Frédéric Courleux

Hervé Guyomard

Fabrice Levert

Laurent Piet

How the EU Single Farm Payment should be modelled: lump-sum transfers, area payments or… something else?

Keywords: European Union, Common Agricultural Policy, Single Farm Payment, Modelling, Area payments, Lump-sum transfers

How the EU single farm payment should be modelled: lump-sum transfers

Introduction

On 26 June 2003, European Union (EU) farm ministers adopted a new reform of the Common Agricultural Policy (CAP). This reform radically changes the way the EU supports its agricultural sector. Among the various features characterizing the horizontal Council Regulation (EC) 1782/2003 (essentially modulation, financial discipline, cross-compliance criteria and new rural development measures), the decoupling of direct payments granted through the so-called first pillar appears to be the most at odds with the previous policy inherited from the 1992 and 1999 reforms. 1 It is implemented through a Single Payment Scheme (SPS) which mitigates into a Single Farm Payment (SFP) a majority of the direct aids that were formerly granted per hectare (cereals, oilseeds and protein crops) and/or per animal head (beef, veal, sheep and goats). 2 The SFP is broken down into a certain number of entitlements which in practice correspond to unit amounts of aids per hectare in so far as each entitlement has to be "accompanied by an eligible hectare" in order to "give right to the payment of the amount fixed by the payment entitlement" (EC 1782/2003, article 44). As a result, one could regard SFP entitlements simply as area payments. However a second feature of the SPS makes SFP entitlements potentially different from area payments. Whatever the national implementation model, 3 actual production of a specific commodity among those which are eligible is no longer required to get the payment attached to entitlements, provided cross-compliance conditions are met on the corresponding hectares. 4 From that perspective, one could be inclined to look at the SFP as a lump-sum transfer to the farmer.

Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

3 From the previous presentation, a difficulty immediately arises. As noted by Bascou et al. (2004), "(t)he way in which the single farm payment is implemented and modelled may notably influence producer decisions and the projected production patterns". Though a model is clearly a simplification of reality, it is always most desirable to adopt an as explicit as possible representation of policies in models. This is the main objective of this paper which tries to bring some clarity into the debate on the way SFP entitlements should be modelled, more specifically as lump-sum transfers, area payments or… something else. To do so, we develop a simplified microeconomic production framework to compare three situations corresponding to, respectively, (i) a zero support regime, (ii) a regime where support is granted through direct aids per hectare and (iii) a regime where support is granted through the SPS. 5 The analytic approach we develop integrates the three main characteristics of the SPS that make payments a priori different from both lump-sum transfers and area subsidies. First production is no longer required to get payments attached to entitlements. Second the scheme maintains a specific link between payments and hectares through the so-called "activation constraint", i.e., the obligation for a farmer to maintain in potential agricultural use (through the respect of GAECs) a number of eligible hectares at least equal to the number of SFP entitlements he holds to get the payment attached to the latter. 6 Third SFP entitlements can be exchanged among farmers, necessarily with a concomitant and equivalent land transfer in the case of a temporary entitlement transaction, with or without land transfer if the entitlement transaction is permanent.

The rest of the paper is structured as follows. Section 2 briefly reviews researches that used one of the two options described above (lump-sum transfers or area payments) to represent the SFP. Section 3 details our modelling framework; we first describe the zero support regime; we then bring in direct aids per hectare equivalent to those which were in place in the EU sector of cereals, oilseeds and protein (COP) crops from the 1992 CAP reform accounted for since the income formation of households is not modelled; as a result, the amount corresponding to the SFP simply accounts for zero in the profit maximisation behavior of agricultural producers. Under this assumption, the 2003 CAP payments have no impact at all on farmers' production decisions, input use (especially land demands) and output supply (especially yields).

In a general equilibrium (GE) setting (Gohin, 2004; Gelan and Schwarz, 2006), the income formation of consumers is modelled and the lump-sum transfer equivalent to the total amount of the SFP is explicitly introduced as accruing to households. Within this framework, the production-decision side is not affected by the SFP. Nevertheless, a certain wealth effect can come into play on the consumption side in so far as the increase in consumers' income can affect their decisions in terms of both resource allocation and income spending. It should be noted though that, in the examples cited above, agricultural households are not explicitly accounted for as only a single representative consumer agent is considered. As a result, the SFP is "diluted" as it was a very generic transfer to all households, agricultural households as well as non-agricultural households.

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Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

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In short, when the new EU payments are modelled as lump-sum transfers, they de facto do not affect output supply and input use, in particular the land demand addressed by farmers to land owners. They do not capitalize into land prices and rents. Models that have adopted this first approach effectively conclude that decoupling should result in land rents to decrease sharply relative to the pre-2003 situation, e.g., -80 % in Gohin (2004).

The area payment solution

The second approach adopted by modellers is to consider SFP entitlements just as if they were area payments. This alternative solution has been adopted in PE models (Junker et al., 2003; Binfeld et al., 2003; Binfeld et al., 2004; Huettel et al., 2005; Balkhausen et al., 2005; Buysse et al., 2007) and GE frameworks (Frandsen et al., 2003; Jensen and Frandsen, 2004; Gohin, 2004, 2006). 8 It is not our purpose here to discuss whether area payments such as those in place in the EU COP sector since 1992 have been satisfactorily or not represented in models so far. However we do need to briefly describe how they have been actually modelled in order to understand implications regarding the effects of SFP entitlements when they are introduced as area payments.

Most PE models do not explicitly represent factor markets, notably the land factor market. 9 Even when they include a land allocation mechanism, and hence product-specific land derived demand equations, they generally do not compute equilibrium land rental prices which could enter these land demand functions. As a result, it is not possible to specify land demand equations in which the land price net of the area payment could be an explicit argument. To overcome this limitation, area payments are then introduced as a complement to the output price in equations that determine the areas devoted to each eligible crop. 10 In order to account for the fact that the supply-inducing effects of area payments are less than the impacts of output price support, the OECD AGLINK model multiplies area payments by a 6 coupling factor of 0.14 (OECD, 2004). As noted by Gohin (2006), only the OECD justifies the value retained for the coupling factor relying on a policy simulation analysis performed with the PEM model which integrates the land market (Dewbre et al., 2001). The value of the coupling factor adopted in other PE models is not justified. In practice, it varies between zero and one reflecting essentially a priori believes of modellers (Gohin, 2006; Balkhausen et al., 2007).

By contrast, GE models do represent the land market. Area payments can then be explicitly introduced in agricultural land demand equations by lowering the endogenous rental price of land. In a general way, GE models allocate land according to constant elasticity of transformation (CET) functions which capture the constrained mobility of total available land among competing uses. As a result, there are several land rental prices reflecting the fact that land is, in practice, a heterogeneous production factor. GE models, as well as PE models which explicitly include the land market, can be used to address the issue of agricultural support capitalisation into land prices and rents. They however suffer from two main drawbacks. First their incomplete agricultural area coverage since in many cases, several agricultural land uses are not included (fodder and pasture area, voluntary set-aside area, etc.).

In addition, the models' product aggregation is not always fully consistent with the one retained by policymakers. Second, as rightfully pointed out by Gohin (2006), EU land rental prices net of per-hectare direct payments are generally negative. 11 Gohin (2006) explains this very partial capitalisation of area payments into land prices by two factors: land price capitalisation takes time in particular because land-leasing contracts are long-term arrangements very difficult to renegotiate; there are rigidities and imperfections in agricultural production factor markets, not only the land market due to, notably, national regulations on farmland uses and prices, but also the labour and capital markets. Accordingly, Gohin (2006) argues that it is not unreasonable to model pre-2003 area payments, for a part as land

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Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

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subsidies, for the remaining as labour/capital subsidies. In his empirical analysis, he assumes an equal sharing. He immediately recognizes that this choice is somewhat arbitrary.

Let us now consider how SFP entitlements are dealt with in simulation models whey they are introduced as area payments. Under this assumption, the 2003 CAP decoupling is depicted as a switch from area payments restricted to cereals, oilseeds and protein crops, as well as mandatory set-aside, to non-product-specific direct aids per hectare for all eligible areas. In the AGLINK model for example, the SFP affects only the first-stage of the three-step area allocation system, i.e., the decision relating to the choice between the total area for cereals and oilseeds on the one hand, the total area for fodder crops and pasture on the other hand. Subsequent area allocation decisions depend only of relative returns (OECD, 2004). To reflect the lower degree of SFP entitlements as compared to the pre-2003 area payments, the coupling factor is now set to 0.06 (instead of 0.14 for area payments). This lower figure is based on Dewbre et al. (2001) who showed that area payments requiring planting of specific crops are slightly more trade distorting than payments not requiring planting of specific crops.

The other models which also adopt the coupling factor approach do not justify the choice of the coefficient ascribed to SFP entitlements. The coefficient is generally assumed lower than the one associated with pre-2003 area payments (0.15 versus 0.50 for the FAPRI-GOLD model, Binfield et al., 2003; Binfield et al., 2004), but it is sometimes maintained unchanged (1 for the ESIM model, Balkhausen et al., 2005). 12

The microeconomic framework

The microeconomic framework developed below takes explicitly into account the three main characteristics of the 2003 EU SPS, i.e., (i) the activation constraint, (ii) the free tradability of SFP entitlements and (iii) production is no longer required but cross-compliance criteria apply. The model is developed progressively. In a first step, we introduce the two first

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Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14). 8 characteristics (section 3.3). In the second step, we add the third feature (section 3.4). We begin the presentation by defining the two comparison regimes, i.e., first the zero support regime or, equivalently here, the lump-sum transfer regime (section 3.1), second a regime of per-hectare direct aids (section 3.2). It is from this comparison that we will derive implications on how SPF entitlements should be modeled.

The zero support regime

We consider a two-producer agricultural economy. Each farmer

i i i i i i i i i i i i h x l r w p l h x f y rh wx y p θ ≡ = - - ,
where i p is the output price, i y is the output level, w is the vector of variable input prices, i

x is the vector of variable input quantities, r is the land rental price, i h is the land quantity, ) , , (

i i i i l h x f
is a well-behaved production function with i l the (fixed) family labour endowment of farmer i .

We retain three simplifying assumptions in order to make things manageable and analytical results more easily interpretable. They do not alter general conclusions of our analysis. First output and variable input equilibrium prices are assumed exogenous and constant. 13 Second land is acquired or let through rental only; the buying or selling price of land is assumed to be adequately approximated by the discounted sum of future rental values so that a prediction about the direction of the land rental price is equivalent to a prediction about the direction of the buying or selling land price (Leathers, 1992). Finally land endowments of farmers are supposed null.

Program 1 defines a profit function ) , , , (

i i i l r w p θ
which is assumed twice continuously differentiable, non negative, non decreasing in output price, non increasing in 9 input prices, non decreasing in family labour quantity, linearly homogeneous and convex in prices, and concave in family labour quantity (Diewert, 1974). The land demand function for farmer i is obtained by differentiation of his profit function with respect to the land rental price (Hotelling's lemma):

(2)

r l r w p l r w p h i i i i i i ∂ -∂ ≡ / ) , , , ( ) , , , ( θ .
The land market equilibrium is then defined by equating farmers' land demands to land supply, i.e., Equation 3 solved for r defines the equilibrium land rental price, wp r , as a function of output and variable input prices, as well as family labour endowments.

The land market is depicted in Figure 1 where equilibrium occurs at point wp E , for an equilibrium land rental price of wp r . For this equilibrium land rental price, farmer 1 leases in the land quantity ) , , , (

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The land demand function of each farmer is still defined by the derivative of the profit function with respect to the land rental price, and the land market equilibrium is still obtained when aggregate demand for land equals land supply:

(5) ) ( ) , , , ( / ) , , , ( 2 1 2 1 a i i i a i i i i i a i i r L l a r w p h r l a r w p ∑ ∑ = = = - = ∂ - ∂ -θ
. where the superscript "a" denotes equilibrium variables in a support regime of per-hectare direct aids.

The comparative static of the land rental equilibrium price in this policy regime is determined by totally differentiating (5) and solving for a dr : 15

(6) ] / / [ . / 2 2 1 2 2 1 2 2 r L r da r dr i i i i i a ∂ ∂ + ∂ ∂ ∂ ∂ = ∑ ∑ = = θ θ .
Equation 6 shows that the equilibrium land rental price is an increasing function of per-hectare direct aids. Per-hectare direct aids capitalize at least partially in land prices and

( . / 2 2 1 2 1 1 2 2 2 2 2 1 2 1 2 2 1 2 2 1 2 2 2 1 2 1 2 1 2 1 r L r da r L da da r r da r L r da r r da dr r dh i i i i i i i a a ∂ ∂ + ∂ ∂ ∂ ∂ - - ∂ ∂ ∂ -∂ = - ∂ ∂ + ∂ ∂ ∂ ∂ ∂ -∂ = - ∂ -∂ = ∑ ∑ ∑
own-aid effect). By contrast, per-hectare direct aids granted to the second product (equivalently here the second producer) have a negative impact on land allocated to the first product (negative cross-aid effect).

The response of total land demand to changes in per-hectare direct aids is readily obtained as the sum a a a dh dh dH

2 1 + = : (8) ] / / [ . / . / 2 2 1 2 2 1 2 2 r L r da r r L dH i i i i i a ∂ ∂ + ∂ ∂ ∂ ∂ ∂ ∂ = ∑ ∑ = = θ θ .
In the case where the land supply function is not perfectly inelastic

( 0 / > ∂ ∂ r L
), perhectare direct aids are coupled at the extensive margin of production since they increase aggregate land used in the farm sector. In the specific case where the land supply function is

perfectly inelastic ( 0 / = ∂ ∂ r L
), they have no impact on aggregate land used in the farm sector.

We summarise the previous analysis by the following proposition. 2007-12-13 -2007-12-14). 12 effects are negative. Except in the specific case where the land supply function is perfectly inelastic, direct aids per hectare increase total land used in the farm sector.

The SPS assuming that production is required

Producer maximization program

In the SFP policy regime, each producer maximizes his profit according to the following program:

(9a) ] 0 ; ) , , ( ; ) ( [ max 0 , , i i i i i i i i i i i i i i n h x h n l h x f y n n v bn rh wx y p ≤ ≤ = - - + - - ,
where b is the unit value of payment entitlements, i n is the number of entitlements for farmer i , v is the rental price of entitlements, and 0 i n is the initial entitlement endowment for farmer i . For convenience, payment entitlements are assumed acquired or let through rental only. For the sake of simplicity, we also consider that they exhibit the same unit value b whatever the farmer. 16 From equation 9a, one sees that the SPS induces three main differences in the producer maximisation program with respect to the regime of direct aids per hectare (equation 4). First total payments the farmer i receives are no longer proportionate to the number of hectares i h he demands but to the number of entitlements i n he claims for. Second the difference ) (

0 i i n n v -
represents either the costs of renting in additional payments at a price v per unit or the earnings of renting out part or all of the initial payment endowment, also at a price v per unit; this accounts for the tradable nature of SFP entitlements. Third the inequality constraint i i h n ≤ captures the fact that payments are granted only for entitlements for which the farmer i holds an eligible hectare; this is the way we represent the "activation constraint".

Program 9a can equivalently be written as: 2007-12-13 -2007-12-14).

13 (9b) ] 0 ; ) ( ) , , , ( [ max 0 , i i i i i i i i i i n h h n n n v bn rh l h w p ≤ ≤ - - + - π , where ) , , , ( i i i i l h w p
π is a well-behaved profit function defined for a given land quantity:

(9c) )] , , ( ; [ max ) , , , ( i i i i i i i i x i i i i l h x f y wx y p l h w p = - ≡ π .
The first-order necessary conditions for program 9b are:

(10a) 0 / ) ( = + - ∂ ∂ λ π r h h i i , (10b) 0 = - + - λ µ v b , (10c) 0 . = i n µ , (10d) 0 ) ( . = -i i n h λ ,
where µ and λ are the Lagrange multipliers associated with the inequality constraints 2007-12-13 -2007-12-14). 14

i n ≤ 0 and i i h n ≤ , respectively.

Land and entitlement demand functions

> i h ) and b v r h h i i - + = ∂ ∂ / ) ( π (from 10a). Let us now assume that b v = . Under this assumption, 0 = = λ µ (from 10b, 10c and 10d), r h h i i = ∂ ∂ / ) ( π (from 10a) and i i h n ≤ ≤ 0 . Finally, let us assume that b v > . Under this assumption, 0 > µ (from 10b), 0 = i n (from 10c), 0 = λ (from 10d) and r h h i i = ∂ ∂ / ) ( π (from 10a). In sum: (11a) when b v < , b v r h h i i - + = ∂ ∂ / ) ( π and i i h n = , (11b) when b v = , r h h i i = ∂ ∂ / ) ( π and i i h n ≤ ≤ 0 , (11c) when b v > , r h h i i = ∂ ∂ / ) (

Land and entitlement market equilibriums

Let us now turn to land and entitlement market equilibriums. The land market equilibrium requires that aggregate land demand equals aggregate land supply. The entitlement market equilibrium condition requires that the total number of entitlements activated by farmers is lower than or equal to the global endowment in entitlements, 0

N . Three regimes have to be distinguished depending on

wp H N ≤ 0 , b wp H N H ≤ ≤ 0 or 0 N H b ≤
, where wp H is total agricultural land used in the zero support reference situation and b H is the number of hectares which would be demanded in a support regime of per-hectare direct aids of unit amount equal to the entitlement unit value b . Annexes 1 to 3 detail why these three regimes have to be considered.

Regime 1. ) ( 0 wp wp r L H N = ≤
In that first regime, the initial number of entitlements is lower than or equal to the number of hectares which would be demanded in the zero support policy reference situation. One then shows that market equilibrium conditions may be defined as (proof in Annex 1):

(12a) b v s = , (12b) r l r w p l r w p h h i s i i i s i i s i ∂ -∂ = = / ) , , , ( ) , , , ( θ ,
(12c) ) ( ) , , , ( 2 1 s i i s i i r L l r w p h = ∑ = , ( 12d
) s i s i h n ≤ , ( 12e
) wp i s i H N n ≤ = ∑ = 0 2 1 ,
where the subscript "s" denotes equilibrium variables in this first SFP regime.

In that first regime, the equilibrium rental price of entitlements equals the unit value of entitlements (equation 12a). With respect to the zero support situation, the SFP scheme has no 15 impact on individual land demands (equation 12b), the aggregate land quantity used in the farm sector and the land rental price (equation 12c which is identical to equation 3). The total number of payment entitlements effectively used by the farmers is equal to the initial endowment in entitlements (first part of equation 12e). There are entitlement exchanges from the over-endowed farmer (if he exists) towards the under-endowed farmer (if he exists). 18 Both the over-endowed farmer and the under-endowed farmer gain from exchanging payment entitlements relative to a regime where entitlements cannot be exchanged. This can be shown graphically as follows. 16 whether area αβδγ is greater or smaller than area K Iεη . The over-endowed farmer 1 does not use all his initial endowment in entitlements, and the under-endowed farmer 2 demands a number of hectares greater than his initial entitlement endowment.

(ii) Let us now assume that payment entitlements can be exchanged. Under this assumption, the aggregate land demand is the broken line YZ GNE wp and there is no impact on the land market: the equilibrium land rental price is

wp s r r =
, individual land demands are

wp s h h 1 1 =
for farmer 1 and

wp s h h 2 2 =
for farmer 2, and total land used in the farm sector is

wp s H H =
(where the superscript "s" denotes equilibrium variables in this regime of tradable SFP). The SFP scheme is decoupled at the extensive margin of production. The over-endowed farmer 1 leases out the entitlement quantity With respect to the zero support regime, the under-endowed farmer 2 gains area αβδγ . With respect to the non tradable SFP regime, he gains K Iεη . Relative to the non tradable regime, both producers thus benefit from exchanging payment entitlements.

(insert Figure 2)

The following proposition summarizes the previous analysis.

Proposition 2. When the initial number of payment entitlements is lower than or equal

to the number of hectares that farmers would demand in a zero support regime, introducing tradable single farm payments has no impact on the land market: the land rental price, the total agricultural area and farmers' land demands are unchanged. All payment entitlements are activated, and there are entitlement exchanges from the over-endowed farmer (if he exists) towards the under-endowed farmer (if he exists). In that second regime, the initial number of entitlements is greater than or equal to the number of hectares which would be demanded in the zero support policy scenario ( 0 N H wp ≤ ), and lower than or equal to the number of hectares which would be demanded in a regime where support would be granted through direct aids per hectare of unit amount b

( b H N ≤ 0 where b H is defined by ) ( ) , , , ( 2 1 b i i b i i b r L l b r w p H = - ∂ - = ∑ = θ
). In that case, equilibrium conditions may be written as (proof in Annex 2):

(13a) b v s ≤ ≤ 0 , (13b) r l b v r w p l b v r w p h h i s s i i i s s i i s i ∂ - + -∂ = - + = / ) , , , ( ) , , , ( θ , (13c) 0
) ( N r L s = , ( 13d) ) ( ) , , , ( 2 1 s
i i s s i i r L l b v r w p h = - + ∑ = , ( 13e
) s i s i h n = , (13f) b i s i wp H N n H ≤ = ≤ ∑ = 0 2 1 .
In that second regime, the equilibrium rental price of entitlements is lower than or equal to their unit value (equation 13a). SFP entitlements now have an impact on individual land demands (equation 13b). Equation 13d defines the equilibrium entitlement price for a given equilibrium land rental price defined by equation 13c. One easily verifies that ), then single farm payments increase the demand for land and capitalize into land rental prices. The higher the number of entitlements, the higher the impact on land demanded by the farm sector, the higher the land rental price and the capitalization into land rental prices, and the lower the entitlement rental price.

N

in Figure 3). This is no longer the case when for farmer 1 and

wp s s h h h 2 ) 1 ( 2 ) 2 ( 2 = >
for farmer 2. Figure 3 ). In that case, equilibrium conditions are defined by (proof in Annex 3):

(17a) 0 = s v , (17b) r l b r w p l b r w p h h i s i i i s i i s i ∂ - -∂ = - = / ) , , , ( ) , , , ( θ ,
(17c) ) ( ) , , , ( 2 1 s i i s i i r L l b r w p h = - ∑ = , (17d) s i s i h n = , (17e) 0 2 1 N H n b i s i ≤ = ∑ = .
In that regime, the equilibrium entitlement rental price is zero (equation 17a).

Individual land demands are defined by equation 17b and the land market equilibrium by equation 17c. The latter shows the equilibrium rental price is the one that would occur in a regime where the support would be granted through per-hectare direct aids of unit amount b ,

Introducing the possibility not to produce on eligible hectares

Producer maximization program

We now introduce the third characteristic of the SPS, i.e., the possibility not to produce on hectares that however can activate payment entitlements. This possibility is constrained by the fact that non-cultivated hectares be maintained in GAECs. Let us denote ) ( i i m CJ the cost function for farmer i of maintaining i m non-cultivated hectares in GAECs. This cost function

) ( i i m CJ
is assumed positive, non decreasing and concave in land quantity. Assuming that there is no specific cost of maintaining land in GAECs on cultivated hectares, the cost of maintaining i g non-cultivated hectares in GAECs when i h hectares are already cultivated can then be expressed as:

(18) ) ( ) ( ) , ( i i i i i i i i h CJ g h CJ g h C - + = .
One immediately verifies that the marginal cost of maintaining non-cultivated hectares in GAECs does not decrease with the number i g of non-cultivated hectares and the number i h

of cultivated hectares ( 0 / ) ( / ) ( / ) , ( ≥ ∂ ∂ - ∂ + ∂ = ∂ ∂ h h CJ h g h CJ h g h C i i i i i i i i
).

The producer maximization program 9b now becomes:

(19) ]. 0 ; 0 ); ( ) ( ) ( ) ( ) , , , ( [ max 0 , , i i i i i i i i i i i i i i i i i i i n g h g g h n h CJ g h CJ n n v bn g h r wx l h w p ≤ + ≤ ≤ + + - - - + + - - π
The first-order conditions associated with this program 19 can be expressed as: , respectively. Plugging 20b into 20a, one yields:

(20a) 0 / ) ( / ) ( / ) ( = + ∂ ∂ + ∂ + ∂ - - ∂ ∂ λ π h h CJ h g h CJ r h h i i i i i i i , (20b) 0 / ) ( = + + ∂ + ∂ - - η λ g g h CJ r i i i , (20c) 0 = + - - µ λ v b , (20d) 0 ) ( = - + i i i n g h λ , (
(20g) 0 / ) ( / ) ( = - ∂ ∂ + ∂ ∂ η π h h CJ h h i i i i
.

Land and entitlement demand functions

In what follows, we only consider the "interesting" case corresponding to an entitlement price v strictly lower than the unit value b . When b v ≥ , the demand for idled hectares maintained in GAECs is null and we are brought back to equation 11b and 11c of the previous subsection.

This last result can be shown as follows. Let us assume that b v = : in that case, 0 = = µ λ (from 20c, 20d and 20e) and hence,

η - = ∂ + ∂ - r g g h CJ i i i / ) ( ( from
η - = ∂ + ∂ - r g g h CJ i i i / ) ( (from 20b)
which is possible if and only if 0 = i g .

We thus only consider an entitlement price regime such that b v < . Under this assumption, 0 > λ (from 20c),

i i i g h n + =
(from 20d) and 0 = µ (from 20e). First-order conditions (20a), ( 20b) and (20f) can then be expressed as:

(20'a) b v r h h CJ h g h CJ h h i i i i i i i - + = ∂ ∂ + ∂ + ∂ - ∂ ∂ / ) ( / ) ( / ) ( π , (20'b) η - - + = ∂ + ∂ - b v r g g h CJ i i i / ) ( , (

prices): this arises because

0 / ) ( / ) ( ≥ ∂ ∂ - ∂ + ∂ h h CJ h g h CJ i i i i i
. Let us then assume that there exists a strictly positive number of hectares

i h ~ such that 0 / ) ( / ) ( < = ∂ -∂ = ∂ ∂ i i i i i c h h CJ h h π ; i h ~ exists if and only if 0 / ) ( / ) ( 2 2 2 2 < ∂ ∂ < ∂ ∂ h h CJ h h i i i i π
, an inequality which is supposed satisfied from now on. Equation (20g) then shows that the number of hectares demanded for cultivation i h is lower than or equal to this threshold i h ~. Two sub-cases have then to be

distinguished depending on b h h CJ i i + ∂ ∂ - / ) (
is positive or negative.

In the first sub-case when 0

/ ) ( ≤ + ∂ ∂ - b h h CJ i i
, let us assume that the land demand for idling under GAECs is strictly positive ( 0 > i g

). In that case, 0 = η (from 20'f), equation

(20g) becomes 0 / ) ( / ) ( = ∂ ∂ + ∂ ∂ h h CJ h h i i i i
v r b h g h CJ i i i + = + ∂ + ∂ - / ) ( which is impossible for 0 > i g under the assumption 0 / ) ( 2 2 < ∂ ∂ h h CJ i i .
As a result, the land demand for idling under GAECs is null and we are brought back to the first regime of the previous subsection 3.3. More specifically, the land demand function for cultivation is defined by equation 21a, the land demand function for idling under GAECs by equation 21b and the entitlement demand function by equation 21c:

(21a) b v r h h i i - + = ∂ ∂ / ) ( π , (21b) 0 = i g , ( 21c
) i i h n = .
In the second sub-case when 0

/ ) ( > + ∂ ∂ - b h h CJ i i ,

(i) When

b g h CJ v r i i + ∂ + -∂ ≥ + / ) 0 (
, the land demand for idling under GAECs is null and the three demand functions are defined by equations 21a to 21c.

(ii) When b g h CJ v r i i + ∂ + -∂ ≤ + / ) 0 (
, the land demand for idling under GAECs is positive and the three demand functions can be expressed as:

(22a) i i h h = , (22b) b v r g g h CJ i i i - + = ∂ + ∂ - / ) ( , ( 22c
) i i i g h n + = ~.
Figure 4 presents the demand functions for cultivated hectares, idled hectares under GAECs and entitlements in this second sub-case when 0

/ ) ( > + ∂ ∂ - b h h CJ i i .

The land demand function for cultivation corresponds to the broken line

i h AB ~: for a price sum b h h CJ v r i i + ∂ -∂ ≥ + / ) ( ) ( ) 1 (
, the land quantity demanded for cultivation ( ) 1 ( i h ) is identical to the total land quantity demanded ignoring the possibility not to produce; for a price sum

b h h CJ v r i i + ∂ -∂ < + / ) ( ) ( ) 2 (
, the land quantity demanded for cultivation is limited to the threshold i h ~, the land quantity demanded for idling under GAECs is strictly positive ( 0

) 2 ( > i g
), and the total land quantity demanded is greater that the land quantity the farmer would have demanded ignoring the possibility not to produce while benefiting from payment entitlements (

) 2 ( ) 2 ( ~i i i h g h < + , where ) 2 ( i h is solution of ) 2 ( ) 2 ( ) ( / ) ( v r b h h i i + = + ∂ ∂π
).

(Insert Figure 4)

Market equilibriums

We only consider the "interesting" case where the demand for idled hectares under GAECs can be positive. More specifically, we assume that the following condition is met for both farmers 1 and 2:

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(condition i)

b g h CJ i i + ∂ + -∂ ≤ / ) 0 ( 0 .
By definition of i h ~, one immediately verifies that

∑ ∑ = = = < = 2 1 2 1 ĩ i i wp i wp h H h H
. But H ~ can be lower than, equal to or greater than b H . As a result, the two orderings are possible:

either H H H b wp ≤ < , or b wp H H H ≤ < ~.
In what follows, we do not explicitly consider the first orderings which leads to a land demand for idling under GAECs equal to zero at equilibrium: we are brought back to the policy situation considered in the previous subsection which ignored the possibility not to produce. We only explicitly consider the second ordering which leads us to distinguish four regimes depending on whether

wp H N ≤ 0 , H N H wp 0 ≤ ≤ , G H N H 0 + ≤ ≤ or 0 ~N G H ≤ +
where the threshold G ~ is defined by: 21 (23a)

∑ = = 2 1 ĩ i g G with i g ~ defined by ) ( )] ( ) / ) ( [( 2 1 1 G i G i i i r L r b g g h CJ = + ∂ + -∂ ∑ = - .
We successively consider the four regimes which are illustrated by Figure 5. The latter is drawn in the simplified case where producers 1 and 2 are assumed identical in terms of production, cost and profit structures; they can however differ in terms of initial endowments in entitlements.

(Insert Figure 5) Regime 1. ) ( 0 wp wp r L H N = ≤
In that first regime illustrated by the limit case where

(24b)

i s i h h = with i h ~ defined by 0 / ) ( / ) , , , ( < = ∂ -∂ = ∂ ∂ i i i i i i i c h h CJ h l h w p π , (24c) H h H i i s 21 = = ∑ = , (24d) ) ( 0 s r L N = , ( 24e
) ) ( )] ( ) / ) ( [( 2 1 1 s i s s i i r L v r b m m CJ = + + ∂ -∂ ∑ = - , (24f) b v r g g h CJ s s s i i i - + = ∂ + ∂ - / ) ( , (24g) H N g G i s i s 0 2 1 - = = ∑ = , ( 24h
)
s i i s i g h n + = ~, (24i) G H N n i s i 0 2 1 + ≤ = ∑ = .
Equation 24d defines the equilibrium land rental price while equation 24e defines the equilibrium entitlement rental price, once the equilibrium land price is determined. Equations 24b and 24c define the individual and total land demand functions for cultivation, respectively. Equation 24f defines the individual land demand functions for idling under GAECs and equation 24g defines the total land demand for idling under GAECs. Finally, equations 24h and 24i define the individual and aggregate entitlement demand functions, respectively.

Payments capitalize in land and entitlement prices; the degree of capitalization in land prices (respectively, entitlement prices) increases (decreases) with the number of entitlements; in the upper limit case corresponding to a number of entitlements 0 N set to G H + , capitalization in land prices is maximum while capitalization in entitlement prices is null

( 0 = s v
).

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28

Relative to the zero support regime, one immediately notes that the SPS has a positive effect on the number of hectares in cultivation ( wp H H > ~): the SPS is not decoupled at the extensive margin of production. More interesting is the comparison of the SPS with a policy regime where support is granted through per-hectare direct aids of unit amount b assuming that production is required to benefit from these area payments. In that alternative policy regime, there is no land demanded for idling and the land demanded for cultivation is equal to b H . Recalling that we assumed here that

b H H < ~, one verifies that G H H b + <
: Total land used in the agricultural sector is greater in the SPF policy regime relative to the regime of perhectare direct aids, but part of the land demanded is not cultivated so that the number of hectares under cultivation is lower in the SPS relative to the policy regime of area payments.

Regime 4.

0 ~N G H ≤ +
In that fourth regime illustrated by the limit case where G H N ) 4 ( 0 5, the number of hectares demanded for cultivation is H ~, the number of hectares demanded for idling under GAECs is G ~, the land equilibrium price is equal to G r (payment capitalization in land prices is maximum) and the entitlement equilibrium price is equal to zero (payment capitalization in entitlement prices is null). There is an excess of entitlements relative to the total number of hectares used in the agricultural sector: the quantity 0

+ = on Figure
) ( 0 ≥ + - G H N of
entitlements is not activated.

Implications and concluding remarks

The main conclusion that can be drawn from the analysis developed in the previous section is that the very nature of the new CAP single farm payment scheme adopted in the UE in 2003 depends crucially on the global number of entitlements which are initially made available.

Two situations have two be distinguished depending on the shapes of (i) the aggregate (Insert Figure 6)

The first case (panel (a) of Figure 6) corresponds to the situation where the number of hectares that would be demanded for cultivation in a policy regime where the support is granted through direct aids per hectare of unit amount b and production is not required is greater than the number of hectares that would be demanded in the same policy regime but production is required (i.e., the case where b H H ≥ ~). Then:

-when the initial number of entitlements is lower than or equal to the number of hectares that would be demanded by farmers for cultivation in a regime where no support is granted ( wp H N ≤ 0 ), SFP entitlements work as lump-sum transfers which only have the effect of raising the income of farmers: relative to the no support regime, neither do they modify the amount of land that is demanded, nor do they capitalize into the land rental price.

-when the initial number of entitlements is greater than or equal to the number of hectares that would be demanded by farmers for cultivation in a no-support regime and lower than or equal to the number of hectares that would be demanded for cultivation in a policy regime where the support is granted through direct aids per hectare of unit amount b and production is required (

b wp H N H ≤ ≤ 0
), SFP entitlements work as direct aids per hectare that would be granted on a binding base area (defined as 0 N hectares): the total land demanded for production increases to the base area 0 N and the land rental price raises as part of the support granted through SFP entitlements capitalize into it.

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30

-eventually, when the initial number of entitlements is greater than or equal to the number of hectares that would be demanded by farmers for cultivation in a policy regime where the support is granted through direct aids per hectare of unit amount b and production is required ( The second case (panel (b) of Figure 6) takes place when the number of hectares that would be demanded for cultivation in a policy regime where the support is granted through direct aids per hectare of unit amount b and production is not required is lower than the number of hectares that would be demanded in the same policy regime but production is required (i.e., when b H H ≤ ~). Then:

-as before, when the initial number of entitlements is lower than or equal to the number of hectares that would be demanded by farmers for cultivation in a regime where no support is granted ( -when the initial number of entitlements is greater than or equal to the number of hectares that would be demanded by farmers for cultivation in a no-support regime and lower than or equal to the number of hectares that would be demanded for cultivation in a policy regime where the support is granted through direct aids per hectare of unit amount b and production is not required ( H N H wp 0 ≤ ≤

), SFP entitlements work as direct aids per hectare that would be granted on a binding basearea-equivalent of 0 N hectares.

-when the initial number of entitlements is greater than or equal to the number of hectares demanded for cultivation and lower than or equal to the total number of hectares demanded (for cultivation and for idling) in a policy regime where the third, the land rental price is raised relative to the no support regime.

-ultimately, when the initial number of entitlements is greater than or equal to the total number of hectares that would be demanded by farmers (both for cultivation and idling) in a policy regime where the support is granted through direct aids per hectare of unit amount b and production is not required ( 32 entitlements acts as a binding base area, or because the possibility not to produce reduces the demand for cultivation). Therefore, for models that cannot fully represent the working of the joint land and entitlements markets and voluntary idling of land as we did in this article, i.e., for models such as those examined in Section 2, the "coupling factor strategy" (be it implicit as in the case of GE models) appears to be a suitable solution; calibrating the coefficient that weights the unit value of entitlements is an empirical, yet difficult, task. Still, modellers who do represent the land market but do not incorporate the voluntary possibility not to produce must keep in mind that they might underestimate the impact of SFP entitlements on the land rental price when the latter are introduced as weighted direct aids per hectare: we have seen that, when some hectares are demanded for idling under GAECs, the total demand for land induced by the SPS overruns the sole demand for cultivation induced by "more decoupled" aids per hectare only.

Finally, we would like to raise the issue that, in reality, the situation is even more complex: all other things equal, when, for some reason, the aggregate demand for cultivated land is translated to the right, the three values of 12c) in the text: this equation shows that there is no impact on the land market.

From (11b), we also have -When both farmers 1 and 2 are under endowed (in the sense where

s i i h n ≤ 0
), there is no entitlement exchange: each farmer activates all his initial endowment in entitlements.

-When one of the farmers is strictly under endowed (say

1 1 n h n h wp s - = -
) which is bought by the under-endowed farmer 2.

As a result,

wp s s s H N n h n n h n N ≤ = - + + - - = 0 0 1 1 0 2 0 1 1 0 1 ) ( ) ( .
Annex 2 (or for referee's use)

Equilibrium conditions of regime II when

b rw wp H N r L H ≤ ≤ = 0 ) (
The demonstration is analogous to that developed in Annex 1. H is the total demanded area in the no-support regime). The superscripts "s" and "sne" denote equilibrium variables, respectively when SFP entitlements are tradable and when SFP entitlements cannot be exchanged. H is the total demanded area in the no-support regime, b H is the total number of hectares that would be demanded in the regime where support would be granted through direct aids per hectare of unit amount b , and H ~ and G ~ are the numbers of hectares that are demanded for cultivation and idling under GAECs, respectively, in a policy regime where income support is granted through direct aids per hectare of unit amount b and production is not required. H is the total demanded area in the no-support regime, b H is the total number of hectares that would be demanded in the regime where support would be granted through direct aids per hectare of unit amount b , and H ~ and G ~ are the numbers of hectares that are demanded for cultivation and idling under GAECs, respectively, in a policy regime where income support is granted through direct aids per hectare of unit amount b and production is not required.

Annex 3 (or for referee's use)

Equilibrium conditions of regime III when

values of SFP entitlements differ among farmers, we have to consider as many entitlement rental prices as agricultural producers. However one shows that equilibrium entitlement rental prices then verify 0

≥ = - d v b i i
, where d is a non-negative common value, whatever the farmer i (intuitively, this occurs to exhaust arbitration possibilities, i.e., the possibility for a farmer say 1 to make a gain by selling his equilibrium entitlement demand and buying the same quantity from another farmer say k in a situation where 17 The analysis excludes the uninteresting case where the land rental price is so high that the marginal profit of the first hectare is lower than the land rental price. In other words, as previously noted, we only consider the case where 0 > i h .

18 A farmer will be said over endowed (respectively under endowed) when his initial endowment in entitlements is strictly higher (lower) than the number of hectares he would demand under a zero support regime.

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Proposition 1 .

 1 Direct aids per hectare capitalize at least partially in land prices. The lower the land supply elasticity, the higher the capitalization in land prices. Capitalization is complete when per-hectare direct aids are identical for all outputs and the land supply function is perfectly inelastic. Own effects of per-hectare direct aids are positive and cross Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (

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  Equations 10a to 10d allow to derive the land demand function and the entitlement net demand function for farmer i as follows. 17 Let us first assume that b

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Figure.

  Figure 2 corresponds to the limit case where

  leased in by the under-endowed farmer 2. With respect to the zero support regime, the over-endowed farmer 1 gains area AMOG . With respect to the non tradable SFP regime, he gains JFMO IJLK + .

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  17

..

  The effects of a change in the number of entitlements on land and entitlement equilibrium prices are obtained by differentiating equations 13c and 13d Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).18An increase in the number of entitlements raises the land rental price (equation 14a) and diminishes the entitlement rental price (equation 14b). The equilibrium land rental price is thus an increasing function in the number of payment entitlements, raising from restates the previous analysis.Proposition 3. When the initial number of entitlements is strictly greater than the number of hectares which would be demanded in the zero support policy reference situation( 0 N H wp <) and lower than or equal to the number of hectares which would be demanded in a regime where support would be granted through direct aids per hectare of unit amount b (

N

  in Figure 3): the land market equilibrium then occurs at Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

  2), one shows that the both farmers gain from exchanging entitlements relative to a non tradable SFP regime. Finally, let us consider the upper bound corresponding toIn that third regime, the initial number of entitlements is greater than or equal to the number of hectares which would be demanded in a regime where support would be granted through direct aids per hectare of unit amount b (

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  20

  As a result, the total number of demanded hectares is follows from this equality and equation 17d that the number of demanded entitlements is that increasing the total number of entitlements over b H has no impact on land and entitlement market equilibriums; but when are not activated.The following proposition summarizes the previous analysis. Proposition 4. When the initial number of entitlements is greater than or equal to the number of hectares which would be demanded in a regime where support would be granted through direct aids per hectare of unit amount b ( equilibrium rental price of entitlements is zero while the equilibrium rental price of land and the total number of demanded hectares are the same as if the support was granted through direct aids per hectare of unit amount b ., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

  21

,

  Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale(2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA(2007-12-13 -2007-12-14). µ and η are the positive Lagrange multipliers associated with the inequality constraints

  a) shows that the number of hectares demanded for cultivation decreases with respect to the situation considered in the previous sub-section where the possibility not to produce on eligible hectares was not taken into account (for identical land and entitlement Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

π

  (the number of hectares demanded for cultivation is equal to the threshold i h ~), and equation 20'b reduces to

  the land demand for idling under GAECs can be positive if the sum of the land price plus the entitlement price is sufficiently low. More specifically: Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

  under GAECs equals zero. Equilibrium conditions are defined by equations 12a to 12e and Proposition 2 holds. In that first regime, the SPS has no impact on individual land demands for cultivation, on total land demanded for cultivation and on the equilibrium land rental price. There are entitlement exchanges at a unit price b v s = from the over-endowed producer (if he exists) towards the under-endowed producer (if he exists). Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14). is still equal to zero. Equilibrium conditions are defined by equations 13a 13f, except that b H should be replaced by H ~, and Proposition 3 holds. In that second regime, the SPS has a positive impact on individual land demands for cultivation, on total land demand for cultivation and on the equilibrium land price (relative to the no-support regime). Payments partially capitalize in land prices: the higher the number of entitlements, the greater the capitalization in land prices. Payments also capitalize in entitlement exchange prices: the higher the number of entitlements, the lower the capitalization in entitlement prices. if he exists) towards the under-endowed farmer (if he exists). More generally, equilibrium conditions in that third regime with G Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

  Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14). 29 marginal profit function, (ii) the aggregate marginal cost function of maintaining noncultivated land in GAECs and (iii) the aggregate marginal land supply function; these two cases are illustrated in the two panels of Figure 6 which helps summarising and interpreting our findings.

  entitlements work just as unlimited direct aids per hectare: the total land demanded for production is b H , the capitalization of support into the land rental price is complete and the base-area-equivalent 0

  entitlements work as lump-sum transfers.

  G ~ will decrease so that the quantity G H + holds constant. The recent and sharp increase in (most) agricultural prices is an illustration of this process; the same reasoning would be true when comparing regions exhibiting different efficiency levels in production or different cost of maintaining land in GAECs. In other words, it appears that the bounds of the intervals on which the SFP entitlements should be regarded as lump-sum transfers or as weighted area payments, and the magnitude of this weight when convenient, should in practice be an endogenous feature of the model.In that case, land and entitlement demand functions by farmers 1 and 2 are defined by conditions (11a) in the text. is satisfied, total land used in the agricultural sector is lower in the SFP support regime relative to the zero support reference situation. As a result, e., an increase in total land supply to the agricultural sector which contradicts the assumption that total land demanded by the farm sector decreases in the SFP support regime relative to the zero support reference situatione., that total land used in the agricultural sector is identical in both the SFP support regime and the zero support reference situation. As a result, the agricultural sector does not change in the SFP support regime relative to the zero support reference situation. land used in the agricultural sector is greater in the SFP support regime relative to the zero Version postprint Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14). total land used in the agricultural sector increases in the SFP support regime relative to the zero support reference situation. To summarize, we cannot have b v s < in the first regime where the initial number of entitlements is lower than or equal to the number of hectares which would be demanded in the zero support reference situation. Case (b): b v s > In that case, land and entitlement demand functions by farmers 1 and 2 are defined by conditions (11c) in the text. Each farmer leases out all his initial endowment in entitlements unit. One immediately verifies that this case (b) is impossible since all farmers sell all their payments entitlements, but there is no entitlement demand. Case (c): b v s = The only possible case is thus characterized by a equilibrium price of entitlements equal to their (common) unit value, i.e., b v s = . In that case, land and entitlement demands by farmers 1 and 2 are defined by conditions (11b) in the text. We thus have b v s = (equation 12a in the text) and r

  in the text). And finally, document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale(2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA(2007-12-13 -2007-12-14). fact that there is a deficit in entitlements with respect to the number of hectares demanded by the agricultural sector (

  and there is entitlement exchange (at a market price of b v s = ) from the over-endowed towards the underendowed producer; more specifically, the over-endowed farmer 1 sells all his

Figure 1 .Figure 2 .

 12 Figure 1. The land market equilibrium in the no-support regime.

Figure 3 .

 3 Figure 3. Land market equilibria in the SFP support regime without the possibility not to produce for different initial global endowments 0 N (a) .

Figure 6 .

 6 Figure 6. The land and entitlement rental prices as functions of the global initial number of entitlements (a) When H ~ is such that H H H b wp ≤ < (b) When H ~ is such that

  the results derived in the text remain valid since, as we will show, what matters in behavioural and equilibrium equations is the difference i i v bfor all farmers i.

3.2. Introducing directs aids per hectare

																			1 h wp ≡	1 h	1 p	w	r	wp		1 l			and farmer 2 leases in the land quantity
	2 h wp ≡	2 h	(	p	2	,	, w	r	wp	,	l	2	)	.
		(insert Figure 1)
	In a regime where agricultural income support is granted through direct aids per hectare,
	program 1 becomes:
	(4)	max , x	h	[	p	i	y	i	-	wx	i	-	i rh	+	a	i	i h	;	y	i	=	f	i	(	x	i	,	i h	,	l	i	)]	≡	θ	i	(	p	i	,	, w	r	-	a	i	,	l	i	)	,
	where i a denotes the per-hectare direct aid for farmer i . 14
																			Comment citer ce document :
	Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale
	(2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or…
	something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p.
	1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

  Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

	support is granted through direct aids per hectare of unit amount b and production is
	not required (	H	≤	N	≤	H	+	G 0 ), SFP entitlements have three effects: first, they
	induce an aggregate land demand for cultivation of H ~ which is greater than the
	demand that would occur in the no support regime (	H H wp ≤ ), but to a lesser extent
	than direct aids per hectare would (	b ~); second, the total land demanded is H H ≤
	constrained by the base-area-equivalent 0 N and part of this land (	N	H 0 -) is idled;
									31

  support into the land rental price, is smaller than the one of true direct payments per hectare of the same unit amount (either because the total number of available Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

								H	+	~N G ≤	0	), H ~ hectares are
	demanded for cultivation, G ~ hectares are demanded for idling under GAECs, the
	capitalization of support into the land rental price is complete, and there exists a
	quantity of	N	0	-	H	+	) ( G entitlements which is not activated.
	Recommendations to modellers can be drawn from this analysis. First, since he SPS put in
	place by the EU in its latest CAP reform does not build on a no-support regime but inherits
	from the previous 1992-199 reforms, it is our believe that SFP entitlements should not be
	modelled as lump-sum transfers; in other words, we think that there is little chance that,
	empirically,	N ≤ 0	H	wp	in the EU. Second, if we thus hypothesise that most likely	H wp ≤	N	0	,
	we have seen that it is then relevant to model the SFP entitlements as "more decoupled" direct
	aid per hectare: here, the expression "more decoupled" means that the impact of the support
	granted through SFP entitlements, both in terms of aggregate land demand for cultivation and
	capitalisation of the

  19 Farmer 1 gains area AFHG = AFJG + JFH and looses area IFHLK = IJLK + JFH.

	20	0 1 n	(	2	)	-	1 h s	(	2	)	=	2 h s	(	2	)	-	0 2 n	(	2	)	since	0 1 n	(	2	)	+	0 2 n	(	2	)	=	N	0	(	2	)	=	H	s	(	2	)	=	1 s h	(	2	)	+	2 s h	(	2	)	.

Prices, costsQuantities

This assumption does not alter our findings regarding the modelling of the SPS. When unit

Version postprint

Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

Version postprint

Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14 2007-12-13 -2007-12-14).

44

Figure 5. Land market equilibrium in the SFP support regime with the possibility not to produce for different initial global endowments 0 N (a) . 4 That is as long as the farmer complies with environmental, animal and plant health, animal welfare and food safety standards, as well as he maintains land in Good Agricultural and Environmental Conditions (GAECs).

5 Farmers are profit maximizers, there is no uncertainty and all markets are competitive.

Hence the zero support regime also depicts a situation where agricultural income support is granted through lump-sum transfers (except that agricultural income is increased by an amount equal to these lump-sum transfers).

Version postprint

Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14). 47 6 Article 44.3 of the Council Regulation (EC) 1782/2003 specifically stipulates that "the parcels shall be at the farmer's disposal for a period of at least 10 months" of the cropping year during which the payments are applied for. 7 Per-hectare direct aids granted to cereals, oilseeds and protein crops can be maintained in Member States which decide to decouple only partially in the COP sector. However unit perhectare amounts are considerably reduced with respect to pre-2003 levels. Only France and Spain chose to maintain partially coupled the support in the COP sector.

8 Gohin (2004, 2006) is actually one of the few who compares the effects of considering 2003 EU payments as either lump-sum transfers versus area subsidies. 9 The Policy Evaluation Model (PEM) developed by the OECD (Organisation for Economic Co-operation and Development) is a noticeable exception. In this PE model, the land market representation is very similar to the one adopted in GE modelling frameworks.

10 Area payments are then expressed per ton of product.

11 See also von Witzke et al. (2007) who conclude that in a typical German farm, the 2005/06 land rental price would be negative in the absence of agricultural subsidies.

12 For a review, see Balkhausen et al. (2007), Table 4. 13 We do not impose that the two farmers produce the same output. 14 We do not constraint per-hectare direct aids to be equal for the two farmers since we do not impose that they both produce the same output (see footnote 13). However we do not allow a given farmer to shift, even partially, from one production to another. 48 15 Equation (6) assumes that output and variable input prices, as well as family labour endowments, are kept constant. One easily shows that the equilibrium land rental price is an increasing function of output prices and as a result, that an output price support policy also capitalizes, at least partially, into land prices.

Comment citer ce document : Courleux, F., Guyomard, H., Levert, F., Piet, L., INRA, Société Française d'Economie Rurale (2007). How the EU single farm payment should be modelled: lump-sum transfers, area payments or… something else ?. In: 1ères journées INRA-SFER de recherches en sciences sociales [Actes] (p. 1-49). Presented at 1. Journées INRA-SFER de recherches en sciences sociales, Paris, FRA (2007-12-13 -2007-12-14).

49 21 The threshold G ~ correspond to the number of hectares that are demanded for idling under GAECs in a policy regime where income support is granted through direct aids per hectare of unit amount b and production is not required.


Kirsten Von Der Heiden

Jane M Weatherley

Mark S Paine

Lotten Westberg

Johanna Björklund

Ulrika Geber

Rebecka Milestad

J W A Langeveld

A Crawford

S Pinheiro

W De Boef

I S Kristensen

J Hermansen

B Dedieu

P Hildebrand

V Cabrera

D Jansen

J Dixon

H Morales

J F Tourrand

P Bommel

Reza Movahedi

Uwe Jens Nagel

Nadarajah Sriskandarajah

Dorthe Christensen

Sofie Kobayashi

Henrik Sønksen

Willem Van Weperen

Changing European farming systems for a better future Lessons learned about instigating change towards an AKIS/RD in Brandenburg, Germany

New ways in the management and valorisation of natural resources? Results of a comparative analysis of a sample of agriculture-environment projects of the

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  Introduction to section 2 -Agriculture, land use and sustainable development Artur Cristóvão, Ken Giller, Luigi Omodei Zorini and Philippe Perrier-Cornet Towards sustainable farming: Regional pilots on changing land use under the European Water Framework Directive Sarie Buijze and Frank van Lamoen Sustainable dairy farming systems for a deregulated market in northern Australia R.G. Chataway, R.G. Walker, M.N. Callow and H.L. Todd Network analysis of farming and non-farming activities for sustainable development Caterina Contini, Luigi Omodei Zorini and Roberto Polidori Local organizations in the Douro-Duero region of Portugal and Spain: Towards a pluralistic local animation system Artur Cristóvão, Alberto Baptista and Raquel Miranda Is there a place for small-scale production and local food systems? Artur Cristóvão, Manuel Luís Tibério, Sónia Abreu and Alberto Baptista Marvão polyculture mosaic's fate: Searching the way for a rural area in transition Milena Andrade Dneboská, Teresa Pinto-Correia and Patricia Pedro-Rêgo Institutions for anthropogenic nature: Case study from Brabant Niels Röling and Janice Jiggins The construction of a coherent vision for territorial development Markus Schermer Urban oriented agriculture: The case of Almere (The Netherlands) Derk Jan Stobbelaar, Marleen Warnaar, Jan Eelco Jansma and Walter A.H. Rossing Evaluation of landscape preferences of Montado in southern Portugal as a contribution for management Diana Ježová and Teresa Pinto The labour organization of small-scale breeders in the Brazilian Amazon is a key point for sustainable development Nathalie Hostiou, Jean-François Tourrand, Jonas Bastos da Veiga, Ailce Margarida Negreiros Alves and Tienne Barbosa Commercial flexibility of beef cattle farms Stéphane Ingrand, Eduardo Chia, Charles-Henri Moulin and Julie Cessieux

	Organic manure availability, food security and poverty relationships at farm level in
	the old cotton basin of Mali
	M.S. Keita, J.F. Bélières, J. Coulibaly, B. Rapidel and R. Poccard-Chapuis
	Modelling environmental benefits of silvoarable agroforestry in Europe
	J.H.N. Palma, A.R. Graves, R.G.H. Bunce, P.J. Burgess, R. de Filippi, K.J. Keesman, How are European farmers dealing with global environmental changes?
	H. van Keulen, F. Liagre, M. Mayus, G. Moreno, Y. Reisner and F. Herzog C. Macombe
	Biomass production, transformation and allocation at the village scale in Southern The future of farming in Norway: Processes of recruitment and intergenerational
	Mali: Development of a conceptual model transitions
	Bruno Rapidel, René Poccard-Chapuis, Jean-François Bélières, Bouba S. Traoré, Kjersti Melberg and Christin Berg
	Jacob Coulibaly, Drissa Diallo and Matthieu Lessnoff
	Farmers' new participation in food supply chains: Making horizontal and vertical
	progress by networking
	Minna Mikkola and Laura Seppänen
	The contribution of non-farm small-medium enterprises to rural development
	H. Theodoropoulou and S. Kyriakopoulou
	Agrobiodiversity as driving force of sustainable rural development
	Menko Wiersema and Frans van Alebeek
	Reconnecting conservation & livelihood objectives through non-timber forest product
	certification
	David S. Wilsey
	Socio-cultural issues of dairy production systems in the Netherlands: Results of farm
	visits with six citizen panels
	B.K. Boogaard, S.J. Oosting and B.B. Bock
	Socio-cultural values of Dutch dairy systems: Case study in the Krimpenerwaard and
	the Alblasserwaard on farm and landscape level
	Daniël de Jong, S.J. Oosting and B.K. Boogaard
	Carbon stocks in smallholder agroecosystems in Malawi: A farming systems approach
	Peter Hildebrand and Paul Thangata

  Regional Action pilot programme in Germany Karlheinz Knickel, Melanie Kröger and Sarah Peter Activating farmers' interests: Action research for biodiversity conservation and enhancement in Brandenburg Andrea Knierim and Harald Kächele Structural development in Danish agriculture and its implications for farmland nature Gregor Levin, Vibeke Langer and Pia FrederiksenThe livestock commodity chain: A lever for monitoring pioneer dynamics in the Brazilian Amazon Region? René Poccard-Chapuis, Marcelo Thales, Adriano Venturieri, Marie-Gabrielle Piketty, Benoit Mertens, Jonas Bastos da Veiga and Jean-François Tourrand Differentiation of territories according to the location of agricultural activities: Methods for regional scale approaches V.Souchère, C. Mignolet, C. Schott, E. Bienaimé and M. Benoît Opportunities and constraints of farming styles to meet the landscape preferences of rural inhabitants Derk JanStobbelaar, Florien Kuijper, Henk Renting, Jeroen C.J. Groot, André Jellema and Walter A.H. Rossing Farmer-driven protection of meadow birds in the Friesian Woodlands (northern Netherlands) Paul Swagemakers Linking landowner type and landscape functions: A proposal for an integrated approach from southeast Portugal Anne van Doorn

	Re-inventing sustainable cropping systems in Costa Chica, Mexico
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	and Ariena H.C. van Bruggen

Towards a dairy system that produces more than milk Jan J.H.M. Ketelaars, Frits K. van Evert and Ben Rutgers Organic and integrated farming systems in Greece: A comparative analysis Eleni Oxouzi, Athanasios Theocharopoulos, Vasilis Bagiatis and Evangelos Papanagiotou

The socioeconomic integration of expatriates in the rural prefecture of Rodopi, Greece H. Theodoropoulou and E. Pastrapa Rural policy in Europe: Experiences with the LEADER approach in the Netherlands Anouk van Gils Supporting discussions on land use: A design instrument that integrates nature conservation, economic performance and landscape quality in agricultural areas Jeroen C.J. Groot, Walter A.H. Rossing, Derk Jan Stobbelaar, Henk Renting and Martin K. van Ittersum


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

Genetic analysis reveals a rapid evolution of population structures of Botrytis cinerea after the introduction of isolates in tomato glasshouses

Véronique Decognet, Marc Bardin, Yannie Trottin-Caudal, Philippe C. Nicot

To cite this version:

Véronique Decognet, Marc Bardin, Yannie Trottin-Caudal, Philippe C. Nicot. Genetic analysis reveals a rapid evolution of population structures of Botrytis cinerea after the introduction of isolates in tomato glasshouses. 14. International Botrytis Symposium, Oct 2007, Cape Town, South Africa.

hal-02755622

Comment citer ce document : Decognet, V., Bardin, M., Trottin-Caudal, Y. (Collaborateur), Nicot, P. (2007). Genetic analysis reveals a rapid evolution of population structures of Botrytis cinerea after the introduction of isolates in tomato glasshouses. In: Abstracts book (p. 57). Presented at 14. International Botrytis Symposium, Cape Town, ZAF (2007-10-21 -2007-10-26).

Genetic analysis reveals a rapid evolution of population structures of Botrytis cinerea after the introduction of isolates in tomato glasshouses

Véronique Decognet 1 , Marc Bardin 1 , Yannie Trottin-Caudal 2 and Philippe Nicot 1

1 INRA, Unité de pathologie végétale, BP94, Domaine St Maurice, F-84140 Montfavet, France, Email: Veronique.decognet@avignon.inra.fr; 2 CTIFL, Centre de Balandran, BP32, F-30127 Bellegarde, France Botrytis cinerea can rapidly produce massive amounts of inoculum on diseased plants. In addition to the endogenous inoculum, the airborne spora of Botrytis over a canopy may also include exogenous inoculum carried from a variety of hosts in open fields or even greenhouses. The relative proportion of both types of inoculum may influence the efficacy of control methods and the impact of selective pressures resulting from their implementation.

A trial was set up to quantify the impact of endogenous inoculum on disease development and on the population structure of B. cinerea in four compartments of an experimental tomato glasshouse of CTIFL (Balandran, France). Plants were grown in quasi-commercial conditions. Isolates were collected from the air spora 4 days before and 14 days after inoculation, of 6 plants per compartment, with one of two reference strains (differing in their microsatellite profile and aggressiveness on tomato). Disease development was monitored and isolates were collected on stem lesions 60 days after inoculation. All the collected isolates were analysed for their diversity according to 9 neutral microsatellite markers.

Among 80 isolates collected in the air spora prior to inoculation (while all plants were healthy), none had microsatellite profiles similar to either of the reference strains. Following inoculation, lesions developed and sporulation was observed on all inoculation points. Within 14 days, microsatellite profiles identical to those of either introduced strain represented 66% of the 353 isolates characterised from the air spora. The other multilocus genotypes detected from airborne spora were very diverse. The extremely high level of diversity confirms earlier data obtained with B. cinerea populations collected on different hosts and suggests that the entry of spores into the glasshouses (although these structures are usually considered as confined) is probably an important phenomenon which occurred regularly during the growing season.

The disease spread steadily to non-inoculated plants and incidence reached an average of 3-7 lesions per plant by 90 days after inoculation. Among 240 isolates collected from stem lesions at 60 days after inoculation, 58% and 33% had microsatellite profiles similar to the aggressive and to the less aggressive reference strains, respectively. This suggests that the displacement of the initially dominant airborne population of Botrytis was concomitant with its negligible contribution to the epidemic on tomatoes.

These results are compatible with the hypothesis of a polycyclic development of Botrytis epidemics in tomato greenhouses and illustrate the importance of endogenous inoculum in this growing system. Furthermore, they raise the question of possible host specificity within Botrytis cinerea in naturally occurring epidemics as few multilocus genotypes were shared between air-borne and plant populations.