDg services

Table 1 :

 1 Main characteristics of the two samples

		Pig farms	mixed farms
			(pig and bovine rearing)
	Structure of the total output
	animal output % total	92.8	90.7
	crops output % total	5.5	5.6
	subsidies % total	1.7	3.7
	Total output (10 3 FF)	2324.8	1733.2
	Total of variable costs ( 10 3 469.8	454.3
	FF)
	Useful agricultural area 50.1	68.1
	(ha)
	Total Nitrogen Livestock 176	168
	Units
	Units of family labour	2.3	2.6
	Units of paid labour	0.6	0.1

It will be defined more precisely in the econometric illustration (section

3).

That implies the non jointness of the technology : this assumption is questionable but imposed by data.

Quasi-fixed factors as land or family labour can be allocatable according to the different activities: Zjk =L, ï.jkm m

THE DESIGN AND IMPLEMENTATION OF TRADABLE MANURE SPREADING

RIGHTS

Instead of the previous « charges and standards» approach, the marketable permit system can be more consistent in the policy arena. Indeed, setting standards in the form of maximum nitrogen units per hectare is similar to a grandfathering system where the govemment can, based on historical levels of emission, distribute tradable emission rights to polluters without charging them. Each polluter thus receives a marketable asset which he can then use either to validate his own emissions or sell to someone else whose marginal benefit of pollution is higher than his on a market of permits [START_REF] Cropper | Environmental Economies: a Survey[END_REF]Schiib, 1996).

Subsequently, targets and standards for environmental quality being defined, farmers will manage their manure surpluses according to their local situation. When a part of their surplus can be applied on deficit farms in the neighbourhood, we are facing a market of spreading rights. Therefore the first sub-section extends the previous microeconomic model whilst the second sub-section i1lustrates the potential equilibrium of such a market using the case of the Brittany region.

Modelling the tradable manure spreading rights

ln order to implement the previous theoretical considerations (sub-section 2.1) and using the same notations, we now define more precisely the technology. Each farmer presents a production plan defined by a set of vectors (xj'Yj,Zj) Le, the input vector k j includes x j which indicates the factors which can be freely adjusted ; and a part of Zj the quasi-fixed inputs as land and labour. Each of these factors is used to produce the output vector yj' T is the set of ail the feasible production plans ; it is assumed to be regular and strictly convex 3 whereas inputs and outputs are strongly 3 Tisclosed,non-empty,if Yj *,0 then (Xj'Zj)*O,if X j <00 and Zj <00 then Y j <00.


Cesare G Pacini

Concetta Vazzana

Luigi O Zorini

An economic-environmental model of an organic dairy farm for an evaluation of sustainability in agriculture

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.