# Assessing Opportunity Costs Under Conflicting Objectives: Application to Profitability, Pesticide Reduction, and Crop Production

Jean-Philippe Boussemart, Maé Guinet, Salomé Kahindo, Nicolas

Munier-Jolain, Raluca Parvulescu

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# Assessing Opportunity Costs Under Conflicting Objectives: Application to Profitability, Pesticide Reduction, and Crop Production

**Jean-Philippe Boussemart**

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 – LEM, F-59000 Lille

**Maé Guinet**

Agroécologie, INRAE, Institut Agro, Univ. Bourgogne, Univ. Bourgogne Franche-Comté, F-21000 Dijon

**Salomé Kahindo**

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 – LEM, F-59000 Lille

**Nicolas Munier-Jolain**

Agroécologie, INRAE, Institut Agro, Univ. Bourgogne, Univ. Bourgogne Franche-Comté, F-21000 Dijon

**Raluca Parvulescu**

r.parvulescu@ieseg.fr

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 – LEM, F-59000 Lille

## Research Article

**Keywords:** activity analysis, opportunity cost, competing objectives, profitability maximization, sustainable agriculture

**Posted Date:** April 3rd, 2025

**DOI:** https://doi.org/10.21203/rs.3.rs-6269365/v1

**License:** © Ⓟ This work is licensed under a Creative Commons Attribution 4.0 International License.
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**Additional Declarations:** No competing interests reported.
Assessing Opportunity Costs Under Conflicting Objectives:
Application to Profitability, Pesticide Reduction, and Crop Production

Jean-Philippe Boussemart

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 – LEM, F-59000 Lille, France

jp.boussemart@ieseg.fr

Maé Guinet

Agroécologie, INRAE, Institut Agro, Univ. Bourgogne, Univ. Bourgogne Franche-Comté, F-21000 Dijon

mae.guinet@inrae.fr

Salomé Kahindo

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 – LEM, F-59000 Lille, France

s.kahindo@ieseg.fr

Nicolas Munier-Jolain

Agroécologie, INRAE, Institut Agro, Univ. Bourgogne, Univ. Bourgogne Franche-Comté, F-21000 Dijon

nicolas.munier-jolain@inrae.fr

Raluca Parvulescu (corresponding author)

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 – LEM, F-59000 Lille, France

r.parvulescu@ieseg.fr

The work was part of the 3rd Program for Future Investments (France 2030) and operated by the SPECIFICS project (ANR-20-PCPA-0008) funded by the “Growing and Protecting crops Differently” French Priority Research Program (PPR-CPA), part of the national investment plan operated by the French National Research Agency (ANR).
**Abstract**

This study proposes a method to evaluate opportunity costs when shifting between competing objectives. We compare three strategies: profitability maximization (baseline), output production maximization and input cost minimization. Our analysis is conducted in two stages. First, using a log-linear production technology and incorporating output prices, we correct for inefficiencies to position all decision-making units (DMUs) on the efficiency frontier, ensuring a relevant comparison. In the second stage, we estimate opportunity costs and related price elasticity when switching strategies. Using a panel of 458 arable farms in the Meuse region (France) observed over 27 years (1991–2017), we analyze the tradeoffs between farmers’ objectives for profitability maximization, the society’s objective to maximize crop production and the environmental concern for pesticide use minimization. The first stage of analysis identifies potential improvements within each objective. In the second stage, when all practices are projected on the frontier, we compute the margin per ha loss when switching from the farmers’ objective of profitability maximization to any of the alternative scenarios and the price elasticities related to these switches. Importantly, our analysis indicates that reducing pesticide use is economically viable, while maximizing production may lead to greater financial trade-offs.

**Keywords:** activity analysis; opportunity cost; competing objectives; profitability maximization; sustainable agriculture.

**JEL codes:** D24; C61; Q12; Q56
# 1. Introduction

The evolution of European agriculture, shaped by both internal and external influences since the 1960s, has been characterized by the adoption of new production techniques such as mechanization, intensive use of pesticides and fertilizers, and specialized crop cultivation (Matson et al., 1997; Tilman et al., 2002). Initially focused on boosting food supply, governments promoted intensive agricultural methods, leading to a 149.8% increase in cereal production from 1961 to 2021 (FAO, 2023). However, this growth came at the expense of natural resources, resulting in environmental degradation (Millennium Ecosystem Assessment, 2005; Pimentel et al., 1997; Travisi & Nijkamp, 2008). As the adverse impacts of this degradation become increasingly severe, threatening the future of agriculture, contemporary production systems are undergoing transformation to adopt more sustainable practices. However, the problem is complex since the different stakeholders involved in this process may have different objectives. Farmers, for instance, focus on maximizing profits, while governments prioritize self-sufficiency whereas the society might target environmental quality. In our study, we address the challenges associated with aligning these competing agricultural goals. Specifically, through performance-based analysis we investigate farm level drivers to balance between the different stakeholders' objectives: farmers' profitability, output production and environmental sustainability.

Activity models offer a practical alternative to parametric models as they do not require a predefined functional form, allowing for greater flexibility in performance assessment. One standard estimation technique is Data Envelopment Analysis (DEA), developed by Charnes et al. (1978) which has been widely used to measure decision-making unit (DMU) efficiency relative to a best-practice frontier. The use of radial DEA models enables researchers to assess the potential for proportional improvements in either inputs or outputs.<fnref n="1" /> For example, an output-oriented radial DEA model estimates the maximum possible crop output that can be achieved proportionally while keeping input levels constant. Similarly, an input-oriented radial DEA model can determine the proportional reduction in inputs, such as pesticides, required to maintain the observed level of output. Thiele & Brodersen (1999) employ a radial input-oriented DEA model to measure technical efficiency, assessing the proportional reduction in all inputs needed to reach the efficiency frontier. Rather than relying solely on pure radial technical efficiency measures, many studies integrate more complex estimation frameworks, such as Lansink & Silva (2004), who assess pesticide use efficiency, and Dimara et al. (2005), who analyze the impact of quality regulations on farm efficiency. The same applies to profitability and profit efficiency. Coelli et al. (2002) measure short-run profit efficiency in airlines using a radial profit efficiency measure, which maximizes profit by proportionally adjusting outputs and variable inputs while keeping fixed inputs constant. They then decompose the profit gap into components reflecting output-mix inefficiency, capacity utilization inefficiency, input-mix inefficiency, and technical inefficiency. One of the main drawbacks of radial efficiency models is their inability to account for trade-offs between different objectives, as they assess efficiency based on proportional input or output adjustments rather than optimizing multiple objectives simultaneously. This limitation helps explain the relatively sparse use of pure radial efficiency measures in isolation, as researchers often seek more flexible approaches that allow for multi-dimensional optimization.

<footnote n="1">¹ Note that, compared to traditional radial models based on proportional changes in outputs (or inputs), Russell-type measures and the Slacks-Based Measure (SBM) account for non-proportional adjustments in efficiency assessment.</footnote>
Introduced by Chambers et al. (1996), directional distance functions (DDF) generalize distance functions by allowing for the simultaneous expansion of desirable outputs and contraction of undesirable outputs or inputs in a pre-specified direction when projecting DMUs onto the efficiency frontier. For example, Picazo-Tadeo et al. (2012) employ DDF to assess eco-efficiency, which is understood as the simultaneous consideration of economic and environmental performance. Economic efficiency is measured as gross margin per hectare, while environmental efficiency accounts for the reduction of environmental pressures, including soil erosion, pesticide risk, and energy balance. Their model employs different directional vectors to evaluate eco-efficiency objectives under alternative environmental and economic performance trade-offs: (i) reducing all environmental pressures while maintaining value added, (ii) increasing value added while keeping environmental pressures constant, and (iii) jointly increasing value added and reducing environmental pressures. While the first two approaches resemble conventional radial efficiency measures, the third approach ensures that economic and environmental performance improve simultaneously, but with independent adjustments reflecting the trade-off between value added and environmental impact. As expected, the magnitude of improvement in each objective is lower when optimizing both simultaneously than when optimizing them separately. Further along this line, Skevas & Serra (2016) extend the DEA framework by integrating a state-contingent production technology that accounts for pest pressure effects on efficiency estimation. Their approach refines farm-level efficiency measurement by explicitly considering stochastic conditions that affect crop production.

On the other hand, Berre et al. (2013) analyzed economic and environmental efficiency at the sectoral level by applying a DDF to estimate shadow prices of greenhouse gases and nitrogen surpluses, comparing the valuation of pollution between farmers and society. Their approach highlights the economic implications of pollution reduction and the potential for aligning policy incentives with sustainability goals in livestock production. Skevas et al. (2014) refine the use of DDF by incorporating risk-adjusted DEA, explicitly treating output variance and an undesirable output including pesticides’ environmental spillovers.

While DDF allows movement in a predefined direction, it still applies a single directional vector to all inputs and/or outputs simultaneously. In cases where different inputs and outputs should be adjusted independently, a more flexible, non-radial approach is required. Russell-type measures (Färe & Lovell, 1978) decompose inefficiency across individual inputs and outputs, rather than applying a single proportional or directional adjustment. This non-radial approach allows independent trade-offs across multiple objectives, making it more adaptable to stakeholder-specific concerns. Skevas et al. (2012) adopt a dynamic DEA approach that incorporates a Russell-type measure to explicitly capture the intertemporal effects of pesticide use on productivity and environmental impact.

While previous DEA models focus on technical efficiency, cost efficiency extends this framework by incorporating input prices to assess the minimum cost required to produce a given output. Traditional cost efficiency DEA assumes a single best-practice production frontier. However, Boussemart et al. (2016) extend this concept by applying cost efficiency analysis to compare distinct production systems, evaluating whether low-pesticide farming can achieve cost competitiveness relative to high-pesticide systems. Their approach highlights how cost efficiency can be used not only to benchmark individual firms but also to compare alternative technologies, offering insights into the economic feasibility of sustainable farming practices.

Ang et al. (2018) address a key limitation of standard DEA models when dealing with positive externalities in agriculture, such as landscape conservation and habitat for birds. Standard DEA assumes a fixed technology set
and convexity, which limits its ability to properly evaluate these externalities. Moving beyond traditional DEA, Ang et al. (2018) develop a nonparametric dynamic profit-maximization model to estimate the opportunity cost of increasing crop diversity.

Nonetheless, DEA-based approaches can also be extended to explicitly structure trade-offs between different objectives. One such extension is the sub-technology approach, introduced by Murty et al. (2012), which models desirable and undesirable outputs using separate production frontiers.<fnref n="2" /> Serra et al. (2014) extended this framework by incorporating state-contingent production technologies into the by-production model, improving efficiency measurement under stochastic conditions. Chambers et al. (2014) further refined this approach by introducing shadow pricing for stochastic pollution and ensuring material balance constraints, enhancing its empirical applicability. Ait Sidhoum et al. (2019) applied the sub-technology framework to farm-level sustainability efficiency analysis, using state-contingent modeling and material balance conditions to structure economic, environmental, and social performance. Dakpo et al. (2016) and Ray et al. (2018) introduced dependence constraints that formally link sub-technologies, addressing a key limitation of earlier models and enabling a more coherent representation of interactions within a unified framework, which laid the foundation for multi-dimensional DEA models. Building on these insights, Boussemart et al. (2020) and Niu et al. (2024) extended DEA applications to sustainability assessment by developing the ‘three-pillar’ approach, which integrates economic, environmental, and social performance indicators into a comprehensive performance measurement framework. Unlike traditional DEA models that rely on a single aggregated efficiency score, these frameworks assess sustainability performance under different weighting scenarios, reflecting stakeholder preferences more accurately. Nevertheless, a key challenge in this literature is testing the sensitivity of results to the choice of weights assigned by the researcher, as these weights significantly impact the final efficiency scores. This may prevent achieving the highest possible gains in any single dimension.

The main contribution of this paper is to propose an extension to the above-mentioned literature by comparing the optimal potentials associated with each objective. This allows us to deduce the opportunity cost involved in shifting from one objective to another. To achieve this, all DMUs must first be positioned on the frontier, meaning their situation must be corrected for any form of inefficiency. This method can therefore be applied in any decision-making process that involves arbitrating between several objectives that may seem conflicting, as long as they are all defined in relation to the same production technology.

In our application, we assume that profitability maximization is the baseline scenario. Thus, any deviation from this objective to achieve a goal set by another stakeholder (such as maximizing output or minimizing a specific input) will incur an opportunity cost for the DMU, which must be assessed. This analysis can be further developed by calculating different types of elasticity between various points on the same frontier, providing insights into DMU's responsiveness to changing objectives. As a result, this analysis allows for the calculation of the necessary compensations to offset the potential decline in profitability when adopting an alternative objective.

We also contribute to non-parametric performance estimation by integrating output price variables, following Boussemart et al. (2022). Prices are important variables for DMU's strategies, and we directly include them into

<footnote n="2">² Related to the sub-technology approach with different competing objectives, we can mention another strand of research, the network models, developed for the banking system by Fukuyama & Weber (2010, 2015, 2017) and Fukuyama & Matousek (2017, 2018).</footnote>
performance analysis and opportunity cost calculations. This allows us to estimate price elasticity when switching
between strategies and identify the optimal price that would make the evaluated DMU indifferent between
profitability maximization and input minimization. By incorporating price information, our approach provides a
more realistic view of how economic, environmental, and productive goals interact.

Additionally, we propose an original empirical application of the log-linear production technology, introduced by Banker & Maindiratta (1986), which is well-suited to estimate production functions expressed in multiplicative form. Moreover, this approach allows for locally increasing or decreasing marginal products based on DMU-specific characteristics, offering greater flexibility than traditional linear models that assume decreasing marginal returns.

Moreover, our work also contributes to the empirical literature dealing with farm adaptation capacities to French/European agricultural policies which aim to improve food self-sufficiency (crop production maximization) with more environmentally-friendly practices (pesticide minimization) while preserving farmers' profitability.

Our analysis is performed in two stages. In the first one, we provide the potential improvements according to each objective taken separately. Compared to the current observed situation, we obtain two key results: first, profitability is improved in all three scenarios considered and second, pesticide use can be reduced compared to the observed situation in the pesticide reduction (obviously) and in the profitability scenarios but not in the crop production maximization. In the second stage, where we compare the three objectives based on an opportunity cost methodology, we show that pesticide reduction policies could be economically viable while output production maximization may appear as less tenable.

Finally, our study uses an original dataset based on accounting data from farms in the Meuse department, eastern France, spanning 1991 to 2017. This dataset offers detailed crop-specific information, including output quantities, prices, and operational costs for each crop. Annual performance scores are calculated for each farm, and the farms' geographical proximity ensures greater homogeneity in pedo-climatic conditions than national datasets. To enhance comparability, we adjusted arable land surfaces using a land quality indicator and included only farms generating over two-thirds of their revenue from field crops, treating other revenues as control variables.

The remainder of this paper is organized as follows: Section 2 outlines our materials and methodology, including the models used. Section 3 presents and discusses our research findings, and Section 4 draws our conclusions.

## 2. Material and methods

### 2.1. Data and variables

We sourced farm data from the Meuse Department, an administrative division in eastern France. Agriculture in Meuse is primarily centered on the production of cereals (44%), milk (19%), and beef cattle farming (13%), collectively constituting the majority of the total output value.<fnref n="3" /> The cultivated area spans approximately 343,000 hectares (ha), with field crops (including cereals, maize, oilseed, and protein crops) occupying 57% of the arable land (AL).<fnref n="4" />

Our analysis is based on a sample of farms obtained from the Centre d'Economie Rurale et de Gestion de la Meuse.<fnref n="5" /> We dispose of a panel of 458 farms specialized in field crops whose revenue represents more than two-

<footnote n="3">³ https://meuse.chambre-agriculture.fr/enregistrements-locaux/interface/menus/menu-acces-pratique/lagriculture-en-meuse/</footnote>

<footnote n="4">⁴ Idem.</footnote>

<footnote n="5">⁵ This is an audit and control organism specialized in farming activities.</footnote>
thirds of total revenue excluding subsidies. These farms were observed over 27 years from 1991 to 2017, resulting in a total of 2,900 observations.<fnref n="6" />

One advantage of this dataset over national-level samples like the FADN (Farm Accountancy Data Network) is its focus on farms within the same local administrative area, ensuring greater homogeneity in pedo-climatic conditions compared to datasets spanning all of France. Additionally, land quality has been controlled for in our analysis. Another benefit is the availability of observed prices and detailed operational cost components for each of the eight crops analyzed across the farms.

Our analysis relies on one main output which is the revenue from crops. As our analysis will show, this variable is further decomposed into a quantity component (the total protein content of crops) and a price component (the farm's price for a kg of protein produced, that we deduce from the observed crop-specific prices). In addition, we use the revenue from other activities (representing less than one third of the total revenue), as a control variable. These outputs are produced using five inputs: arable land, other surfaces, labor, fixed capital, and intermediate consumption. The farms in our sample average 175.8 ha, larger than the Meuse 2020 average of 144.4 ha (Agreste-RA 2020). To account for land quality differences, we adjusted land measurements using a district-specific yield index. Labor includes both hired and family labor, averaged at 1.7 full-time equivalents per farm. Fixed capital use is measured by depreciation costs associated with buildings, equipment, and agricultural machinery services. Intermediate consumption includes expenses like fertilizers, seeds, fuel, and pesticides, with a further breakdown into pesticide costs (P) and intermediate consumption without pesticides (ICWP). Descriptive statistics are shown in Table 1.

Our estimations are conducted on an annual basis, comparing farms to their peers within the same year. As a result, the efficiency estimation is not affected by monetary depreciation within the year, as all farms are subject to the same inflation rate. To facilitate the analysis of performance changes over time, all monetary values have been deflated using the global consumer price index and standardized to constant 2010 euros (€2010).

<table><caption>Table 1. Descriptive statistics for all variables over the period 1991-2017
(per farm and per year)</caption><thead><tr><th></th><th>Mean</th><th>Min</th><th>Max</th><th>CV</th></tr></thead><tbody><tr><td>Crop product (€<sub>2010</sub>)</td><td>164,795</td><td>15,558</td><td>972,265</td><td>63%</td></tr><tr><td>Protein (kg of DM)</td><td>111,633</td><td>12,747</td><td>499,870</td><td>57%</td></tr><tr><td>Protein price (€<sub>2010</sub>/kg of protein)</td><td>1.5</td><td>0.9</td><td>2.9</td><td>22%</td></tr><tr><td>Other products (€<sub>2010</sub>)</td><td>33,464</td><td>0</td><td>256,382</td><td>91%</td></tr><tr><td>Arable land (ha)</td><td>176</td><td>25</td><td>708</td><td>54%</td></tr><tr><td>Other surfaces (ha)</td><td>28</td><td>0</td><td>183</td><td>106%</td></tr><tr><td>Labor</td><td>1.7</td><td>0.2</td><td>6.4</td><td>52%</td></tr><tr><td>Fixed Capital (€<sub>2010</sub>)</td><td>62,842</td><td>5,776</td><td>399,321</td><td>63%</td></tr><tr><td>Intermediate consumption without pesticides (€<sub>2010</sub>)</td><td>61,209</td><td>6,610</td><td>322,920</td><td>61%</td></tr><tr><td>Pesticide cost (€<sub>2010</sub>)</td><td>28,985</td><td>2,484</td><td>162,582</td><td>64%</td></tr><tr><td>Pesticide cost/ha (€<sub>2010</sub>)</td><td>165</td><td>45</td><td>349</td><td>27%</td></tr></tbody></table>

<footnote n="6">⁶ Note however that we estimate yearly production frontiers to account for variations in the climatic conditions.</footnote>
On average, over the specified period, farms in our dataset yielded 111,633 kg of protein from the diverse range of crops cultivated. A more detailed presentation of the eight crops cultivated can be found in Appendix 1. ICWP averaged at 61,209 €$_{2010}$ (348 €$_{2010}$ per ha), while pesticide costs averaged 28,985 €$_{2010}$ (165 €$_{2010}$ per ha), as shown in Table 1. The main components of ICWP were fertilizers (53%), seeds (20%), fuel (15%) and other expenses (12%).

## 2.2 Methods

Our research aims to quantitatively assess trade-offs among three farm performance objectives using a two-stage analysis. In the first stage, we estimate a production frontier using a non-parametric activity model, following Koopmans' (1951) approach and applying data envelopment analysis (DEA) as developed by Charnes et al. (1978). The non-parametric approach, which avoids the need to specify a precise functional form for the production technology, offers an advantage over traditional parametric methods.

The benchmark establishes optimal input-output relationships, enabling us to assess productive efficiency based on deviations from the non-parametric frontier. Farms on the frontier are deemed efficient, while deviations for inefficient farms highlight areas for potential improvement, assuming similar production conditions. We assess each farm's performance across objectives such as profitability maximization, crop production maximization, and pesticide cost minimization, analyzing gaps using indicators like revenue, protein yield, price, cost, pesticide intensity, and gross margin per hectare.

A key empirical contribution of our study lies in the second step of the analysis, where we calculate the opportunity costs—measured as potential margin loss per hectare—of pursuing alternative objectives like crop production maximization or pesticide cost minimization instead of profitability maximization. This comparison is only relevant for farms free from technical inefficiencies, as these farms have optimized production characteristics. By projecting farms onto the efficient frontier, we ensure meaningful opportunity cost analysis and can assess the economic and technical adjustments required to switch between objectives.

### 2.2.1 Modelling farming activities

We consider here a set of N observed farms operating under homogenous conditions (the Meuse department). They use five inputs to produce two outputs. The input vector is composed of the arable land (AL), other surfaces ((OS); i.e., pasture), labor (L), intermediate consumption (IC) and fixed capital (K). The input vector is then:

$$ \mathbf{x} = (AL, OS, L, IC, K) \qquad (1), $$

At the farm level, AL is obtained by summing up the land allocated to each different crop. The land vector comprising each crop area is:

$$ \mathbf{AL} = (AL_{wt}, AL_{wb}, AL_{sb}, AL_{mz}, AL_{pa}, AL_{rs}, AL_{sf}, AL_{fw}) \qquad (2), $$

where wt= wheat, wb= winter barley, sb= spring barley, mz= maize, pa=peas, rs= rapeseed, sf= sunflower and fw=fallow.

We denote by the subscript “c” any variable related to a specific crop. Thus, ALc is a component of AL and the total land for crops is a scalar obtained as:

$$ AL = \sum_{c=1}^{8} AL_{c} \qquad (3). $$

The intermediate consumption (IC) is obtained as the sum of two components, namely the cost for intermediate consumption without pesticides (ICWP) and pesticide cost (P), and for each farm, we get:
$$IC = ICWP + P \qquad (4).$$

For each of the eight possible crops cultivated by the farms, we retrieve the quantity produced ($q_c$) and the corresponding market price in $\epsilon_{2010}$ per kg ($p_c$). The revenue of each crop is given by:

$$R_c = q_c * p_c \qquad (5).$$

Consequently, total crop revenue is obtained by summing up the crop revenue for all eight crops:

$$R^1 = \sum_{c=1}^{8} R_c \qquad (6).$$

Regarding the definition of the total crop production quantity, several metrics can aggregate the quantities produced from different crops at the farm level.<fnref n="7" /> One possible metric is crop protein production, contributing to the ongoing debate advocating for the promotion of plant-based proteins in France and Europe.<fnref n="8" /> For each crop $c$, we use the standard protein content of harvested biomass provided by the online encyclopedia Feedipedia,<fnref n="9" /> an open access information system that provides information on nature, occurrence, chemical composition, nutritional value and safe use of nearly 1400 worldwide feed resources. The protein content is provided in % of dry matter. A standard rate of humidity for each crop (Std-Hmd_c) allows to convert the gross harvested quantity into dry matter. For each crop, we denote its observed yield by (Obs-YLD_c) and we calculate the dry matter yield (DM-YLD_c) as follows:

$$DM-YLD_c(\text{in kg/ha}) = \frac{\text{Obs-YLD}_c \times (100-\text{Std-Hmd}_c)}{100} \qquad (7).$$

For each crop, the dry matter yield is multiplied by the per crop protein content (Prot-cont_c), to obtain the protein yield (YLD_c):

$$YLD_c(\text{in kg/ha}) = DM-YLD_c \times Prot-cont_c \qquad (8).$$

A specific crop protein production ($y_c$) is obtained by multiplying the protein yield by the land attributed to that crop. The total production of protein ($y^1$) is obtained from:

$$y^1 = \sum_{c=1}^{8} y_c \qquad (9).$$

In this paper, we apply the approach developed by Boussemart et al. (2022), which views economic performance as driven by two factors: optimizing input and output quantities while explicitly considering output prices as a decision variable. With our detailed dataset, we retrieve crop-specific prices for each farm, enabling a more comprehensive analysis. We estimate the indirect price of protein (pp) measured in $\epsilon_{2010}$ per kg of protein, by the ratio between the total crop revenue ($R^1$), and the total production of protein ($y^1$):

<footnote n="7">⁷ The standard aggregator is the monetary unit price of each crop, as in equations (5) and (6) but in this case, the overall result measured in value, is affected by a price effect that obscures the pure quantity component, which we explicitly want to distinguish from the revenue previously defined. Alternatively, we can use the energy content for each crop. The estimations run with energy content instead of protein production do not show any significant difference from the ones presented here.</footnote>

<footnote n="8">⁸ Since the 1960s, the evolution of the production systems in France and Europe have shown a considerable decline in protein production from crops. As a result, France and Europe have experienced a high level of dependence on foreign protein imported from Brazil, Argentina, and the USA (Watson et al., 2017), and the consumption of animal protein has increased at the expense of plant protein (Bues et al., 2013). Due to the adverse effects of these changes on the environment, the French government has committed to mitigate these external impacts by enhancing the local production of plant protein.</footnote>

<footnote n="9">⁹ https://feedipedia.org/</footnote>
$$pp = \frac{R^1}{y^1} \qquad (10).$$

The indirect protein price level may vary across farms due to two primary effects. Firstly, the crop mix plays a significant role, because the protein price varies strongly across crops (see Figure B in the Appendix 2). Secondly, differing crop prices can also result from each farm's selling strategies, influenced, for instance by their storage capacity to seize market opportunities.

Some farms in our sample engage in supplementary activities like cattle breeding or vegetable production, which are included as control variables for two reasons. First, accounting data provides costs at the farm level, making it difficult to separate crop and livestock expenses. Second, livestock and crop production are interrelated—crops can serve as animal feed, and animals provide organic fertilizers. The revenue from these activities, labeled R², is incorporated into our analysis.

The final output vector is then:

$$y = (y^1, R^2) \qquad (11).$$

We define the production possibility set as T, the set of all feasible input-output combinations that a farm can achieve under given technological constraints. It represents the boundary and interior of the production possibilities available within a given decision environment. Assumptions regarding the production possibility set associated to the farm activity model are “no free lunch”, free disposability, inclusion of observations, minimum extrapolation and geometric convexity. Related to this latter assumption, we remind that it offers the benefit of being applicable to more complex production situations, thereby accommodating local non-concavity and effectively dealing with a nonconvex production possibility set (see Banker & Maindiratta, 1986).

In line with our previous presentation, x is the five-dimensional vector for inputs with components $x_i$ for $i = 1, ..., 5$ defined in equation (1) and y the two-dimensional vector for outputs with components $y_o$ for $o = 1, 2$ defined in equation (11). Therefore, for a set N observed farms, we can define T as:

$$T = \left\{ (x, y) \in \mathbb{R}_+^5 \times \mathbb{R}_+^2 \mid \begin{array}{l} x_i \ge \prod_{n=1}^N x_{i,n}^{\mu_{i,n}}, \quad \forall i \in \{1, \dots, 5\}, \\ y_o \le \prod_{n=1}^N y_{o,n}^{\mu_{o,n}}, \quad \forall o \in \{1, \dots, 2\}, \\ \sum_{n=1}^N \mu_n = 1, \quad \mu_n \ge 0, \quad \forall n \in \{1, \dots, N\} \end{array} \right\} \qquad (12).$$

However, this production possibility set can further be estimated by applying the logarithmic transformation. For this, throughout the following, the symbol “overline” will denote the natural logarithm of the variable. For instance, $\bar{z} = \ln(z)$. The logarithmic transformation of the technology in equation (12), $\bar{T}$ is then defined as:

$$\bar{T} = \left\{ (\bar{x}, \bar{y}) \in \mathbb{R}_+^5 \times \mathbb{R}_+^2 \mid \begin{array}{l} \bar{x}_i \ge \sum_{n=1}^N \mu_n \bar{x}_{i,n}, \quad \forall i \in \{1, \dots, 5\}, \\ \bar{y}_o \le \sum_{n=1}^N \mu_n \bar{y}_{o,n}, \quad \forall o \in \{1, \dots, 2\}, \\ \sum_{n=1}^N \mu_n = 1, \quad \mu_n \ge 0, \quad \forall n \in \{1, \dots, N\} \end{array} \right\} \qquad (13).$$

Our estimation strategy, using a piecewise log-linear model, is more flexible than traditional piecewise linear approaches, which assume always decreasing marginal products. In contrast, our model allows for locally increasing or decreasing marginal products, depending on each farm's characteristics.
### 2.2.2 Estimation strategies

#### Max PROF: profitability maximization scenario

Profitability, denoted $\pi$, is defined, for each farm as the ratio of crop revenue ($R^1$) to intermediate consumption (IC). Thus, the function to be maximized is multiplicative.

$$ \pi = \frac{R^1}{IC} = \frac{y^1 * pp}{IC} \qquad (14). $$

Denote $\pi^*$ the optimal level for profitability, i.e. the profitability that would be attained by a farm by adopting the same practices as their benchmark. Denote $\theta$ the gap between the observed profitability level and the optimal level, i.e. $\pi^* = \pi\theta$, with $\theta \ge 1$. Thus, an efficient farm will obtain a coefficient $\theta = 1$ whereas for an inefficient farm, $\theta > 1$. Such an inefficient farm should increase its profitability by $(\theta - 1)\%$ to reach the maximum profitability level of efficient farms, in the same production context.

The profitability extension coefficient $\theta$ can be further broken down into a revenue change coefficient and a cost change coefficient. The revenue change, in turn, is decomposed into a crop quantity effect and a protein price effect:

$$ \pi^* = \frac{(\alpha y^1)(\beta pp)}{\gamma IC} = \frac{\alpha\beta}{\gamma}\pi \quad \text{with } \alpha, \beta, \gamma > 0 \quad \text{and} \quad \frac{\alpha\beta}{\gamma} \ge 1 \qquad (15), $$

where:

$\alpha$ = the coefficient for the crop quantity change to reach the optimal level ensuring the maximum profitability achievable,

$\beta$ = the coefficient for the price variation to reach the optimal level ensuring the maximum profitability achievable,

$\gamma$ = the coefficient for intermediate consumption variation to reach the optimal level ensuring the maximum profitability achievable.

Note that in the above equation (15), the only restriction on the profitability components efficiency scores is that they are positive, and that their combination $\frac{\alpha\beta}{\gamma} \ge 1$. To reach the maximum profitability level, a farm can appropriately adapt its protein production, protein price and intermediate consumption policies (see a more detailed explanation after the LP\_MaxPROF below).

This way, estimating the optimal profitability level for each farm, with our log-linear model in equation (13) goes down to estimating the optimal values for $\bar{\theta}$, or in other words, the optimal values for $\bar{\alpha}$, $\bar{\beta}$ and $\bar{\gamma}$.<fnref n="10" />

$$ \bar{\pi}^* = \bar{\alpha} + \bar{\beta} - \bar{\gamma} \qquad (16). $$

The (log) linear program under the variable returns to scale assumption, corresponding to the maximization of profitability for an evaluated farm $a$, is as follows:

<footnote n="10">¹⁰ Adapting the methodology developed in Boussemart et al. (2022) to our specific case is straightforward and conducive to a solution that is a general optimum.</footnote>
Moreover, literature on pesticide use at the farm level suggests that a decrease in pesticide intensity may lead to substitution or complementarity effects regarding the use of other inputs, such as land surfaces allocated to other activities, labor, equipment, and other intermediate consumption without pesticides (Boussemart et al., 2016). To account for these potential substitution and/or complementarity effects, we omit the associated constraints in LP\_MinPEST. Consequently, we can determine whether the "optimal" levels of input use are higher (indicating substitution effects), lower (indicating complementarity effects), or equal to the observed levels. The corresponding logarithmic linearization of this model is as follows:

$$
\begin{array}{ll}
\min_{\sigma, \mu} & \bar{\sigma} \\
\sum_{n=1}^{N} \mu_n \overline{R_n^1} \geq \overline{R_a^1} \\
\sum_{n=1}^{N} \mu_n \overline{R_n^2} \geq \overline{R_a^2} \\
\sum_{n=1}^{N} \mu_n \overline{AL_n} = \overline{AL_1} \\
\sum_{n=1}^{N} \mu_n \overline{P_n} \leq \bar{\sigma} + \overline{P_a} \\
\sum_{n=1}^{N} \mu_n = 1 \\
\mu_n \geq 0, \forall n \in N
\end{array}
\qquad (LP\_MinPEST).
$$

In LP\_MinPEST, $\bar{\sigma}$ gives the optimal decrease in the pesticides cost. For an efficient farm, we have $\bar{\sigma} = 0 \Leftrightarrow$
$\sigma = 1$, and for an inefficient one: $\bar{\sigma} < 0 \Leftrightarrow 0 < \sigma < 1$.

2.2.3 Various performance indicators and opportunity cost analysis

Our two stages analysis first assesses performance gaps between actual farm situations and benchmarks across three objectives, using metrics like revenue, protein yield, and gross margin per hectare. In the second stage, we compare three optimal scenarios—free of inefficiency—on these metrics. Assuming profitability as the primary goal, we calculate the opportunity costs of choosing alternatives, such as maximizing crop production or minimizing pesticide costs, against this goal.

Revenue performance indicators

In LP\_MaxPROF revenue is a component of the objective function. Additionally, both crop production its price<fnref n="13" />
are treated as variables to optimize and are thus linked to specific efficiency scores. In LP\_MaxCROP, the focus
is on maximizing crop production for each farm, without direct consideration of their respective prices. Revenue
is calculated by multiplying the optimal crop production by the price associated with the farms comprising the
benchmark. In LP\_MinPEST, revenue is regarded as a constraint and its components are not directly maximized.

<footnote n="13">¹³ As mentioned before, crop average prices can vary from one farm to another due either to a specific sales strategy or to a distinct crop mix.</footnote>
Crop production and prices are determined in this program based on their respective levels associated with the farms comprising the benchmark.

### Crop diversification indicator

Crop diversification boosts profitability and ecosystem services, such as soil and water quality (Beillouin et al., 2020; Nilsson et al., 2022; Tamburini et al., 2020). In the first two scenarios, arable land can be adjusted to improve efficiency, while in the pesticide scenario, land remains constant to reduce pesticide intensity. Crop diversification is measured using the Herfindahl-Hirschman Index (HHI)<fnref n="14" />, where a more diversified crop mix results in an HHI closer to 0, and a single-crop farm has an HHI of 1.

### Cost performance indicators

Costs are divided into two components: intermediate consumption without pesticides (ICWP) and pesticide costs (P). In *LP_MaxPROF*, costs are part of the objective function. The benchmark helps derive the optimal intermediate consumption (IC), allowing for possible substitution between ICWP and P. For example, reducing pesticide use may increase mechanical weeding costs or decrease fertilizer use, which could lower fertilizer costs. In *LP_MaxCROP*, intermediate consumption is treated as a constraint, with cost components derived from the benchmark farms. Substitution effects between IC components are also possible in this scenario. In *LP_MinPEST*, ICWP is not a constraint, with its level determined by the benchmark farms. Substitution or complementarity effects between ICWP and P may also occur in this scenario.

### Profitability and gross margin per ha performance indicators

The profitability ratio indicates the farm's relative capability to convert one euro of intermediate consumption into crop related revenue. This analysis extends to the gross margin per ha, defined as the difference between revenue and intermediate consumption expressed with regard to the arable land.

In *LP_MaxPROF*, we establish the optimal level of profitability, from which we derive associated revenue and cost levels to subsequently calculate the optimal gross margin per ha. Previously, we outlined methods for determining revenue and cost performances in *LP_MaxCROP* and *LP_MinPEST*. These variables enable us to infer the profitability ratio and associated gross margin for these two scenarios.

### Opportunity cost analysis

The three scenarios represent efficient production on the frontier, all showing improved profitability and gross margin per hectare compared to current practices. However, achieving each scenario requires adjustments in crop choices, valorization, and cost management. Farmers aiming to reduce inefficiencies would likely prioritize profitability, meaning alternative scenarios could reduce their gross margin. The difference in gross margin between the Max PROF scenario and any alternative scenario reflects the opportunity cost, which can be broken down into revenue and cost components.

Furthermore, in the case of the Max CROP scenario, we quantify the relative impact of a 1% increase in crop yield on the percentage change in gross margin per ha. By denoting the gross margin per ha as MRGN and crop yield

<footnote n="14">¹⁴ Denoting $s_c = \frac{AL_c}{AL}$, the share of crop c in the total arable land, we compute $HHI = \sum_{c=1}^{8} s_c^2$.</footnote>
as YLD, and utilizing the scenario employed for computing the respective variable as a subscript, this measure is obtained as follows:

$$ \epsilon_{MRGN/YLD} = \frac{\frac{MRGN_{MaxCROP}}{MRGN_{MaxPROF}} - 1}{\frac{YLD_{MaxCROP}}{YLD_{MaxPROF}} - 1} \quad (17). $$

Another indicator of interest is the % change of pesticide cost per ha (PHa) due to a 1% increase in the crop yield between the two scenarios considered, as in the equation (18) below.

$$ \epsilon_{Pest/YLD} = \frac{\frac{PHa_{MaxCROP}}{PHa_{MaxPROF}} - 1}{\frac{YLD_{MaxCROP}}{YLD_{MaxPROF}} - 1} \quad (18). $$

In the case of the pesticide minimization scenario, we can estimate the relative impact of 1% decrease in the pesticide cost per ha on the percentage change in the gross margin per ha by:

$$ \epsilon_{MRGN/Pest} = \frac{\frac{MRGN_{MinPEST}}{MRGN_{MaxPROF}} - 1}{\frac{PHa_{MinPEST}}{PHa_{MaxPROF}} - 1} \quad (19). $$

In this case too, we can compute the % change in the crop yield due to a 1% decrease in the pesticide cost per ha as follows:

$$ \epsilon_{YLD/Pest} = \frac{\frac{YLD_{MinPEST}}{YLD_{MaxPROF}} - 1}{\frac{PHa_{MinPEST}}{PHa_{MaxPROF}} - 1} \quad (20). $$

We explore a method to ensure farmers maintain the same gross margin per hectare under a pesticide reduction policy as they would by maximizing profitability. The strategy incentivizes farmers to reduce pesticide use by increasing the protein price to offset potential revenue losses. A label signaling their commitment to pesticide reduction could help them negotiate higher prices to cover opportunity costs. For a given level of achievable intermediate costs per ha in the pesticide minimization scenario ($ICHa_{MinPest}$), we calculate the average revenue per ha, $R^*$, assuming it compensates for the gross margin reduction in a scenario where pesticide use is minimized.

$$ \begin{aligned} MRGN_{MaxPROF} &= MRGN_{MinPEST} \Leftrightarrow \\ MRGN_{MaxPROF} &= R^* - ICHa_{MinPest} \Leftrightarrow \\ R^* &= MRGN_{MaxPROF} + ICHa_{MinPest} \end{aligned} \quad (21). $$

Then, for a given yield obtained in this scenario, we deduce the associated protein price denoted $pp^*$ by:

$$ pp^* = \frac{R^*}{YLD_{MinPEST}} \quad (22). $$

Thanks to the above pesticide-reduction compensating price, we compute its % change when, departing from a profitability maximization scenario, the pesticide cost per ha decreases by 1% as:

$$ \epsilon_{pp^*/Pest} = \frac{\frac{pp^*}{PPMaxPROF} - 1}{\frac{PHa_{MinPEST}}{PHa_{MaxPROF}} - 1} \quad (23). $$
# 3. Results and discussion

## 3.1 Performance analysis in the three scenarios with regards to the observed situation

### 3.1.1. Revenue performance

The first two scenarios, focused on profitability maximization (Max PROF) and crop production maximization (Max CROP), provide an increase in the protein yield by 5% and 10%, respectively (Figure 1). This increase goes hand in hand with a 4% improvement in crop prices in the scenario Max PROF while the protein price remains unchanged in scenario Max CROP, suggesting that protein yields and prices do not appear to be correlated in this context. Only the scenario focused on minimizing pesticide use (Min PEST) results in a slight decrease in the protein yield (-2%). Nevertheless, this quantity is better valued on the market, with a price increase of +5%. Therefore, in this scenario, the protein yield is negatively correlated with the protein price, most likely due to a shift in the crop mix in favor of higher valued products, such as maize and sunflower (see Figure 3.d for the optimal crop mix in this scenario as well as the Figure B in the Appendix 2 for the per crop protein prices).

The combined effect of protein yield and price leads to a positive impact on farmers' crop revenue in all three scenarios. Even in scenario Min PEST, where associated protein yields decrease, the potential for revenue increase remains positive, at 3%.

Crop yield increases for each crop in both the Max PROF and Max CROP scenarios (Figure 2). However, the reduction in pesticide intensity in the Min PEST scenario leads to lower crop yield improvements than in the previous two scenarios. Moreover, for some crops such as wheat, winter barley, and rapeseed, potential yields even slightly decrease. This decrease in crop yield could be partly related to incomplete control of weeds, diseases or pathogens, but also to technical options of farmers wishing to decrease the reliance on pesticide (e.g., choice of cultivars based on resistance to diseases rather than on yielding potential, delay in cereal sowing to escape weeds and diseases associated to moderate fertilization, see for example Lechenet et al., 2016).

<figure><img src="image_2.png" /><figcaption>Figure 1. Variation in protein yield and price and its impact on farms’ revenue per ha in each scenario compared to the observed situation</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Figure 2. Variation in yields per crop, for the entire sample and the entire period 1991-2017, in each scenario, compared to the observed situation</figcaption></figure>

### 3.1.2. Variation in crop areas and crop diversification index

The optimal total crop area decreases by -16% in the Max PROF scenario, compared to the observed level, indicating that smaller-sized farms yield higher profitability per ha than larger ones (Table 2). Conversely, in the Max CROP scenario, the optimal total crop area remains almost unchanged, with a marginal difference of -1% from the observed level. Lastly, in the pesticide cost minimization scenario, our objective is to reduce pesticide intensity rather than alter total crop area. Therefore, we maintain the total crop area unchanged, focusing instead on decreasing pesticide use per ha.

<table><caption>Table 2. Impact of each scenario on the evolution of the whole sample total crop area and the average per farm for the entire period (in ha)</caption><thead><tr><th>Situation</th><th>Global (ha)<sup>1</sup></th><th>Average per farm (ha)</th><th>Variation with regard to the observed in %</th></tr></thead><tbody><tr><td>Observed</td><td>509,887</td><td>176</td><td>/</td></tr><tr><td>Max PROF</td><td>426,707</td><td>147</td><td>-16%</td></tr><tr><td>Max CROP</td><td>504,466</td><td>174</td><td>-1%</td></tr><tr><td>Min PEST</td><td>509,887</td><td>176</td><td>0%</td></tr></tbody></table>

(1): the surfaces are computed as the cumulated total arable land surface for the entire period analyzed.

Scenarios Max PROF and Max CROP do not have a substantial impact on the distribution of area per crop (Figure 3). This suggests that the specialization in some crops such as wheat and rapeseed can be an effective way to maximize profitability or crop production according to our sample of farms, when pesticide reduction is not a concern. Note that the objective of maximizing crop production does not lead to an increase in the share of protein-
rich legume crops.<fnref n="15" /> In the third scenario, the minimization of pesticide cost leads to a slight decrease in wheat (from 33% to 30%), winter barley (from 14% to 10%), and rapeseed (from 26% to 18%). In contrast, the shares of maize, sunflower and spring barley increase. In a study on pesticide use in France, Guinet et al. (2023) showed that rapeseed, winter wheat and winter barley required higher pesticide inputs compared to sunflower, maize and spring barley. Adjusting the share of crops in favor of those crops requiring less pesticides contributes to minimize pesticides in the third scenario.

<figure><img src="image_4.png" /><figcaption>Figure 3. Evolution of crop distribution</figcaption></figure>

Related to these results, it is interesting to study the HHI index for crop diversification in each scenario. In Table 3 we notice that the HHI remains stable in the Max PROF and Max CROP scenarios compared to the observed

<footnote n="15">¹⁵ This result might be related to the farm sample in the Meuse district, that includes very few legume crops, hence leaving little opportunity to have legume crops in benchmark farms, even in this scenario Max CROP.</footnote>
situation. This prompts the idea that higher yields obtained for these scenarios are not associated with crop diversification (Figure 3 above). Instead, they can be associated to a better technical efficiency (e.g., improved nitrogen use efficiency due to better synchronization between crop nitrogen requirements and fertilizer nitrogen inputs). However, in the Min Pest scenario, the HHI is lower compared to the observed situation due to crop rotation diversification (see Figure 3 above).

<table><caption>Table 3. HHI index for crop diversification at the global scale over the period 1991-2017</caption><thead><tr><th>Observed situation</th><th>Max PROF</th><th>Max CROP</th><th>Min PEST</th></tr></thead><tbody><tr><td>0.222</td><td>0.232</td><td>0.236</td><td>0.188</td></tr></tbody></table>

### 3.1.2. Cost performance

Projecting farms onto the benchmark enables a decrease in total intermediate consumption of 13 % in the Max PROF scenario and 8 % in the Min PEST scenario (Figure 4). Conversely, there is no notable decrease in intermediate consumption in the Max CROP scenario (-1%).

In Figure 4, the percentage changes in each component are obtained as variations with regards to the intermediate consumption (IC). The ICWP component decreases by -10% for the Max PROF scenario and -2% for the Max CROP scenario. However, in the Min PEST scenario, the associated ICWP increases above their observed level by 2%. This indicates a substitution effect in this scenario between the decrease in pesticide use and the increase in other intermediate consumption. In the Min PEST scenario, as expected, the decrease in the pesticide cost with regards to the intermediate consumption is the most notable one, -10% whereas in the Max PROF scenario, this reduction is only -3%. However, the objective of maximizing protein production appears to be incompatible with reducing pesticide intensity, as we observe a slight increase in pesticide costs in the total intermediate consumption of +1%.

<figure><img src="image_5.png" /><figcaption>Figure 4. Potential variation of intermediate consumptions per ha and its components, ICWP and pesticide cost (in % of the observed total intermediate consumption level) for each scenario with regards to the observed situation</figcaption></figure>
Compared to the observed pesticide intensity, the Min PEST scenario decreases pesticide intensity by -31%, the Max PROF scenario decreases it by -9%, while this indicator increases in the Max CROP scenario by 3%. Appendix 3 presents a more detailed analysis regarding the ICWP components.

### 3.1.3. Profitability and gross margin performances

Unsurprisingly, compared to the observed situation, the highest profitability ratio increase is obtained in the Max PROF scenario, with +26%, against +11% in both Max CROP and Min PEST scenarios (Figure 5). In the scenario minimizing pesticide, despite the decrease in crop yields described above, profitability is increased thanks to an increase in the crop price and a simultaneous decrease in intermediate consumption (cf. Figures 1 and 4, respectively). All three scenarios lead to a positive impact on the gross margin.

<figure><img src="image_6.png" /><figcaption>Figure 5. Profitability ratio and gross margin (per ha) evolutions compared to the observed levels, in the three scenarios.</figcaption></figure>

## 3.2. Opportunity cost analysis and the tradeoffs between the three scenarios

This section analyses the tradeoffs between the profitability maximization scenario, considered as the baseline, and either the protein maximization scenario or the pesticide minimization scenario. We assume that farmers' primary rationale is to increase profitability through an optimal allocation of resources. Given this assumption, the alternative scenarios may incur potential financial losses compared to the baseline, representing opportunity costs for the farmer.<fnref n="16" />

<footnote n="16">¹⁶ Nevertheless, it is worth reminding that the preceding sub-section has shown that the three benchmarks all lead to an improvement in the revenue and cost indicators compared to the observed situation (with one very minor exception, regarding pesticide cost in the protein maximization scenario which observed an increase of 5€$_{2010}$ per ha).</footnote>
The baseline scenario, focused on profitability maximization, delivers the highest gross margin, as expected (Figure 6). However, a closer look reveals more complexity. The profitability scenario has the lowest intermediate consumption (excluding pesticides) at 295 €2010/ha, while the pesticide minimization scenario achieves the expected outcome of the lowest pesticide cost at 113 €2010/ha. Interestingly, the crop maximization scenario records the highest revenue per hectare at 1032 €2010/ha.

Shifting from maximizing profitability to maximizing crop production results in a modest revenue increase of 8 €2010/ha (+0.7%), driven by a 4.5% rise in crop yield, though offset by a 3.6% decrease in crop market value. However, this scenario also increases intermediate consumption by 64 €2010/ha, including 43 €2010/ha for ICWP and 21 €2010/ha for pesticides, leading to a 55 €2010/ha reduction in gross margin. This means a 1% increase in crop yields would cause a 2.12% decrease in gross margin. Additionally, a 1% increase in crop yields leads to a 3.01% rise in pesticide intensity. These high elasticity values for gross margin and pesticide use suggest that productivity-focused strategies may not improve financial or environmental sustainability.

Shifting from maximizing profitability to minimizing pesticide inputs would incur an opportunity cost of 63 €2010/ha, a 6.2% revenue decrease, largely due to a 7.4% drop in crop yield, slightly offset by a 1.3% price increase. Intermediate consumption would rise by 65 €2010/ha, while pesticide costs would drop by 36 €2010/ha, leading to an overall operational cost increase of 29 €2010/ha and a net decline in gross margin of 92 €2010/ha. A 1% reduction in pesticide costs would lower the gross margin by 0.66% and crop yields by 0.31%. These low elasticity values suggest that pesticide reduction policies could be economically viable while addressing crop self-sufficiency concerns.

<figure><img src="image_7.png" /><figcaption>Figure 6. Potential progression in gross margin and its components in each scenario</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7. Variation in the revenue components between the different scenarios (in %)</figcaption></figure>

This analysis has important implications for agricultural policy, especially regarding price compensations to farmers for opportunity losses. While the protein price under the Min PEST scenario is 1.55€$_{2010}$, the price needed to offset the gross margin loss compared to profitability maximization is 1.70€$_{2010}$. A 1% reduction in pesticide intensity would raise the protein crop price by 0.45%, suggesting relatively low opportunity costs for downstream clients.

One way to promote reduced pesticide use in farming is to hold downstream partners—such as supermarkets and consumers—accountable by introducing a price increase, supported by transparency on pesticide use, possibly through labeling. This adjustment would help farmers engaged in pesticide-reduction practices reach the maximum margins of the profitability scenario. Final consumer price variations could depend on agro-industrial negotiations and may be less than the 11% increase<fnref n="17" /> needed to make pesticide minimization as profitable as maximizing profitability, offering an incentive for change.

4. Conclusion

This study examined the interactions between profitability, crop production, and pesticide use on arable farms in France's Meuse department across three scenarios: maximizing profitability, maximizing crop production, and minimizing pesticide use. Methodologically, our approach extends previous work by positioning all farms on the efficiency frontier before comparing optimal potentials, i.e., gross margin per ha, crop yield or pesticide use, ensuring that opportunity costs reflect trade-offs between fully efficient situation. By integrating output price variables into non-parametric performance estimation and applying a log-linear production technology, we offer a more flexible framework for analyzing multi-objective decision-making in agriculture. This framework offers valuable insights for practitioners and policymakers seeking to design incentives and strategies that balance economic, productive and environmental goals.

<footnote n="17">¹⁷ The necessary price increase to ensure that farmers are indifferent between the two scenarios is obtained as $\frac{pp^*}{pp_{MaxPROF}} - 1$, where $pp^*$ is computed with equation (22) and $pp_{MaxPROF}$ is defined as the optimal price per kg of protein resulting from the Max PROF scenario.</footnote>
Our analysis is conducted in two stages. In the first stage, we correct for inefficiencies to position all farms on the efficiency frontier, allowing for a valid comparison of their potential performance under each objective. We found that profitability would increase under any scenario, but aligning all farms with the most profitable or crop production-maximization practices would require better crop and farm management without diversifying crops. High crop yields depend on intensive pesticide use, while reducing pesticides would require greater crop diversification. However, these results should be interpreted with caution. The evaluated crop production strategy, measured by the total quantity of protein produced, reflects current practices in the Meuse department, where legume cultivation remains limited. A combined approach of reducing pesticide use and increasing protein supply would likely require a shift toward legume crops, an option that remains largely unexplored in the region. Unlike the current Max CROP scenario, which relies on input intensification to maximize yields, a greater emphasis on legumes—benefiting from nitrogen fixation—could alter the economic and environmental trade-offs by reducing intermediate consumption.

In the second stage, comparing the profitability maximization scenario with alternatives of crop production maximization and pesticide minimization revealed potential trade-offs. On one hand, the suppression of all inefficiencies within a strategy of crop production maximization by intensifying inputs would result in opportunity costs of 55 €2010/ha compared to the suppression of inefficiencies within a strategy of profitability maximization. Moreover, on the frontier of efficient systems, a 1% increase in crop production leads to a decrease of the gross margin per ha by 2.1% and requires a 3% increase in pesticide inputs. On the other hand, the suppression of inefficiencies within a strategy of pesticide minimization compared to a suppression of inefficiencies through a profitability maximization objective would result in opportunity costs of 92 €2010/ha. Thus, on the frontier of efficient systems, a 1% decrease in pesticide inputs leads to a decrease in the gross margin per ha by 0.66%, and a decrease in crop production by 0.31%.

This study suggests that the opportunity costs of minimizing pesticide use could be offset by higher market prices, given the inelasticity of protein prices and consumer willingness to pay for quality. Intra-industry negotiations could also help secure better prices for farmers adopting sustainable practices. Secondly, maximizing yields, though seemingly beneficial, results in significant margin losses compared to prioritizing profitability. Lastly, in the Meuse department, compensating for the costs of maximizing production through market prices is difficult due to consumer reluctance, especially when higher yields require more pesticide use.

This study focuses on agricultural farms that exhibit a certain degree of homogeneity in cultural practices and crop choices. Since developing sustainable agriculture requires significant operational changes, expanding this analysis to more innovative farms could help validate or refine these findings across different agricultural models. For example, introducing protein-rich legume crops could help reconcile the often-conflicting goals of various stakeholders, such as improving food self-sufficiency, enhancing profitability, and promoting more environmentally sustainable practices.
References

Agreste-Recensement Agricole. (2020). https://www.agreste.agriculture.gouv.fr/agreste-web/

Ait Sidhoum, A., Serra, T., & Latruffe, L. (2019). Measuring sustainability efficiency at farm level: A data envelopment analysis approach. *European Review of Agricultural Economics*, 7(1), 200-225.
https://doi.org/10.1093/erae/jbz015

Ang, F., Mortimer, S. M., Areal, F. J., & Tiffin, R. (2018). On the Opportunity Cost of Crop Diversification. *Journal of Agricultural Economics*, 69(3), 794-814. https://doi.org/10.1111/1477-9552.12272

Ballot, R., Guilpart, N., & Jeuffroy, M.-H. (2023). The first map of crop sequence types in Europe over 2012–2018. *Earth System Science Data*, 15(12), 5651-5666. https://doi.org/10.5194/essd-15-5651-2023

Banker, R. D., & Maindiratta, A. (1986). Piecewise Loglinear Estimation of Efficient Production Surfaces. *Management Science*, 32(1), 126-135.

Beillouin, D., Ben-Ari, T., Malézieux, E., Seufert, V., & Makowski, D. (2021). Positive but variable effects of crop diversification on biodiversity and ecosystem services. *Global Change Biology*, 00, 1–14. https://doi.org/10.1111/gcb.15747

Berre, D., Boussemart, J.-P., Leleu, H., & Tillard, E. (2013). Economic value of greenhouse gases and nitrogen surpluses: Society vs farmers’ valuation. *European Journal of Operational Research*, 226(2), 325-331.
https://doi.org/10.1016/j.ejor.2012.11.017

Boussemart, J.-P., Leleu, H., & Ojo, O. (2016). Exploring cost dominance in crop farming systems between high and low pesticide use. *Journal of Productivity Analysis*, 45(2), 197-214. https://doi.org/10.1007/s11123-015-0443-1

Boussemart, J.-P., Leleu, H., & Parvulescu, R. (2022). Value-Based Performance and Its Decomposition into Direct Price and Quantity Effects. *European Journal of Operational Research*, 303(1), 298-311.
https://doi.org/10.1016/j.ejor.2022.02.039.

Boussemart, J.-P., Leleu, H., Shen, Z., & Valdmanis, V. (2020). Performance analysis for three pillars of sustainability. *Journal of Productivity Analysis*, 53(3), 305-320. https://doi.org/10.1007/s11123-020-00575-9

Bues, A., Preißel, S., Reckling, M., Zander, P., Kuhlman, T., Topp, K., Watson, C., Lindström, K., Stoddard, F.L., & Murphy-Bokern, D. (2013). The environmental role of protein crops in the new common agricultural policy: Study. *European Parliament*. IP/B/AGRI/IC/2012-067.

Butault, J.-P., Delame, N., Jacquet, F., & Zardet, G. (2011). *L'utilisation des pesticides en France : État des lieux et perspectives de réduction*. *Notes et Études Socio-Économiques*, 35, 7-26.

Chambers, R. G., Chung, Y., & Färe, R. (1996). Benefit and Distance Functions. *Journal of Economic Theory*, 70(2), 407-419. https://doi.org/10.1006/jeth.1996.0096

Chambers, R. G., Serra, T., & Oude Lansink, A. (2014). On the pricing of undesirable state-contingent outputs. *European Review of Agricultural Economics*, 41(3), 485-509. https://doi.org/10.1093/erae/jbu018

Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the Efficiency of Decision Making Units. *European Journal of Operational Research*, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8.

Coelli, T., Grifell-Tatjé, E., & Perelman, S. (2002). Capacity utilisation and profitability: A decomposition of short-run profit efficiency. *International Journal of Production Economics*, 79(3), 261-278.
https://doi.org/10.1016/S0925-5273(02)00236-0
Dakpo, K. H., Jeanneaux, P., & Latruffe, L. (2016). Modelling pollution-generating technologies in performance benchmarking: Recent developments, limits and future prospects in the nonparametric framework. *European Journal of Operational Research*, 250(2), 347-359. https://doi.org/10.1016/j.ejor.2015.07.024

Dimara, E., Pantzios, C. J., Skuras, D., & Tsekouras, K. (2005). The impacts of regulated notions of quality on farm efficiency: A DEA application. *European Journal of Operational Research*, 161(2), 416-431.
https://doi.org/10.1016/j.ejor.2003.07.016

FAO. (2023). FAOSTAT. https://www.fao.org/faostat/en/#data/QCL.

Färe, R., & Knox Lovell, C. A. (1978). Measuring the technical efficiency of production. *Journal of Economic Theory*, 19(1), 150-162. https://doi.org/10.1016/0022-0531(78)90060-1

Fukuyama, H., & Matousek, R. (2017). Modelling bank performance: A network DEA approach. *European Journal of Operational Research*, 259(2), 721-732.
https://doi.org/10.1016/j.ejor.2016.10.044

Fukuyama, H., & Matousek, R. (2018). Nerlovian revenue inefficiency in a bank production context: Evidence from Shinkin banks. *European Journal of Operational Research*, 271(1), 317-330.
https://doi.org/10.1016/j.ejor.2018.05.008

Fukuyama, H., & Weber, W. L. (2010). A slacks-based inefficiency measure for a two-stage system with bad outputs. *Omega*, 38(5), 398-409. https://doi.org/10.1016/j.omega.2009.10.006

Fukuyama, H., & Weber, W. L. (2015). Measuring Japanese bank performance: A dynamic network DEA approach. *Journal of Productivity Analysis*, 44(3), 249-264. https://doi.org/10.1007/s11123-014-0403-1

Fukuyama, H., & Weber, W. L. (2017). Measuring bank performance with a dynamic network Luenberger indicator. *Annals of Operations Research*, 250(1), 85-104. https://doi.org/10.1007/s10479-015-1922-5

Guinet, M., Adeux, G., Cordeau, S., Courson, E., Nandillon, R., Zhang, Y., & Munier-Jolain, N. (2023). Fostering temporal crop diversification to reduce pesticide use. *Nature Communications*, 14(1), 7416.
https://doi.org/10.1038/s41467-023-43234-x

Koopmans, T. C. (1951). Analysis of production as an efficient combination of activities. In T.C. Koopmans (Ed.), *Activity Analysis Of Production And Allocation*. New York: John Wiley.

Lansink, A. O., & Silva, E. (2004). Non-Parametric Production Analysis of Pesticides Use in the Netherlands. *Journal of Productivity Analysis*, 21(1), 49-65. https://doi.org/10.1023/B:PROD.0000012452.97645.30

Lechenet, M., Makowski, D., Py, G., & Munier-Jolain, N. (2016). Profiling farming management strategies with contrasting pesticide use in France. *Agricultural Systems*, 149, 40-53.
https://doi.org/10.1016/j.agsy.2016.08.005

Matson, P. A., Parton, W. J., Power, A. G., & Swift, M. J. (1997). Agricultural Intensification and Ecosystem Properties. *Science*, 277(5325), 504-509. https://doi.org/10.1126/science.277.5325.504

Mémento. (2022). *Agreste Grand Est*. Published on 17/01/2023. https://draaf.grand-est.agriculture.gouv.fr/memento-de-la-statistique-agricole-edition-2022-a3070.html

Millennium Ecosystem Assessment. (2005). *Ecosystems and human well-being: Synthesis*. Island Press, Washington, DC.

Murty, S., Robert Russell, R., & Levkoff, S. B. (2012). On modeling pollution-generating technologies. *Journal of Environmental Economics and Management*, 64(1), 117-135. https://doi.org/10.1016/j.jeem.2012.02.005
Nilsson, P., Bommarco, R., Hansson, H., Kuns, B., & Schaak, H. (2022). Farm performance and input self-sufficiency increases with functional crop diversity on Swedish farms. *Ecological Economics*, 198, 107465.
https://doi.org/10.1016/j.ecolecon.2022.107465

Niu, Y., Boussemart, J.-P., Shen, Z., & Vardanyan, M. (2024). Performance evaluation using multi-stage production frameworks: Assessing the tradeoffs among the economic, environmental, and social well-being. *European Journal of Operational Research*, 318(3), 1000-1013. https://doi.org/10.1016/j.ejor.2024.05.046

Picazo-Tadeo, A. J., Beltrán-Esteve, M., & Gómez-Limón, J. A. (2012). Assessing eco-efficiency with directional distance functions. *European Journal of Operational Research*, 220(3), 798-809.
https://doi.org/10.1016/j.ejor.2012.02.025

Pimentel, D., Wilson, C., McCullum, C., Huang, R.,wen, P., Flack, J., Tran, Q., Saltman, T., & Cliff, B. (1997). Economic and Environmental Benefits of Biodiversity. *BioScience*, 47(11), 747-757.
https://doi.org/10.2307/1313097.

Ray, S. C., Mukherjee, K., & Venkatesh, A. (2018). Nonparametric measures of efficiency in the presence of undesirable outputs: A by-production approach. *Empirical Economics*, 54(1), 31-65.
https://doi.org/10.1007/s00181-017-1234-5

Schaak, H., Bommarco, R., Hansson, H., Kuns, B., & Nilsson, P. (2023). Long-term trends in functional crop diversity across Swedish farms. *Agriculture, Ecosystems & Environment*, 343, 108269.
https://doi.org/10.1016/j.agee.2022.108269

Serra, T., Chambers, R. G., & Oude Lansink, A. (2014). Measuring technical and environmental efficiency in a state-contingent technology. *European Journal of Operational Research*, 236(2), 706-717.
https://doi.org/10.1016/j.ejor.2013.12.037

Skevas, T., Lansink, A. O., & Stefanou, S. E. (2012). Measuring Technical Efficiency in the Presence of Pesticide Spillovers and Production Uncertainty: The Case of Dutch Arable Farms. *European Journal of Operational Research*, 223(2), 550-559. https://doi.org/10.1016/j.ejor.2012.06.034.

Skevas, T., & Serra, T. (2016). The role of pest pressure in technical and environmental inefficiency analysis of Dutch arable farms: An event-specific data envelopment approach. *Journal of Productivity Analysis*, 46(2-3), 139-153. https://doi.org/10.1007/s11123-016-0476-0

Skevas, T., Stefanou, S. E., & Oude Lansink, A. (2014). Pesticide use, environmental spillovers and efficiency: A DEA risk-adjusted efficiency approach applied to Dutch arable farming. *European Journal of Operational Research*, 237(2), 658-664. https://doi.org/10.1016/j.ejor.2014.01.046

Tamburini, G., Bommarco, R., Wanger, T. C., Kremen, C., Van Der Heijden, M. G. A., Liebman, M., & Hallin, S. (2020). Agricultural diversification promotes multiple ecosystem services without compromising yield. *Science Advances*, 6(45), eaba1715. https://doi.org/10.1126/sciadv.aba1715

Thiele, H., & Brodersen, C. M. (1999). Differences in farm efficiency in market and transition economies: Empirical evidence from West and East Germany. *European Review of Agriculture Economics*, 26(3), 331-347.
https://doi.org/10.1093/erae/26.3.331

Tilman, D., Cassman, K. G., Matson, P. A., Naylor, R., & Polasky, S. (2002). Agricultural sustainability and intensive production practices. *Nature*, 418(6898), 671-677. https://doi.org/10.1038/nature01014
Travisi, C. M., & Nijkamp, P. (2008). Valuing Environmental and Health Risk in Agriculture: A Choice Experiment Approach to Pesticides in Italy. *Ecological Economics*, 67(4), 598-607.
https://doi.org/10.1016/j.ecolecon.2008.01.011.

Watson, C. A., Reckling, M., Preissel, S., Bachinger, J., Bergkvist, G., Kuhlman, T., Lindström, K., Nemecek, T., Topp, C. F. E., Vanhatalo, A., Zander, P., Murphy-Bokern, D., & Stoddard, F. L. (2017). Grain Legume Production and Use in European Agricultural Systems. In *Advances in Agronomy* (Vol. 144, p. 235-303).
Elsevier. https://doi.org/10.1016/bs.agron.2017.03.003
**Appendix 1.**

Wheat (33%) and rapeseed (26%) were the predominant crops, trailed by winter and spring barley at 14% and 13%
respectively (Figure A).<fnref n="18" /> Maize and fallow land occupied nearly equal proportions (6% and 5%, respectively).
Peas were the least prevalent, accounting for slightly less than 1% of the total area. For comparison, the main crops
cultivated in the Meuse department included winter wheat, barley (both spring and winter varieties), and rapeseed,
accounting for 82% of the total field crop land in 2021 (Mémento, 2022).

<figure><img src="image_9.png" /><figcaption>Figure A. Shares of crops in the total crop agricultural land</figcaption></figure>

<footnote n="18">¹⁸ In our sample, wheat, barley, and rapeseed, accounted for 84% of our total crop area comparatively to 82% in the Meuse department in 2021.</footnote>
## Appendix 2.

<figure><img src="image_10.png" /><figcaption>Figure B. Distribution of crop protein prices expressed in constant $\epsilon_{2010}/\text{Kg}$ over the period 1991-2017</figcaption></figure>

## Appendix 3.

Furthermore, we explored the evolution of the various components of ICWP related to crop activity (Figure C). All costs decrease in the Max PROF scenario. In the Max CROP scenario, expenses generally remain constant, except for seed costs, which marginally decrease. In the Min PEST scenario, the reduction in pesticide use is combined with a decrease in fertilizer costs, while seed costs increase. There is no remarkable impact on fuel while electricity cost increased slightly in this scenario. Improved cost efficiency in each scenario can be achieved through a variety of strategies. For instance, in the Max PROF scenario, where crop distribution remains largely unchanged (Figure 3 in the paper), fertilizer use efficiency may has been improved thanks to timely spreading, fractioned fertilization and the use of decision-support tools. In contrast, the Min PEST scenario demonstrates how crop rotation diversification could lead to reduced fertilization. Figure 3 in the paper indicates for this scenario an increase in crops that require less nitrogen, such as sunflower and fallow, as opposed to more demanding crops like rapeseed or winter cereals. Additionally, in the Min PEST scenario, the presence of more spring and summer crops (spring barley, maize, sunflower) may account for higher seed costs, as illustrated in Figure C. This increase could be due to the introduction of cover crops between two cash crops.
<figure><img src="image_11.png" /><figcaption>Figure C. Main components of ICWP in €2010/ha</figcaption></figure>

Considering that the estimations aimed at achieving minimum pesticide use (LP\_MinPEST) did not directly account for the other resources required for crop production (such as other surfaces, labor, and equipment), it is intriguing to identify the levels that would be attained if all farms had reached their benchmarks. From this perspective, the farms would not need to alter their other activities, as the area used for other activities (OS) remains consistent with the observed area for the entire sample and throughout the entire period (+0.1%). Aligning with minimal pesticide use does not imply a change in capital depreciation cost either (-0.3%). However, we do observe a substitution effect regarding the total labor used at the farm level, which would need to increase by 12% to minimize pesticide use. Potentially, efficient practices compatible with the Min PEST scenario require in general a higher quantity of labor dedicated to implementing alternative practices for managing pests, for example, mechanical weeding. These practices also involve a higher fuel consumption, which is slightly observed in Figure C.