Optimal management of perennial energy crops by farming systems in France: A supply-side economic analysis

Biomass and Bioenergy 116 (2018) 113–121

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Research paper

Optimal management of perennial energy crops by farming systems in France: A supply-side economic analysis

T

Nosra Ben Fradja,b,∗, Pierre-Alain Jayetb a b

Institute of Soil Science and Plant Cultivation, State Research Institute, Dept. of Bioeconomy and Systems Analysis, 24-100, Pulawy, Poland UMR Economie Publique, INRA, AgroParisTech, Université Paris-Saclay, 78850, Thiverval-Grignon, France

A R T I C LE I N FO

A B S T R A C T

Keywords: Perennial energy crop Optimal management Faustmann rule Stochastic process Net present value Optimal rotation period

This paper aims at analysing the sensitivity of supply of a perennial energy crop, i.e. Miscanthus x Giganteus, in France, to yield and economic parameters. We use a decision-making method over natural resources, commonly applied in sustainable forest management, to evaluate the economic potential of the crop at plot level. The method allows us to determine the optimal rotation period (ORP) and the net present value (NPV) of Miscanthus in different farming system types when growth function is accounted for in a non-stochastic way as well as when it is governed by a random process. The short-term agricultural supply model, AROPAj, is used to highlight the competitiveness of Miscanthus regarding other crops within the 157 French farm groups portrayed in the model. We also detail the impact assessment regarding NPV and ORP, land use, Nitrogen (N) fertiliser demand and losses. We find that yields, price, renewal cycle costs and the discount rate may interact with yield randomization and significantly affect the future profitability of Miscanthus. As a result of our economic optimization, and in contrast to the common view of Miscanthus grown on marginal land, this crop could be profitable on the most productive land, generally devoted to food crops. For a price contracted at €70 tons of dry matter and fixed rotation cost given at €3000 per hectare, farming systems are predicted to grow Miscanthus on more favourable areas when its yield potential is high, thus leading to a substantial decrease in N input levels and losses.

1. Introduction Changes in the world's climate and the increased interest in energy security have led to numerous studies on non-food biomass production. If we are to fuel our energy needs with biomass rather than petroleum, large-scale production of biomass is required. Moreover, greenhouse gas emissions (GHG), one of the driving factors behind climate change, can be reduced by using plant-based biofuels because the useful biomass can fix atmospheric carbon [10] and sequester carbon in the soil [4]. Based on lignocellulosic biomass, one of the benefits of second generation (2G) biofuels is that they reduce GHG emissions by up to 85% compared to conventional fuels [26] and can be produced from diverse raw materials such as wood, grasses and crop residues. It is also known that 2G feedstock is more land-use efficient than 1G crops [13] and may therefore be used to ensure bioenergy demand. In fact, growing a high-yielding crop, i.e. Miscanthus, would require 87% less land to produce the same amount of 1G biomass, given that Miscanthus yields are about 15–20 tons dry matter per hectare per year (tdm ha−1y−1) [17]. Miscanthus has other features that make it a sustainable source of

∗

2G bioenergy. With an average lifespan of between 15 and 25 years, Miscanthus is a C4 herbaceous grass suitable for a wide range of European climatic conditions [20]. Moreover, it is an environmentallyfriendly crop, requiring low levels of Nitrogen (N) fertilisers and consequently having a lower risk of nitrate contamination of groundwater. In this study, we have chosen a natural hybrid between Miscanthus sinensis and Miscanthus sacchariflorus, i.e. Miscanthus x Giganteus [16], which is the most experimentally developed hybrid in France. From the economic standpoint, Miscanthus x Giganteus (hereafter referred to as Miscanthus) is harvested annually, thus providing farmers with a yearly income. Since it is sterile, this hybrid requires vegetative multiplication by rhizomes and therefore entails high establishment costs ranging between €2400 and €4800 ha−1 [8]. In addition, Miscanthus is intended to be grown on marginal land in order to circumvent the heated ”Food vs. Fuel” debate. However, some studies have shown this crop has a high-yield potential when it is cultivated on good-quality soil [24]; [25]. Thus farmers opting to cultivate Miscanthus are faced by a major question. They have to reserve the land for a long rotation period of at least 15 years, yet want to ensure a rapid return on investment and a yearly income more or less equivalent to that of existing crops. At

Corresponding author. Institute of Soil Science and Plant Cultivation, State Research Institute, Dept. of Bioeconomy and Systems Analysis, 24-100, Pulawy, Poland. E-mail addresses: [email protected] (N. Ben Fradj), [email protected] (P.-A. Jayet).

https://doi.org/10.1016/j.biombioe.2018.06.003 Received 15 September 2017; Received in revised form 25 May 2018; Accepted 1 June 2018 0961-9534/ © 2018 Elsevier Ltd. All rights reserved.

Biomass and Bioenergy 116 (2018) 113–121

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respectively under non stochastic and random conditions. The value of Miscanthus is determined by using the Faustmann rule, usually associated with forest that is harvested at the end of the cycle. In our case, it is applied to Miscanthus, which is harvested annually.

which date, therefore, will the crop provide the highest market value? In other words, in which year should the final cutting take place, especially given that an expensive biomass resource is being cultivated and that land is needed for other production. In the field of natural resource economics involving perennial landconsuming plants, studies have sought to answer the question of timing by applying Faustmann's rule [12], the method commonly used to address questions of optimal resource management. The rule is well applied especially when the growth function and price of trees are assumed to be known over time. Nonetheless, numerous methods have been developed to generalize the application of this rule. Focusing on optimal rotation, some studies have accounted for uncertainty. Resulting from random fluctuations in the productivity level or from random changes in natural conditions, biomass uncertainty can play a central role in forest management. Different approaches have been developed to deal with this uncertainty. Tree size is modelled through a diffusion process [22] as well as through a geometric Brownian motion [9], with a view to solving the rotation problem [27]. Considers a general stochastic differential equation model for the growth process in continuous time [6]. Models the growth process in discrete time by employing Markov decision processes. Despite the fact that Miscanthus raises a similar question of harvest timing under biomass uncertainty, Faustmann's formula has not to our knowledge been used to analyse this issue. To manage the random yield of Miscanthus, we develop a simple stochastic model in which the yield process is based on a popular distribution, the so-called beta-distribution. Because of its versatility, this distribution has been used by Ref. [23]; among others, to model a variety of uncertainties. It is generally used for representing processes with lower and upper limits, while at the same it has the flexibility to model both positive and negative skewed data. In this study, we address the question of biomass uncertainty in continuous time for a perennial resource. By applying two Faustmann models, we derive harvesting rules to deal with the optimal rotation age and the economic value of Miscanthus when its growth function is accounted for in a non-stochastic way as well as when it is governed by a random process. Given the differences in results between these two cases, we make use of the AROPAj model to highlight them. AROPAj is an optimization economic model of European agricultural-supply. It is a one-year period mathematical programming model, based on a micro-economic approach [2]. Covering most arable crop, grasslands, fodder and livestock farming sectors, the model describes the supply choices of individual farm groups in terms of land allocation and plant and animal production. Farms are grouped into farm groups, within each region, according to their technico-economic orientation, economic size and altitude class. Representative farm groups are assumed to maximise their total gross margin. The feasible production set is driven by modules representing farm characteristics (i.e. crop rotation, animal demography, livestock limit, animal feeding, fertiliser consumption) and different policy measures related to the Common Agricultural Policy and the application of agro-environmental instruments. Other modules describe environmental impacts such as Nlosses, i.e. ammonia (NH3 ), nitrous oxide (N2 O ) and nitrate (NO3 ). Computation of these outputs can be refined when estimated by linking AROPAj with the STICS crop model [15]. In the light of the above, we firstly identify the economic parameters that affect harvest timing and the economic value of Miscanthus, in addition to yield potential. Secondly, we show how the issues of timing and valuation alter when the farmer cannot foresee the future (the stochastic approach) compared to when he can foresee it (the nonstochastic approach). Finally, we address the question of differences between the non-stochastic and random cases, in terms of production, land use and N-losses.

2.1. Non-stochastic value expectation of miscanthus The method we used to calculate the value and optimal rotation age of Miscanthus in the non-stochastic case is explained in Refs. [5] and [3]. These papers detail the two-step procedure used to integrate perennial crops into a one-year period optimization model. First, the continuous time-yield function is correlated with a control plant yield, i.e. cereals, to deal with the lack of information on yield. Second, the optimal rotation period and value are estimated using a Faustmann dynamic approach. Based on the Faustmann decision rule, the farmer's goal is to decide on the rotation period T that maximises the intertemporal economic value of Miscanthus. The net cumulative profit over one rotation of duration T is as follows: T

Vm (T ) = −c0 +

∑ M (t ) e−(δ −α) t

(1)

t=1

where c0 is the establishment cost paid off over each T-cycle duration at t = 0 , and δ and α are the discount and inflation rate, respectively. M (t ) is the annual gross margin. Commercial harvesting starts at the second year, so that M (1) = 0 , and for t 2, t ≥ 2 , M (t ) = pt y (t ) − ct , where ct are the annual production costs paid at any of the T years and pt is the price of a ton dry matter of the harvested yield at t. In opting for cultivating Miscanthus on 1 ha, the farmer is assumed to maximise its cumulative profit over infinite time denoted by W (T ) ∞

W (T ) =

∑ Vm (T ) e−δnT

(2)

n=1

The general principle of our optimization process is divided into three steps: (i) we first maximise W against T; (ii) we deduce the annual net equivalent value Vm (T ) and average yield over one period; and (iii) we integrate the new crop, i.e. Miscanthus, into the set of eligible activities in AROPAj in which land allocation is optimally computed. The first step of the process is based on a yield estimation according to a growth function y (t ) defined for a growing cycle and expressed as follows:

⎛ 1 y (t ) = a ⎜ b−t ⎜ 1+e c ⎝

(

−

1

) (1 + e ) b c

⎞ ⎟ e−dt ⎟ ⎠

(3)

The y-parameters reflect three phases: an initial increasing phase with a possible inflexion point (b), an intermediate stabilisation phase at a maximum level (a), and lastly a decline phase described by a spreading parameter (c) and an attenuation coefficient (d). 2.2. Introduction of a random process into the faustmann modelling In this section, we suppose that only biomass quantity is random and all the other economic factors are unchanged. The random yield process is based on a beta distribution that represents how the harvest yield expectations change during a rotation period. The first period begins at time t = 0 , the planting date, and continues to t = T , the clear-cutting date. We are interested in yield expectations at each time t. We assume that yield realizations are positive and finite, and that the distribution is restricted to values between 0 and the value given by the potential function y (t ) . To generate a random process, each yearly expected yield is multiplied by εt = E [y͠ (t )] and each random yield y͠ follows a beta distribution. The standard beta probability distribution function for a random variable y͠

2. Materials and methodological approach for economic estimates We calculate the optimal value and rotation age of Miscanthus 114

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Fig. 1. Miscanthus yield distribution of generated random yields (dotted lines) fitted by three potential yield curves (solid lines): low, medium and high.

low and nitrate leaching is possibly high in the two first years following planting [19]. We thus assume that little N fertiliser (around 60 kgN ha−1) is applied from the third year, when the rhizome system has become well developed, until the end of the rotation period. Hence Nlosses are assumed to be equal to zero (fertilising cost is included in ct ).

is

f (y͠ , β , γ ) =

y͠ (β − 1) (1

y͠ )(γ − 1)

− B (β , γ )

(4)

1 β−1 t (1 0

− where B (β , γ ) = ∫ , 0 < y͠ < 1, and β, γ > 0 . The proposed technique consists of generating, at each time t, samples of yield according to the theoretical beta function given by Equation (4). This randomized generation is renewed over a large number of succeeding cycles, when the cycle length is given. The sample beta distribution is fitted by an envelope represented by y(t) (Equation (3)). Random samples generated for three cases of yield potential, respectively low, medium and high potential, are illustrated in Fig. 1. In the random case, the farmer who opts to grow Miscanthus is ∼ assumed to choose the rotation period T that maximises the expected economic value of Miscanthus. The objective function now refers to the expected sum of the annually discounted profits in an infinite sequence, at time t = 0 . Accordingly, the discounted expected value of the cumulative net income is as follows: ∞

⎡ ∼ Wm (T ) = E ⎢ ∑ ⎣n=1 ∼ where M (t ) = pt

⎛ ⎜−c0 + ⎝

T

t ) γ − 1dt

We first provide a sensitivity analysis of Miscanthus to physical parameter (yield) in non-stochastic and random cases at the French scale and to economic parameters ( pt , c0 , ct , and δ) in the non-stochastic case. We then highlight the differences between the non-stochastic and random yield expectations for Miscanthus in terms of land use allocation and N consumption and losses. 3.1. Sensitivity to yield Based on the initial estimates of parameter values, the Cumulative Net Margin (CNM) is calculated by adding the potential net margins acquired over the rotation period, thus showing when the farmer maximises his profit if he decides to plant Miscanthus. We consider the case of a farm group with medium calibrated yield when opting for Miscanthus (i.e. around 18 tdm ha−1 y−1 at its maximum over a period of years). As illustrated by Fig. 2, the higher the Miscanthus yield, the earlier the investment pays off. Indeed, with its high establishment cost, this hybrid requires a large initial investment that cannot produce a return when the yield potential is low (maximum of 10 tdm ha−1 y−1). On the other hand, if the potential is high enough (cycle peak above 18 tdm ha−1 y−1), the return on investment starts from the 7th and 11th year in the non-stochastic and random cases, respectively. We focus on the economically Optimum Rotation Period (ORP), defined as the age at which the harvest generates the maximal CNM. According to Table 1 presenting the detailed evolution over time of CNM for the selected farm group, ORP is set at 19 years in the nonstochastic case. Integrating a random factor into the average growth function extends the optimal rotation by 4 years–23 years. We expect strong amplitude in such time gap variation, which leads us to carry out numerous random simulations on series of rotations.1 Regarding the yearly estimated yields and Net Present Value (NPV) as well as ORP over AROPAj farm groups, Fig. 3 shows the frequency for three yield potential scenarios: non-stochastic low, random (fitted to the medium yield function) and non-stochastic high. Results lead us to consider the random case as the most reasonable with regard to the distribution of yields, NPV and ORP. Indeed, the typical yield among AROPAj farm groups is about 16 tdm ha−1y−1. Yields between 12 and 18 tdm ha−1y−1 are frequent. Regarding NPV, values between €500 and €800 ha−1y−1 are very frequent. ORP is typically about 19 years and rotation periods between 16 and 24 years are frequent. In the low

⎤

∼

∑ M (t ) e−(δ−α) t ⎞⎟ e−δ (n−1) T ) ⎥ t=1

3. Results and discussion

⎠

⎦

(5)

f (y͠ t , β , γ ) − ct .

2.3. Generation of miscanthus-related yield and economic data as input to the AROPAj model In the version of AROPAj model used in this study, French farming systems are represented by 157 farm groups clustered into 21 regions. The integration of Miscanthus into the model requires estimates of its per hectare economic value at farm group level. The economic value is settled on yield functions, which need to be calibrated against real data. However, Miscanthus has been only recently introduced in France, and there is little or no available data on yield for the full rotation period. As corroborated by statistical analysis, we assume that Miscanthus yield increases with the quality of the land, as does that of wheat, which is a common crop present in 80% of the French farm groups in AROPAj [3]. We introduce the constraint that Miscanthus area does not exceed 20% of farm groups Utilized Agricultural Area (UAA) in setting up the AROPAj optimization. This constraint is a way of accounting for limitations highlighted by agronomists in terms of soil recovery after growing Miscanthus. In addition, AROPAj simulations are realized for series of homogeneous decreases in Miscanthus yields from 0 to 100% by 10% increments, compared to the benchmark calibrated yields, over farm groups to test the sensitivity of results against yields. For the inter-temporal optimization program, economic data used in this study are in line with published studies [3]; [5]. The price of Miscanthus pt is fixed at €70 tdm−1 and the discount rate δ at 5%. The establishment cost c0 equals €3000 ha−1 and annual costs ct are about 350 ha−1. We assume that prices and costs increase constantly over time according to an inflation rate α stated as 1.5%. Miscanthus N-demand is

1

115

Computations are realized with the software ®Mathematica.

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Fig. 2. Changes over time in Miscanthus cumulative net margin in non-stochastic (solid lines) and random (dotted lines) cases for low (left) and medium (right) yield potential.

3.2. Sensitivity to economic parameters

Table 1 Evolution over time of the cumulative net margin (in €k ha−1) in non stochastic and random cases for a medium Miscanthus yield potential - the case of one farm group. Values in bold refer to the optimal rotation periods maximizing the cumulative net margin. Period (year)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Potential CNM

Random CNM

(medium yield level)

(meduim yield level)

−62.488 −32.025 −18.957 −11.145 −5.785 −1.949 0.833 2.863 4.352 5.450 6.259 6.854 7.287 7.598 7.814 7.956 8.040 8.079 8.083 8.059 8.012 7.948 7.871 7.783 7.687 7.585 7.479 7.370 7.259 7.147

−61.513 −31.525 −20.489 −13.125 −8.957 −6.095 −4.102 −1.892 −1.355 −0.560 0.745 1.682 1.820 1.712 2.273 1.946 2.419 1.816 1.650 1.022 1.907 1.767 2.808 2.647 0.963 2.267 2.645 1.395 1.980 0.954

A positive NPV provides a good argument in favour of crop adoption, but it needs to be examined more rigorously. It is thus important to test alternative assumptions in order to provide some indication of how crop profitability might be sensitive to economic parameters. In the case of Miscanthus, the parameters are mainly the establishment cost (c0 ), the annual cost (ct ), the discount rate (δ) and the price. The price is regarded as certain since the crop is assumed to be sold under contract on the renewable energy market at a fixed price ( pt = p ). Fig. 4 shows the sensitivity of both the Optimal Rotation Period (ORP) and the net present value (NPV) to change in these parameters. From this figure, we see that the ORP and NPV are very sensitive to c0 and δ. Raising these parameters decreases the NPV and consequently delays the ORP. Indeed, if c0 were 30% higher than expected, the ORP would increase, and the NPV would be almost €100 ha−1y−1 less. If c0 were 30% lower than expected, the ORP would decrease, and the NPV would be almost €100 ha−1y−1 higher than expected. However, if c0 were 80% lower than expected, the ORP would decrease down to 1 year, and the NPV would be almost €1000 ha−1y−1 higher than expected. In this case, the farmer would consider Miscanthus as an annual crop and clear-cut it at the end of the 1st year and would replant it the following year. As regards δ, a variation in this parameter would delay the ORP and decrease the NPV. A noticeable change would occur only when δ is lower than 3%. In fact, if δ equalled 20%, the NPV would be almost €500 ha−1y−1 higher and the Miscanthus would be clear-cut at the end of the 8th year instead of the 16th year. Nevertheless, an increase in ct would move forward the ORP and decrease the NPV. In fact, if ct were 10% higher than expected, the NPV would be almost €100 ha−1y−1 less, but the ORP would move forward to 15 years. If ct were 10% lower than expected, the NPV would be almost €100 ha−1y−1 higher and the ORP would remain the same (16 years). A strong decrease in ct would have an impact on the NPV and the ORP. If ct were 80% lower than expected, the ORP would increase up to 18 years, and the NPV would be almost €200 ha−1y−1 higher than expected. Compared to c0 , the annual costs are lower. The farmer can incur them by delaying the rotation period, especially when the value of Miscanthus is sufficiently high. Regarding p, the more it increases, the greater the economic value and the ORP moves forward from 17 to 15 years. The NPV rises for prices higher than €70 tdm−1.

potential case, the typical yield is about 12 tdm ha−1y−1 and yields between 10 and 13 tdm ha−1y−1 are very frequent. ORP is typically about 18 years. The highest NPV does not exceed €500 ha−1y−1 and values mostly range between €100 and €400 ha−1y−1. In some farm groups, especially those located in the south, negative NPV is recorded. In the most favourable case, i.e. the high potential yield case, the yield is typically about 25 tdm ha−1y−1. Yields between 20 and 30 tdm ha−1y−1 are very frequent. Regarding NPV, the typical value is about €1300 ha−1y−1 and the lowest is €300 ha−1y−1. NPV between €1000 and €1400 ha−1y−1 are very frequent. ORP is typically about 17 years.

3.3. Impacts on land use allocation As a result of AROPAj economic optimization, agricultural land is reallocated in favour of perennial crops. Requiring far greater quantities of water during the first growth phase (see section 2.1), Miscanthus is 116

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Fig. 3. Distribution over AROPAj farm groups regarding yields (left), Net Present Value (NPV) and Optimal Rotation Period (ORP) for three yield potential levels: low (green), random (blue) and high (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

cost. Crop yield potential is usually sensitive to soil quality: the greater the soil fertility, the higher the crop productivity. This is also the case for Miscanthus, whose yield records on marginal land are not high enough to generate a decent profit margin. And when the yield is low, the farmer is discouraged from planting the crop. On the assumption of a high establishment cost (€3000 ha−1), the farmer has to be careful before deciding to allocate a portion of land to Miscanthus. Thus if he decides to adopt Miscanthus, he will cultivate it on areas that provide a higher revenue. Based on our Miscanthus yield estimation, three scenarios were tested for three yield potential levels (low, medium and high). We also tested the scenario designed to randomize the medium potential level. Accordingly, the optimal yield over the lifespan varies among AROPAj groups. For the low and high potential cases, optimal yields range between 10 and 13 tdm ha−1 y−1 and 20–30 tdm ha−1 y−1 respectively. In the case of low yields, the NPV is too low to justify growing Miscanthus. The random case portrayed a realistic situation when the average optimal yield is about 16 tdm ha−1 y−1, and yields between 12 and 18 tdm ha−1 y−1 are frequent. This is in line with findings of [18], who considered an average of 16.8 tdm ha−1 y−1 associated with a large variability of 6.86 tdm ha−1 y−1. Marginal areas and grasslands should be the first to be converted to Miscanthus. However, the progressive introduction of Miscanthus with increasing yield potential reduces not only grasslands and marginal areas, but also profitable areas mostly allocated to food production, i.e. cereals. From the environmental point of view, integrating Miscanthus into the farming system replaces arable areas generally allocated to conventional high N-demanding crops, i.e. cereals, and consequently reduces N-emissions. This conclusion follows from the hypothesis stipulating that Miscanthus demands low N-fertilising over a cycle by means of its perennial rhizome system, as well as having low nitrate leaching, apart from the two first years after planting [19]. As a matter of fact, the crop presents a high nutrient uptake efficiency. After being stored in below-ground components at the end of the growing season, nutrients are transferred to above-areal parts in the spring [1]. The mulch, made from the fallen leaf material, is then progressively decomposed and turns nutrients back to the soil. These dynamics allow building and maintaining soil organic matter, and hence reducing fertilising requirements [7]. Notwithstanding, some nutrients are eliminated at harvest, thus leading to a long-term depletion of soil nutrients reserve [11]. N-fertilisation can therefore be applied to sustain significant production levels over a cycle [11]; [7]. Yet, despite this advantage, some soil scientists argue that the depth and perennial character of rhizome system should be investigated more thoroughly, regarding land cover reversibility. According to the economic optimization approach which frames our model, farmers decisions are assumed to be perfectly-rational maximizing agents, so that growing Miscanthus would be gainful on productive soils. Consequently, this situation leads to both direct and indirect changes in land allocation due to the displacing of food activities

more cultivated in northern than in southern France (Fig. 5). High yields are mostly recorded in the north where climatic conditions are more favourable and soil water availability is high. Moreover, areas allocated to Miscanthus are sensitive to yield potential, so that the greater the yield potential, the more farmers integrate Miscanthus into their farming system. In the non-stochastic case, Miscanthus is grown on 2.5 million ha (10% UAA) for a medium yield potential (50% of yield potential) and this area goes up to 4.5 million ha (17.5% UAA) in the case of high yields (up to 100% of yield potential). However, introducing yield uncertainty delays the adoption of Miscanthus until its potential is sufficiently high to motivate the farmers decision. For instance, in the non-stochastic case, Miscanthus is adopted when 30% of potential is reached. In the random case, this occurs at 60% of the yield potential. Thus favourable yield helps the farmer to decide on Miscanthus adoption despite the high degree of uncertainty. In the latter case, the area allocated to Miscanthus barely exceeds 3 million ha (12.5% UAA) for 100% of yield potential. Fig. 6 shows a significant decrease in the food-crop areas when Miscanthus is progressively introduced with increasing yield potential in non-stochastic and random cases. Cereals and grassland areas are the most affected and undergo noticeable changes. Specifically, when the Miscanthus yield reaches its full potential (as estimated by our method), the area planted with cereals decreases by 25% in the non-stochastic case, and by 7% in random case. At the same time, grasslands decrease by 13% and 7.5% in the non-stochastic and random cases respectively. Moreover, there is a reduction in fallow lands, which are considered as abandoned areas in our model. These areas decrease to 28% in the first case and to 14% in the second. Simulations show that changes in land allocation have a substantial effect on N-input demand and N-losses. Even though the results in the non-stochastic and random cases seem to be alike in terms of trend, they are of different magnitudes. Fig. 7 shows that fertiliser consumption decreases when Miscanthus becomes more profitable. Lower Ninput levels are achieved by increasing the Miscanthus yield level. For instance, we see a 22% decrease in fertiliser demand in the non-stochastic case and a 13% decrease in the random case when the Miscanthus yield reaches its full potential. This decrease in N-demand leads to a 26% and 13% reduction in nitrate (NO3) emissions in the nonstochastic and random cases respectively. The introduction of Miscanthus also decreases NH3 and N2 O emissions, but this decrease is insignificant in comparison to NO3 emissions. 3.4. Discussion We addressed the Miscanthus profitability issue by testing various favourable assumptions with regard to integrating it into French farming systems with a view to achieving a grater profit. Sensitivity analysis over yield and economic parameters showed to what extent producing Miscanthus becomes more cost-effective by improving the yield potential, increasing the price, or by decreasing the establishment 117

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Fig. 4. Sensitivity of Optimal Rotation Period (ORP) and Net Present Value (NPV) of Miscanthus to price, establishment and annual costs, and discount rate as modelled for one French farm group. 118

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Fig. 5. Land area allocated to Miscanthus in non-stochastic (left - Fig. 5a) and random (right - Fig. 5b) cases according to different levels of yield potential (x-axis): a comparison between northern and southern regions of France.

alternatives for widespread biomass production. On the one hand, they could refine the establishment techniques of some Miscanthus hybrids, e.g. Miscanthus sinensis, that have more or less the same yield potential and environmental characteristics and above all have a cheaper vegetative multiplication phase (seeds). On the other hand, decision-makers should target to a greater extent the promotion of other lignocellulosic crops, e.g. switchgrass, characterized by a low establishment cost, low water requirements and high adaptability to poor quality soil. Another alternative for increasing Miscanthus profitability is to give it an advantageous price. In France, Miscanthus, unlike other agricultural products, is not integrated into a structured market, with the consequence that a novice Miscanthus grower has no guarantee of selling his product at a given price. To overcome this problem, Miscanthus should be sold by contract in the renewable energy market at a fixed price. Thus, before planting this perennial crop, farmers should first evaluate its profitability on the basis of yield and economic parameters and, second, should identify potential purchasers of the

and the conversion of cultivated areas to biofuel production, although the UAA allocated to this crop does not exceed 13% in the most reasonable scenario (random case fitted to the medium yield function). Nevertheless, farmers decisions are also driven by behavioural factors, following the bounded rationality theory [21]. Accordingly, the willingness to grow Miscanthus is currently low, depending on policy, farming system [28], farm size, and personal features such as education, age, and risk perception [14]. Displacing food crops could be made difficult for strategic and food security reasons. In fact, with respect to sustainable production criteria, lignocellulosic crops should preferably be grown on marginal areas in order to reduce competition with food-crop areas. In France, Miscanthus x Giganteus is the most experimentally developed hybrid of Miscanthus because of its high potential, environmental profile and low nutrient requirements [19]. However, it requires an expensive establishment phase since it is propagated by rhizomes, thus limiting extensive planting [8]. Decision-makers should therefore invest in various

Fig. 6. Changes in land use allocation in non-stochastic (left - Fig. 6a) and random (right - Fig. 6b) cases according to different levels of Miscanthus yield potential (xaxis) at the scale of France. 119

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Fig. 7. Changes in N-fertiliser consumption (left - Fig. 7 a & Fig. 7 C) and losses (right - Fig. 7 b & Fig. 7d) in non-stochastic (top) and random (bottom) cases according to different levels of Miscanthus yield potential (x-axis) at the scale of France.

large initial outlay that cannot be covered when yield potential is low. In the case of higher yields, i.e. greater than 15 tdm ha−1y−1 on average over a cycle, Miscanthus proves to be profitable in the non-stochastic case to a much greater extent than in the random case. Integrating a random factor into the yield function also delays the optimal rotation period. Moreover, a decrease in establishment costs increases the net value and consequently moves forward the optimal rotation period. Sensitivity to annual costs is lower since the farmer can offset these by delaying the rotation period, especially when the Miscanthus value is sufficiently high, as when prices are higher than €70 tdm−1. In sum, as expected, the adoption of and land use allocation to Miscanthus are highly dependent on its yield potential, but more interestingly, relative gross margins for different crops may enable Miscanthus to compete with profitable food crops in northern regions, and it could do so on marginal land in both northern and southern France. However, uncertainty delays the adoption of Miscanthus until its potential is sufficiently high to motivate the farmer's decision. As

product. 4. Conclusion In this study, we have assessed the supply sensitivity of a perennial N-low-demanding crop dedicated to bioenergy, i.e. Miscanthus x giganteus, to physical and economic factors. We used Faustmann's approach to ensure optimal resource management. Two economic models were therefore applied to calculate the optimal rotation period and net present value in two cases, that is, when the yield function is non-stochastic and when it is governed by a random process. Differences between these cases in terms of land allocation and N consumption and emissions were highlighted using the AROPAj agricultural supply model. Results show to what extent uncertainty in yield potential, price, establishment cost and discount rate alter the future economic value and the optimal rotation period. Miscanthus x giganteus requires a 120

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regards policy making, apart from the issue of energy security, the extension of Miscanthus brings positive externalities in terms of farming systems sourced from N-losses.

[13]

[14]

Acknowledgements The authors gratefully acknowledge the financial support brought by the FUTUROL-PROCETHOL 2G Project (Cellulosic Ethanol Industrial Project). They also warmly thank Michael Westlake for his re-reading of this article.

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