Alice Audrezet
email: alice.audrezet@isg.fr

Béatrice Parguel
email: beatrice.parguel@dauphine.fr

Square but Straight: Measurement Tool Design to Improve Response Task Fluency and Certainty

Keywords: Attitude certainty, processing fluency, attitude measurement, evaluative space grid, tool design

 Zanna 1978, Antil 1983). The present article builds on previous research to investigate the influence of different formats of the ESG on response task fluency and certainty. To do so, an experiment specifically manipulating the ESG dimension and the presence of verbal labels in the cells was conducted on a sample of 105 undergraduate students. We demonstrate that the use of verbal labels, rather than a reduction in response alternatives, is a promising way to increase response task fluency and, in turn, improve individuals' response certainty. This work advocates for tool design reflection to create responding behavior incentives and reduce survey drop-out rates which is especially challenging within self-administered electronic settings.

Introduction

The assessment of overall customer satisfaction is an important issue in market research because it is considered a barometer of business performance [START_REF] Lee | Does Advertising Exposure Prior to Customer Satisfaction Survey Enhance Customer Satisfaction Ratings?[END_REF] that predicts other key marketing variables, such as profit or loyalty [START_REF] Haumann | Footprints in the Sands of Time: A Comparative Analysis of the Effectiveness of Customer Satisfaction and Customer-Company Identification over Time[END_REF][START_REF] Homburg | Internal and External Price Search in Industrial Buying: The Moderating Role of Customer Satisfaction[END_REF]. Customer surveys, therefore, generally begin with or include a measure of the overall customer satisfaction resulting from a consumption experience. As an illustration, after each online purchase or booking experience, customers are systematically asked to assess the product or service for which they have paid, usually on a five-point rating scales (e.g., Amazon, Trip Advisor). Comparable to bipolar scales, these tools are effective in making a distinction between polarized evaluations (i.e., either strong positivity or strong negativity). However, the literature on methodology reveals serious problems related to the mid-point displayed on these continuums [START_REF] Kaplan | On the Ambivalence-Indifference Problem in Attitude Theory and Measurement: a Suggested Modification of the Semantic Differential Technique[END_REF][START_REF] Thompson | Let's not Be Indifferent About (Attitudinal) Ambivalence[END_REF]. Actually, this mid-point inappropriately aggregates uncertain responses (difficult evaluation) with ambivalent (a combination of moderate to high positivity and negativity) or indifferent (low positivity and negativity) ones, when these different responses have been shown to reflect different attitudes and drive distinct behavioral responses [START_REF] Yoo | Two Types of Neutrality: Ambivalence versus Indifference and Political Participation[END_REF][START_REF] Thornton | Ambivalent or Indifferent? Examining the Validity of an Objective Measure of Partisan Ambivalence[END_REF].

The Evaluative Space Grid (hereafter, ESG), developed in psychology by Larsen and colleagues (2009), could help address part of this methodological issue. The ESG comprises a 5×5 grid that measures both the degree of positivity of a stimulus and its degree of negativity within a bidimensional matrix (see Figure 1). One dimension of the matrix is dedicated to the measurement of the respondent's degree of negativity (from "not at all negative" to "extremely negative"), and the other dimension is dedicated to the measurement of the respondent's degree of positivity (from "not at all positive" to "extremely positive"). The combination of the two dimensions allows the respondent to choose which of the grid's 25 cells best describes its evaluation. The ESG has been validated in psychology with respect to unipolar measurement of positivity and negativity [START_REF] Larsen | The Evaluative Space Grid: A Single-Item Measure of Positivity and Negativity[END_REF]. Going further, applying the ESG in a service marketing context, Audrezet and colleagues (2016) have recently demonstrated its relevance to measure overall customer satisfaction.

Figure 1: Evaluative Space Grid [START_REF] Larsen | The Evaluative Space Grid: A Single-Item Measure of Positivity and Negativity[END_REF] Regarding the practical implementation of ESG, Larsen and colleagues (2009) formulate 2-minute generic instructions before using paper-and-pencil or computerized versions of the ESG. In both cases, their instructions include the presence of an experimenter to show the grid and accompany the respondents in their task. However, they do not discuss the extent to which the grid could be easy to use in self-administered surveys, which have become the most common mode of administration for customer satisfaction surveys. Yet, a rapid qualitative survey shows that the ESG could disrupt unfamiliar respondents, who may find it counterintuitive to distinguish variables they usually assess on a continuum, difficult to interpret certain zones (e.g., the dissatisfaction axis), and puzzling to face a 25-cell consideration response set. Consequently, the ESG could hinder response task fluency, which could negatively affect response certainty [START_REF] Regier | Task Complexity and Response Certainty in Discrete Choice Experiments: An Application to Drug Treatments for Juvenile Idiopathic Arthritis[END_REF] or the subjective sense that one knows what one's response should be. This, in turn, could potentially be very detrimental to market research as attitude certainty is a crucial determinant of data and prediction quality (Rucker andPetty 2004, Rucker et al. 2014).

To keep the ESG response task fluent, the results of our informal exploratory survey suggest developing starting instructions and offering an experience phase before collecting the assessment. In a less intrusive way, they also suggest that reducing the grid dimension and pre-identifying zones with the adjunction of labels could help the grid's spontaneous understanding. Although these suggestions appear promising, their relevance remains unknown in the absence of further research. Therefore, the present article builds on previous research to investigate the influence of different formats of the ESG on response task fluency and certainty.

To do so, an experiment specifically manipulating the ESG dimension and the presence of verbal labels in the cells was conducted on a sample of 105 undergraduate students. The next sections present our conceptual framework, experimental methodology, and results. Finally, contributions for academics and practitioners conducting market research alike are discussed.

Conceptual framework 2.1 Processing fluency

Processing fluency refers to the ease of executing a cognitive task. This might result from the "perceptual fluency" [START_REF] Whittlesea | Illusions of Familiarity[END_REF][START_REF] Winkielman | The Hedonic Marking of Processing Fluency: Implications for Evaluative Judgment[END_REF] of a stimuli to be processed or from the "conceptual fluency" [START_REF] Mandler | Nonspecific Effects of Exposure on Stimuli that Cannot be Recognized[END_REF] of the mental operations to be performed [START_REF] Tulving | Priming and Human Memory Systems[END_REF]. More precisely, stimuli that have been previously processed as well as mental operations that have been previously performed are easier (i.e., "more fluent") to execute. The perception of such ease in the execution of a cognitive task affects judgments and behaviors. Consumer behavior literature highlights that processing fluency can influence individual evaluations of brands, purchase intention, and product choice [START_REF] Lee | The effect of conceptual and perceptual fluency on brand evaluation[END_REF][START_REF] Labroo | Between two Brands: A Goal Fluency Account of Brand Evaluation[END_REF][START_REF] Novemsky | Preference fluency in choice[END_REF] as well as eating or recycling behaviors [START_REF] Capaldi | Why we eat what we eat: The Psychology of Eating[END_REF][START_REF] White | It's the mind-set that matters: The role of construal level and message framing in influencing consumer efficacy and conservation behaviors[END_REF].

Although processing fluency has received a great amount of attention within marketing literature, its potential effects have been ignored by methodological research. In this study, we further extend previous research on processing fluency by suggesting that a fluently designed measurement tool should make the response task easier to execute and increase the respondent's ability to use it and respond with certainty. The exploratory findings of our informal survey highlight two primary ways to improve the ease of executing response tasks by manipulating the ESG format: (1) a reduction of the ESG dimension and (2) the adjunction of verbal labels in the cells to characterize each response alternative in a clearer way. We examined the literature on the optimal number of response alternatives as well as the effects of verbal labels in measurement tools to construct a conceptual framework.

Reducing the ESG dimension

The debate regarding the optimal number of response alternatives began conjointly with the widespread use of rating scales [START_REF] Cox Iii | The Optimal Number of Response Alternatives for a Scale: A Review[END_REF]. On the one hand, respondents may randomly respond when few alternatives are available [START_REF] Lehmann | Are Three-point Scales Always Good Enough?[END_REF]. On the other hand, as they exhibit limited ability in detecting small stimuli variations [START_REF] Pollack | The Information of Elementary Auditory Displays[END_REF], respondents may not be able to make sense of too many response alternatives [START_REF] Green | Rating Scales and Information Recovery. How Many Scales and Response Categories to Use?[END_REF][START_REF] Morrison | Regressions with Discrete Dependent Variables: The Effect on R2[END_REF][START_REF] Hulbert | Information Processing Capacity and Attitude Measurement[END_REF], which results in random response behavior. Based on these two rationales, [START_REF] Alwin | The Reliability of Survey Attitude Measurement: The Influence of Question and Respondent Attributes[END_REF] postulate a curvilinear relationship between the number of response alternatives and measurement reliability. However, when comparing various number of response alternatives, from 2 to 11, they only observe a monotonic relationship. These results has been confirmed by [START_REF] Alwin | Feeling Thermometers Versus 7-Point Scales Which are Better?[END_REF]Perterson (1997).Yet, as these studies did not consider more than 11 response alternatives, we cannot state that measurement reliability does not decrease beyond this.

Although the literature did not produce a definitive answer, it appears that "the most frequently used rating scale contains seven categories" (Peterson 1997, p. 11) . If we do not really know if individuals are able to discriminate between more than nine response alternatives, then we know from practice that they are used to answering questionnaires in their daily life and, therefore, suggest that they develop competencies regarding measurement tool formats. As respondents more often perform rating tasks on 9-rather than 25-point measurement tools, they should, thus, be more familiar with measurement tools that offer nine or fewer response alternatives, and perceive them as more fluent. Consequently, rating a stimulus on a 3×3 ESG (i.e., nine alternative responses cells) must be more conceptually fluent than rating it on a 5×5 ESG (i.e., 25 alternative responses cells). Based on this development, we formulate the following hypothesis: H 1a : Compared with the 5×5 ESG, the 3×3 ESG results in better response task fluency.

However, as suggested by Cox III (1980, p. 420), "even a few response alternatives may be too many for the respondent if comprehensible instructions and labeling of response alternatives are not included to enable the respondent to conceptualize and respond in spatial terms." This assertion invites us to explore the literature regarding the potential benefits of using verbal labels to clarify the meanings of ESG's response alternatives.

Adding verbal labels in the ESG's cells

Another way to improve the ease of use of ESGs might be to accompany response process with verbal labels to characterize the meaning attributed to the different response cells. As pointed out by the literature, verbal labels reduce the perceived ambiguity between response alternatives and increase measurement reliability (Zaller 1988, Alwin and[START_REF] Alwin | The Reliability of Survey Attitude Measurement: The Influence of Question and Respondent Attributes[END_REF]. [START_REF] Garland | A Comparison of Three Forms of the Semantic Differential[END_REF] also highlights their influence on a scale's ease of use.

More precisely, he shows that labeled measurement tools are easier to understand and to complete as they reassure respondents about alternatives' precise meanings. This results in respondents' general preference for labeled measurement tools since verbal labels reduce the cognitive effort.

Applying this rationale to the ESG, an unlabeled format may appear difficult to process for the respondents who have to infer the meaning of those cells by combining the information from the two axes of the grid. On the contrary, adding verbal labels in the cells allows direct characterization of each response cell and implies one less step when executing the response task. This, in turn, should enhance the conceptual fluency of the response task; that is, the ease of the mental operations concerned with stimulus interpretation [START_REF] Whittlesea | Illusions of Familiarity[END_REF][START_REF] Winkielman | The Hedonic Marking of Processing Fluency: Implications for Evaluative Judgment[END_REF]. We therefore formulate the following hypothesis: H 1b : Compared with the unlabeled ESG, the labeled ESG results in better response task fluency.

Mediation role of response task fluency on the influence of tool format in response certainty

Working on processing fluency, [START_REF] Song | If it's Hard to Read, it's Hard to do: Processing Fluency Affects Effort Prediction and Motivation[END_REF] also demonstrate that an individual's difficulty to read behavioral instructions (manipulated by a modification of font readability) results in barriers to executing the proposed behavior. Simply put, when individuals perceive a message as easy to process, they are more likely to engage in the behavior advocated by the message. Going further, White and colleagues (2011) suggest that the perceived ease of processing a message (namely, a recycling claim) leads to enhanced perceptions in the ease of engaging in the behavior (engaging in recycling). They actually show the mediating role of the ease of executing a cognitive task between a stimulus and one's self-efficacy, i.e., the "belief in [one's] abilities to perform a given action" (van't Riet et al. 2010, p. 340).

In this article, we aim to extend this rationale to the domain of response behaviors and suggest that response task fluency should increase the perceived ease of engaging in the act of responding. Indeed, people sometimes have difficulties to access the reasons for holding a given attitude [START_REF] Wilson | Introspection, Attitude Change, and Attitude-Behavior Consistency: The Disruptive Effects of Explaining why we Feel the Way we do[END_REF], meaning that they often lack ready-made attitudes when asked to report them [START_REF] Hastie | The Relationship Between Memory and Judgment Depends on Whether the Judgment Task is Memory-based or On-line[END_REF]. Their attitudes may, therefore, be unclear, resulting in a discrepancy in response certainty. Following White and colleagues' (2011) demonstration of a mediating effect of processing fluency, we postulate that the ESG format will impact response task fluency, thus enhancing respondents' beliefs in their capacities to access their attitudes and finally resulting in better response certainty. We derive the following hypothesis from what precedes: H 2 : Response task fluency mediates the influence of the ESG format on response certainty.

Methodology

A between-subject online experiment is conducted to test the hypotheses. It provides three stimuli: the classic 5×5 ESG (the format proposed by Larsen and colleagues in 2009), a 3×3 reduced ESG, and a 3×3 reduced ESG with verbal labels. Figure 2 displays an illustration of two of the experimental stimuli.

The sample consists of 105 undergraduate students of a major university in Paris (mean age = 21 years, 50% women). Within a lab experiment, respondents were randomly assigned to one of the three experimental conditions. Their last visit to their doctor was used to observe the effects of the ESG formats on response task fluency and certainty. The multidimensional nature of patient satisfaction [START_REF] Sitzia | Patient Satisfaction: a Review of Issues and Concepts[END_REF] justifies the choice of this experimental setting.

After starting instructions to get more familiar with one of the three ESGs under survey, respondents' frequency of visits to their doctor was recorded to control for their involvement with their doctor, which may affect their satisfaction [START_REF] Cho | The Impact of Visit Frequency on the Relationship Between Service Quality and Outpatient Satisfaction: a South Korean Study[END_REF]. Respondents then rated their overall satisfaction toward their doctor using the ESG they had been assigned to before assessing response task fluency and response certainty using a seven-point Likert scale. Response task fluency was measured using six items inspired by [START_REF] Lee | Bringing the frame into focus: the influence of regulatory fit on processing fluency and persuasion[END_REF] (i.e., "Using this grid to evaluate my last consultation was… simple/ clear/ obvious/ ambiguous [rev.]/ natural/ complicated [rev.]"). Response certainty was measured using four items borrowed from Petrocelli and colleagues (2007) (i.e., "I am sure that the opinion I have expressed on my last consultation truly reflects my evaluation," "My opinion of my last consultation is clear in my mind"). We checked the unidimensionality and the reliability of response task fluency and response certainty ( = .93 and = .87, respectively).

Results

The results are presented in the following manner. First, we present the univariate analysis results and describe the main effects of the different ESG formats that were tested on response task fluency. Second, we delve into the potential mediating role of response task fluency to explain the effects of the ESG format on response certainty.

The first analyses pertain to the relative effects of the different ESG formats that were tested on response task fluency. These effects were tested using analyses of variance (ANOVA), including respondents' frequency of visits to their doctors as a covariate. As shown in Figure 3, the experimental stimuli influenced response task fluency (F (2,100) = 4.23, p < (2,100) = 1.68, p respondents' frequency of visits to their doctors did not have any significant effect on dependent variables (all Fs > .40).

Focusing on the comparison of effects between the 5×5 and 3×3 formats, the results reveal no significant difference in response task fluency (M 5×5 = 4.38, M 3×3 = 4.49; F (1,64) = .10, n.s.), providing no support for H 1a . However, the results show significant differences in the effects of the 3×3 labeled format compared with the unlabeled formats. Precisely, response task is more fluent in the case of the 3×3 labeled format compared with the 3×3 unlabeled format (M 3×3labeled = 5.18, M 3×3 = 4.49; F (1,68) = 6.78, p led format (M 3×3labeled = 5.18, M 5×5 = 4.38; F (1,67) = 6.94, p 1b .

Response Task Fluency

Response Certainty ** p < .05, * p < .10

Figure 3: Univariate analysis results

To test of the mediating influence of response task fluency to explain ESG format effects on response certainty we followed the procedure proposed by Zhao and colleagues (2010). A bootstrapping procedure with 5,000 samples helped counteract the assumption of normality of the sampling distribution of the indirect effect (ab) as required by the Sobel test [START_REF] Hayes | Beyond Baron and Kenny: Statistical Mediation Analysis in the new Millennium[END_REF]. For each analysis, the 3×3 labeled condition was coded 1, such that a positive effect of the independent variable on the mediator in the indirect path indicates the effect of the 3×3 labeled format. Mediation analyses also controlled for respondents' frequency of visits to their doctors. The results are displayed in Table 1.

First, when compared with the 5×5 unlabeled format, the 3×3 labeled format exerts a positive indirect effect (ab = .44) on response certainty through response task fluency (confidence interval of [.0984; 1.0324]). More precisely, when compared with the 5×5 unlabeled format, the 3×3 labeled format increases response task fluency (a = .85), which appears to increase response certainty (b = .51). Second, when compared with the 3×3 unlabeled format, the 3×3 labeled format exerts a positive indirect effect (ab = .29) on response certainty through response task fluency (confidence interval of [.0545; .6999]). More precisely, when compared with the 3×3 unlabeled format, the 3×3 labeled format increases response task fluency (a = .68), which appears to increase response certainty (b = .42). Altogether, these results emphasize the role of response task fluency as a mediator of the effects of the ESG format on response certainty, thus bringing support for H 2 .

Discussion

Summary

This study conducted a between-subjects experiment to assess the impact of measurement tool formats on response task fluency and certainty in customer surveys. It proves that the adjunction of verbal labels on the ESG has a positive influence on response task fluency, which actually mediates the relationship between the grid's format and response certainty. No such effects were found when reducing the grid's dimensions.

These findings extend the literature on the use of a bidimensional matrix to assess overall customer satisfaction. More precisely, Larsen and colleagues (2009) have developed the ESG in psychology and Audrezet and colleagues (2016) recently demonstrated its relevance to measure overall customer satisfaction in marketing. In this paper, we go further by testing formats that could be easier to process in an online selfadministered context. Similar to the literature, which did not present a definitive answer about the optimal number of response alternatives in rating scales, we did not find any influence on the reduction of the ESG dimension on response task fluency and certainty; that is, respondents do not process the two grid axes separately, but rather as an integrated two-dimensional space. Our findings also support the methodological literature on verbal labels benefits. Taken together, such results have a relatively plausible interpretation linked to the design of the ESG. Although we expected that reducing the grid's dimension would increase response task fluency because respondents are more likely to be familiar with 9 than 25 response alternatives tools, the grid's unexpected square design may have counterbalanced this potential gain. On the contrary, the adjunction of labels, likely to clarify the meaning of the different response alternatives, provides a real gain in response task fluency, which in turn improves response certainty.

Theoretical implications

From a broad perspective, this research extends the work on the influence of certain format or design parameters on response rate or data quality [START_REF] Hu | Impact of the Level of Aggregation on Response Accuracy in Surveys of Behavioral Frequency[END_REF][START_REF] Sheehan | Response Variation in E-mail Surveys: An Exploration[END_REF][START_REF] Couper | Web Survey Design and Administration[END_REF][START_REF] Manfreda | Design of Web Survey Questionnaires: Three Basic Experiments[END_REF][START_REF] Deutskens | Response Rate and Response Quality of Internet-Based Surveys: An Experimental Study[END_REF]. In line with this body of research, we apply a framing effect approach to measurement tool design. We highlight that a small modification of the tool appearance improves the respondents' own belief in their capability to succeed in the response task. In other words, we argue that researchers as well as practitioners might design tools likely to achieve respondents' non-forced compliance to the response task through a positive reinforcement or an indirect suggestion that is easy to use. Thus, similar to other "choices architectures," measurement tools deserve design reflection to create responding behavior incentives or nudges [START_REF] Thaler | Nudge: Improving Decisions about Health, Wealth and Happiness[END_REF].

From a specific point of view, this study extends the application boundaries in marketing of the concept of processing fluency, currently limited to the examination of traditional stimuli, such as pictures, sounds, or commercial messages (e.g. Reber andSchwarz 1999, White et al. 2011). This study illustrates how processing fluency can be applied successfully to the market research measurement tools' issues and contributes to the discussion on the measurement of individuals' overall evaluations in market research. More precisely, to analyze responding behaviors issues, we extend the so-called concept of processing fluency into response task fluency, a new variable that may be considered in future methodological research.

Managerial implications and directions for future researches

From a managerial point of view, response task fluency improvement may be even more relevant in an electronic setting, where respondents usually do not like to spend too much time reading instructions or answering surveys [START_REF] Dolnicar | Quick, Simple and Reliable: Forced Binary Survey Questions[END_REF]. In light of the dictatorial rule of "five questions, two minutes completion" adopted by market research institutes when developing questionnaires, this new approach offers promising perspectives to address online survey challenges. First, because response task fluency improves the belief in one's ability to succeed in a response task, or self-efficacy, we argue that tool design reflection might offer an interesting way to reduce survey drop-out rates. From this perspective, future research could explore how to improve response task fluency for other existing tools or in the perspective of new tool development. It could also provide avenues for explaining consistent results in the methodological literature. For example, previous research pointed out that enhancing questionnaires with visual element, such as product images is a good way to improve response quality [START_REF] Deutskens | Response Rate and Response Quality of Internet-Based Surveys: An Experimental Study[END_REF]). It may be argued that this is because pictures increase response task fluency. More broadly, works on response task fluency could further explore how instruction design could enhance perceived processing fluency so as to initially engage respondents in the task of completing a questionnaire. Second, because response task fluency improves response certainty, reflections regarding a tool's design are relevant to reinforce data quality and, in turn, derive more relevant managerial predictions. As highlighted in previous researches, improving consumer certainty positively impacts consumers' behaviors (e.g. [START_REF] Maier | The Double Benefits of Consumer Certainty: Combining Risk and Range Effects[END_REF]). In the context of online data collection, response certainty improvement offers respondents a more comfortable posture, which may again result in a stronger benevolence.

Limitations

The present study has some limitations. First, we ran this study on a sample of students, although it has been shown that education level impacts response behaviors [START_REF] Alwin | The Reliability of Survey Attitude Measurement: The Influence of Question and Respondent Attributes[END_REF]. We actually highlighted that educated individuals (undergraduate students) perceive that it is easier to answer using well-designed tools. Although we could argue that this effect would be even stronger among other profile of respondents because less-educated individuals might be even more influenced by the design of tools, a replication of the results on a more representative sample is necessary to test this. Furthermore, our study is limited to a specific context of evaluation; that is, respondents' last visit to their doctor. We do not expect that this specific context affects the results negatively because the study investigated the effects of tool formats rather than the absolute or relative evaluation of the doctor. Optimally, however, other contexts of evaluation, especially situations likely to generate ambivalence, such as food behaviors or societal issues, should be included to empirically ensure generalizability.

Figure 2 :

 2 Figure 2: Illustration of experimental stimuli

Table 1 :

 1 Mediation results

	5×5 Unlabeled Format Compared with 3×3 Labeled Format
	Direct Model	Coefficient	T
		.85	2.63**
	certainty	.51	3.47***
		.24	.59
	Indirect Model
	Coefficient of mediation	.44
	Confidence interval	[.0984; 1.0324]
	3×3 Unlabeled Format Compared with 3×3 Labeled Format
	Direct Model	Coefficient	T
		.68	2.60**
		.42	2.63**
		.12	.34
	Indirect Model
	Coefficient of mediation	.29
	Confidence interval	[.0545; .6999]

*** < .01; ** < .05; * < .10

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.


Alexis Bocquet
email: alexis.bocquet@mines-paristech.fr

Andrea Michiorri

Arthur Bossavy

Robin Girard

Georges Kariniotakis

Assessment of probabilistic PV production forecasts performance in an operational context

Keywords: Photovoltaic, probabilistic forecasting, models, evaluation analysis I

Assessment of probabilistic PV production forecasts performance in an operational context

INTRODUCTION

Power generated by photovoltaic (PV) plants is highly dependent on variable weather conditions. To operate a power system with high PV penetration in a secure and economical way, it is crucial to estimate the future PV production. In the literature several forecasting techniques have been developed for PV forecasting. These methods can be classified into 3 families: the statistical, the physical and the hybrid one. These methods use as input combinations of data such as historical measurements, Numerical Weather Prediction (NWP) forecasts, satellites or on-site cameras images.

Nice Grid is the first smart solar-energy district demonstration project to be conducted in France. It is one of the demo cases of the Grid4EU European project. Its objective is to develop a smart electricity grid that harmoniously integrates a high proportion of solar panels, energy storage batteries and intelligent power meters installed in the homes of volunteer participants. Forecasting PV generation accurately is one of the main challenges addressed in the Nice Grid project.

In this paper, we propose initially a short presentation of the state of the art on photovoltaic power forecasting techniques. Then, we describe the method proposed to generate short-term probabilistic PV production forecasts. This method is implemented into an operational forecasting system which is installed and evaluated under real conditions in the frame of the Nice Grid demonstrator. The paper presents the evaluation results for both deterministic (i.e. NBIAS, NMAE and NRMSE) and probabilistic criteria (reliability and sharpness diagrams). The evaluation results are given in comparison to two simple modules based on persistence module and on climatology. In this paper we also compare two sources of NWP models. One has a spatial resolution of 0.25° and a temporal resolution of 3 hours (GFS -NOAA) and the other one has a spatial resolution of 0.1° and a temporal resolution of 3 hours (ARPEGE -METEOFRANCE).

II. FORECASTING MODELS

A. A state of the art on short-term PV forecasts

Recent research work has undertaken the development of dedicated short-term (from a few hours to a few days ahead) PV forecasting models based on NWP, basically solar irradiation forecasts [START_REF] Bacher | Online short-term solar power forecasting[END_REF], [START_REF] Chen | Online 24-h solar power forecasting based on weather type classification using artificial neural network[END_REF], [START_REF] Lorenz | Irradiance forecasting for the power prediction of grid-connected photovoltaic systems[END_REF], [START_REF] Lorenz | Regional PV power prediction for improved grid integration[END_REF], [START_REF] Grimaccia | Neuro-fuzzy predictive model for PV energy production based on weather forecast[END_REF] and [START_REF] Shi | Forecasting power output of photovoltaic systems based on weather classification and support vector machines[END_REF].

Detailed modelling of the electrical power output of a PV plant as a function of solar irradiance1 has been investigated over the years. It generally relies on a parametric modelling of PV modules' efficiency with the incidental irradiance level and ambient temperature [START_REF] Beyer | A robust model for the MPP performance of different types of PV-modules applied for the performance check of grid connected systems[END_REF] and [START_REF] Huld | Mapping the performance of PV modules, effects of module type and data averaging[END_REF]. In a short-term forecasting context however, such a refined modelling may be unnecessary when considering the overall accuracy of other input variables like the NWP forecasts. Thus, a linear relationship between irradiance and power may be assumed [START_REF] Bacher | Online short-term solar power forecasting[END_REF]. When forecasting PV production from only past production data and solar irradiation forecasts, a statistical linear model may turn in fact, as performant as more complex nonlinear ones [START_REF] Bossavy | The impact of available data history on the performance of photovoltaic generation forecasting models[END_REF]. Nonlinear statistical models must nevertheless be useful if deciding to incorporate additional information such as temperature, air humidity or wind speed forecasts as input [START_REF] Chen | Online 24-h solar power forecasting based on weather type classification using artificial neural network[END_REF], [START_REF] Grimaccia | Neuro-fuzzy predictive model for PV energy production based on weather forecast[END_REF] and [START_REF] Shi | Forecasting power output of photovoltaic systems based on weather classification and support vector machines[END_REF]. More generally, they may be useful when considering any additional source of nonlinearity.

NWP solar irradiation forecasts are generally provided on horizontal plane. On the other hand, PV plants generally have tilted, potentially multiple, panels' orientation(s) 2involving complex shading conditions. The relationship between irradiance levels, respectively on horizontal plane and on the panels' surface, may be complex and highly nonlinear [START_REF] Hay | Estimating solar irradiance on inclined surfaces: a review and assessment of methodologies[END_REF], [START_REF] Loutzenhiser | Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation[END_REF] and [START_REF] Demain | Evaluation of different models to estimate the global solar radiation on inclined surfaces[END_REF]. Thus, in some cases, a raw linear assumption between power and forecast irradiance may not be satisfying (even) for short-term forecasting purposes. Advanced non-linear statistical algorithms may perform NWPs' recalibration to PV plant's orientation automatically. An alternative can be to re-estimate solar irradiance forecasts from horizontal to PV plant's orientation, using dedicated models, before carrying the conversion into power forecasts [START_REF] Lorenz | Irradiance forecasting for the power prediction of grid-connected photovoltaic systems[END_REF] and [START_REF] Lorenz | Regional PV power prediction for improved grid integration[END_REF]. In [START_REF] Tao | Forecasting power output for gridconnected photovoltaic power system without using solar radiation measurement[END_REF], the conversion from horizontal to PV plant's orientation is first applied to clear-sky irradiance estimates. Then, tilted clearsky irradiance estimates are combined with NWP forecasts characterizing future sky-clarity conditions as input of a Neural-Network.

B. The proposed forecasting model

In this article, we describe a short-term probabilistic PV forecasting model incorporating PV plant's orientation data. As in [START_REF] Tao | Forecasting power output for gridconnected photovoltaic power system without using solar radiation measurement[END_REF], it relies on clear-sky irradiance estimates derived for the PV plant's orientation.

The considered forecasting approach is as follows: one considers a statistical model to forecast the PV production from surface solar irradiance's weather forecasts. Parameter's values are estimated depending on the time of day so as to capture interactions between the sun's course, the PV panels' orientation, potential shadowing effects, etc. It also allows capturing other effects from diurnal variations of meteorological parameters, such as the influence of temperature on modules' efficiency. Moreover the model's parameters are estimated adaptively using the most recent data available, so as to capture seasonal/climatic variations not explicitly modelled or even represented in the training data set (e.g. variations due to NWP model's updates, to ageing or dirt on PV panels, etc.).

The chosen statistical model is a non-parametric model which has been considered in estimating the whole power distribution at once. It is based on a kernel density estimator (KDE) and can be written as:

̂ ( | ) ( ) ∑ ( ) { ( ( ) ) ( ( ) ) ( ( )
)}

where is the power plant's nominal capacity and the weights ( ) are given by:

( ) ( ̂ ( )
),

and ∑ ( ) ⁄ .
where ̂ is the forecast surface solar irradiance on horizontal plan at time for horizon and is a fixed factor.

The model proposed above is a conditional kernel density estimator of the power distribution estimated conditionally to the forecast irradiance level I. The bandwidth selection procedure is a k-nearest neighbours' procedure (see [START_REF] Hastie Tat | The elements of statistical learning, second edition: Data mining, inference, and prediction[END_REF]), with the same value k assumed for both the variable p and the covariate I and selected through trials and errors 3 .

III. CASE STUDY

The algorithm has been implemented as an operational module to produce PV production forecasts every day for the case study provided by the Nice Grid project. The project aims at developing a smart solar neighbourhood in the urban area of Carros near the city of Nice in the south of France. The network in the considered urban area has been chosen because of its exposure to two common problems: the expected growth of solar power production at the distribution level and the risk of disconnection from the transmission grid. The project, which started in January 2012 and ends in October 2016, includes a high proportion of solar-power panels connected to distributed energy storage systems.

The idea behind Nice Grid is to combine controllable distributed electricity and thermal storage devices with forecasts of solar power production and load in a local energy management system. The project is centred on a network energy management (NEM) system which enables financial transactions among the different actors of the power system. A schematic representation of the architecture being developed and deployed is presented in Figure 1. This paper is dedicated in the evaluation results of the PV production forecasts highlighted in red in the diagram.

The Nice Grid demonstrator involves different types of actors either in the residential or in the tertiary sector. More than 1500 consumers and 50 production sites equipped with PV panels are involved in this project. The total PV installed capacity represents more than 600 kW. Forecasts are calculated for both small producers (from the residential sector) equipped with Linky smart meters and large producers (from the tertiary sector) equipped with an Orange meter. The production data used as input to the forecasts are provided by the smart meters. The forecasts are delivered every day once a day for the next 48 hours with a temporal resolution of 30 minutes. It is required to deliver PV production forecasts to the "Network Constraints Prediction Tool" (NCPT) for all PV producers before 11.00 a.m. local time. The NCPT evaluates the network conditions for each future time step and estimates the flexibilities that have to be mobilized by the different actors like the storage aggregators or the domestic clients aggregators. 3 Adaptive selection of an optimal value through cross-validation has been first considered but left apart because of the computational burden. EVALUATION RESULTS

The objectives of this evaluation are multiple. First, it is necessary to assess whether the performance obtained by the predictive models developed are comparable to the performance of similar models in the literature. For this we adopt a set of evaluation criteria that are considered standard for the assessment of PV production. The assessment relates to both deterministic and probabilistic forecasts.

A. Evaluation Criteria 1) Deterministic forecasts

To evaluate deterministic forecasts, we chose to follow the standardized methodology proposed in different research projects like the SafeWind FP7 project or other international exercises on benchmarking for PV and wind power forecasts [START_REF] Sperati | The " Weather Intelligence for Renewable Energies " Benchmarking Exercise on Short-Term Forecasting of Wind and Solar Power Generation[END_REF], [START_REF] Zhang | A suite of metrics for assessing the performance of solar power forecasting[END_REF], [START_REF] Madsen | A Protocol for Standardizing the Performance Evaluation of Short-Term Wind Power Prediction Models[END_REF] and [START_REF] Kariniotakis | What Performance Can Be Expected by Short-term Wind Power Prediction Models Depending on Site Characteristics?[END_REF]. The criteria considered here are:  Normalized mean Bias (NBIAS), for each forecast horizon h, expressed in percentage:

( ) ∑ ( ̂ ) (2)
 Normalized Mean Absolute Error (NMAE), for each forecast horizon h, expressed in percentage:

( ) ∑ | ̂ | (3)
 Normalized Root Mean Squared Error (NRMSE), for each forecast horizon h, expressed in percentage:

( ) √ ∑ ( ̂ ) (4)
Where:

̂ is the PV power forecast made at time t for horizon is the observed PV power at time t + h is the number of considered values is the peak power of the PV panel or plant

2) Probabilistic forecasts

To evaluate probabilistic forecasts, we chose to follow the methodology presented in [START_REF] Pinson | Non-parametric Probabilistic Forecasts of Wind Power: Required Properties and Evaluation[END_REF] and [START_REF] Sharry | Methodology for the evaluation of probabilistic forecasts[END_REF]. The criteria considered here are:

 Reliability:
Reliability is a term dedicated to the assessment of probability forecasts that matches a criterion that measures the performance of quantile forecasts. It measures the similarity between predictions and observations. This criterion is obtained by calculating, for the evaluation period, the percentage of the measured values (observations) that exceed a certain quantile relative to the total number of observations. In other words, reliability here relates to the "bias" of quantile forecasts. If denoting ̂ a quantile forecast at time for horizon the mathematical formulation of this criterion presented in [START_REF] Pinson | Non-parametric Probabilistic Forecasts of Wind Power: Required Properties and Evaluation[END_REF] is as follows:

∑ ̂ (5)
This ratio should be as close as possible to the nominal value of the quantile. Deviations above approximately 3% on the nominal value of quantile indicate that this quantile forecast is unreliable. Reliability is evaluated for each forecast period separately. This criterion is fundamental when probabilistic forecasts are considered in a process of decision making that considers the uncertainty. Reliability is a property that can be improved by the calibration process of probabilistic prediction models.

 Sharpness:

The sharpness of probabilistic forecasts is a property that represents their ability to provide finely particular situations. It represents the degree of "concentration" of the expected distribution. A good forecast should have a very low value of this parameter. A model without "sharpness" is a standard "climate" model where uncertainty is expressed in a constant and independent way in regards to particular meteorological situations. For predicting PV this property is important because the level of uncertainty is different for sunny or cloudy days. The mathematical formulation for this criterion given in [START_REF] Pinson | Non-parametric Probabilistic Forecasts of Wind Power: Required Properties and Evaluation[END_REF] is as follows:

∑ ( ̂ ̂ ) (6)
Unlike the reliability, the sharpness is an inherent property of a forecasting system that cannot be improved by a calibration method [START_REF] Sharry | Methodology for the evaluation of probabilistic forecasts[END_REF].

B. PV production forecasts evaluation

This paper presents the evaluation results of the advanced KDE module, using as input the weather forecasts GFS (KDE-1) and ARPEGE (KDE-2). The evaluation results of the advanced KDE model are compared to two single reference methods which do not involve any mathematical model to generate predictions: the persistence and the climatology (mentioned as global_average in the diagrams below). A first condition for an advanced model is to have a better performance than persistence. Persistence characterizes the weather in the short term. Despite its simplicity the performance of this method is not always low. Persistence is obtained here using a forecast equal to the measured value of the previous day at the same time. Climatology considers that the forecast for any given time of the day is equal to the average of all the observed values at the same time of day over a long period (i.e. one year). This explains in particular that the value of the mean bias of the evaluation period is zero for climatology. Probabilistic forecasts were generated for each time of day covering the entire distribution of PV production. These quantile forecasts are given in 10%-steps of the nominal probability. Predictive models are optimized with respect to the prediction that corresponds to the mean of the distribution. Hereby, the assessment using deterministic criteria is made using the average rather than the 50% quantile forecast (median).

The evaluation was conducted on 35 producers after eliminating time series productions for producers for which there were insufficient data. The evaluation covers the period from 01/11/2014 to 01/09/2015. During this period we received 96.7% of the measurement data and 99.9% of the PV forecasts are available. For practical use, in the figures below, we chose to show the evaluation results from a large PV producer which is representative of all of them as it represents almost 10% of the installed capacity of all PV plants.

1) Normalized BIAS

The bias is the average of prediction errors. A good forecast should have a bias close to zero. The chart from Figure 2. shows the evolution of the bias over the forecast horizons, for the two configurations of KDE model KDE-1 and KDE-2 with GFS and ARPEGE respectively, in comparison to the persistence and climatology models, for the PV producer taken into account during this assessment. The figure shows that both configurations of KDE model tend to have a bias slightly higher than the persistence. However this bias remains at low values, around 1%. In this figure, we can see that the ARPEGE forecasts help to improve the bias for the times of day that are critical for the grid operator. The diagram shows the reliability of PV forecasts for forecast horizons 9.00, 13.00 and 17.00 local time, for the considered PV producer. We note that overall all the models are "reliable" with better performance for the KDE-2 model. The deviations from the optimal value are limited. We can see that for this PV producer, the curves from horizons 9.00 and 17.00 overlap quite well with the reference diagonal line. This means that for horizons 9.00 and 17.00, we observed as many values as expected in each confidence interval.

5) Sharpness

Sharpness measures the difference between two quantiles. In this case, considered quantiles are quantile 20% and quantile 80%. The chart from Figure 6. shows the evolution of sharpness for each forecast horizon of the day for the KDE model for the considered PV producer. We note that weather forecasts ARPEGE allow an improvement in this criterion.

6) Summarising evaluation results

The forecasts were evaluated using standard criteria for evaluating forecasts of renewable production. The values of these criteria were calculated for all producers and the results of this evaluation are summarized in TABLE I. for both configurations KDE-1 and KDE-2 of the advanced PV forecasting model, KDE. The evaluation results from this table only concern horizons between 9.00 and 17.00 local time, as it corresponds to daylight hours.

The work on probabilistic forecasting models led to the development of state of the art equivalent services even for household producers with very low power. In general, even at the household producer level, forecasts yield good performance, with a mean error of approximately 8% between 9.00 and 17.00 local time. This value is deemed satisfactory for practical applications.

V. CONCLUSION

The improvement obtained by the use of higher resolution weather forecasts is significant (i.e. the use of configuration KDE-2 in comparison to configuration KDE-1). This element is useful in a potential cost-benefit analysis of forecasts.

Eventually, in the improvement opportunities of the performance observed here we can mention the potential contribution of intraday forecasts using updated weather forecasts. Intraday forecasts would also allow the use of improved NWP model, such as METEOFRANCE's model AROME, with a spatial resolution of 0.025° and a temporal resolution of one hour. We can therefore reasonably expect improvements on the evaluation of PV production forecasts.

Figure 1 .

 1 Figure 1. Nice Grid Architecture IV.EVALUATION RESULTS

Figure 2 .

 2 Figure 2. NBIAS over forecast horizons for both configurations of KDE in comparison to the persistence and the climatology2) Normalized Mean Absolute ErrorThe NMAE is probably one of the most intuitive assessment criteria, representing the average deviation in absolute values between the forecasted values and the observed ones, normalized to the peak power of the producer. The chart from Figure3. shows the evolution of NMAE over the forecast horizons, for both configurations of KDE model, persistence and climatology, for the PV producer taken into account during this assessment. The figure shows that the KDE-2 model still has a better performance.

Figure 3 .

 3 Figure 3. NMAE over forecast horizons for both configurations of KDE in comparison to the persistence and the climatology3) Normalized Root Mean Squared ErrorThis criterion is the standard deviation of prediction errors, normalized to the peak power of the producer. Compared to NMAE, the NRMSE gives more weight to the errors with significant values. The chart from Figure4. shows the evolution of NRMSE over the forecast horizons, for both configurations of KDE model, persistence and climatology, for the PV producer taken into account during this assessment. The diagram shows that the KDE-2 model still has a better performance. It also shows that the KDE-1 model gives a significant improvement in comparison to the persistence for all horizons during daylight hours. This indicates that even with a low spatial resolution's NWP model, weather forecasts help to improve significant errors.

Figure 4 .

 4 Figure 4. NRMSE over forecast horizons for both configurations of KDE in comparison to the persistence and the climatology 4) Reliability Figure 5. shows the "reliability diagram" from which optimal reliability is the one corresponding to the diagonal.The diagram shows the reliability of PV forecasts for forecast horizons 9.00, 13.00 and 17.00 local time, for the considered PV producer. We note that overall all the models are "reliable" with better performance for the KDE-2 model. The deviations from the optimal value are limited. We can see that for this PV producer, the curves from horizons 9.00 and 17.00 overlap quite well with the reference diagonal line. This means that for horizons 9.00 and 17.00, we observed as many values as expected in each confidence interval.

Figure 5 .

 5 Figure 5. Reliability diagram for both KDE configurations for all 10%steps quantiles for forecast horizons 9.00, 13.00 and 17.00 local time, in comparison to the persistence and the climatology

Figure 6 .

 6 Figure 6. Sharpness criterion diagram over forecast horizons for both KDE configurations for prediction intervals defined by quantiles 20% and 80%, in comparison to the persistence and the climatology

TABLE I .

 I OVERVIEW OF THE EVALUATION RESULTS

	Criteria	Min	Average	Max
	(9h-17h)	KDE-1 KDE-2	KDE-1	KDE-2	KDE-1	KDE-2
	NBIAS	0.06%	-0.2%	1.4%	1.2%	10.95%	10.4%
	NMAE	3.64% 3.10%	8.85%	7.90%	16.62%	15.50%
	NMRSE 5.19% 4.60% 12.23%	11.19%	19.73%	18.80%

Min: minimal values of evaluation criteria over all PV producers Average: average value of evaluation criteria over all PV producers Max: maximal values of evaluation criteria over all PV producers

One has to distinguish solar irradiation which represents the solar radiation energy by surface unit, from solar irradiance which is the solar power by surface unit (i.e. the solar radiation energy by unit of surface and unit of time). The latter is generally expressed in W.m -2 .

We consider here plants with no sun-tracking system of any kind, thus with fixed panels' orientation.

ACKNOWLEDGMENTS

This work was performed in the frame Nice Grid, project supported by ADEME (Agence de l'Environnement et la Maitrise de l'Energie) in the frame of the initiative "Investments for the Future". Nice Grid is also part of the European Project GRID4EU (Grant No 268206) funded in part by the European Commission under the 7th Framework Program. The authors would also like to thank METEO FRANCE for providing the NWP forecasts used in this project.


Magali Pierre
email: magali.pierre@edf.fr

Eleonora Morganti

Virginie Boutueil

Will fleet managers really help vehicle fleets to become electric?

Over the last few years, obligations to reduce carbon dioxide emissions have led European States to propose ambitious targets concerning electrifying car fleets. In France for instance, electric vehicles are required to cover a quarter of all new car purchases in big companies and public administrations. In these organizations, departments that are traditionally in charge of company vehicles have thus been tasked to implement these policy decisions. General Resources have become de facto responsible for testing and managing these new EVs. Illustrating our results through five case-studies that took place in France in 2012-2015, we will show how these departments, and notably fleet managers, carry out the numerous tasks accompanying the spreading of EVs in their organizations: acquiring these vehicles (and the charging infrastructure), allocating them and managing the charging of the cars. The allocation, whether as fleet cars or executive ones, is an important step for the success of their implementation in these companies. We will also point out the contradictory significations and powerful constraints that complicate the performance of these tasks. Their achievement strengthens the role of the fleet managers, who turn out to be crucial but unexpected players in electricity demand.

Introduction

Many European governments including France recently set about electrifying their administrations' car fleets in order to meet their targets of transport-related CO2 emission reduction and to lighten their dependency on fossil energy resources. In France a memorandum from the 3th December 2012 imposes that EVs represent a quarter of new vehicle acquisitions; it's a mandatory target for state services and a recommendation for big public companies. Public authorities thus sustain the EV industry and concentrate on car fleets due to three main reasons. First, such a deployment will benefit from a massive range of end-users despite of concentrating decision processes on a small range of people. Secondly, car use and car parking patterns of such administrations and big companies are considered as favourable to EVs [START_REF] Globisch | Acceptance of electric vehicles by commercial users in the electric mobility pilot regions in Germany[END_REF], as most professional journeys are regular, predictable, cover short distances and cars generally stay parked all night long. Lastly these fleets may constitute strong influence conveyors towards mass market in this early deployment phase, as many of these logotyped cars will be quite eye-catching in public places. Indeed, in recent years, EVs have been offered to organisations (companies of all sizes, institutions and local authorities). Based on CCFA and SNLVLD statistics, [START_REF] Boutueil | Towards a sustainable transport system: Leveraging corporate car fleets to foster innovation[END_REF] states that "every year in France, 4 out of 10 new light-duty vehicles (including passenger cars and light commercial vehicles) are sold to corporations". In order to introduce properly EVs on site, these organisations have worked with a great diversity of departments such as General Resources but also very unexpectedly with departments which do not usually deal with car issues such as Human Resources, Sustainable Development, Purchasing, Real Estate, etc. (see [START_REF] Boutueil | Fleet management and the adoption of innovations by corporate car fleet: an exploratory approach[END_REF]. All kinds of players have been involved in the deployment of these cars in business units. In many companies, fleet managers have become de facto responsible for testing and managing these new EVs.

Illustrating our results through five case-studies that took place in France in 2012-2015, we will show how these departments and notably fleet managers carry out the numerous tasks accompanying the spreading of EVs in their organizations. We will point out the contradictory significations and powerful constraints that complicate the performance of these tasks. Our paper thus borrows concepts from the sociology of professions to study this professional appropriation in its organizational dimension.

Social science literature often considers EVs from a usage dimension (through short-term tests). And sociology of organisations often considers companies as a relational system without taking into account material arrangements structuring them. We will concentrate here on how these cars are spread through the organisations with the help of fleet managers, which means at the same time focusing on the inherent qualities of these cars and on the circumstances surrounding their introduction; and exploring how the cars modify social relations and professional practices within the companies.

This paper is organized as follows. The next section presents the methodology. The following section describes results gathered from the selected five case studies. The last section presents the discussion and a conclusion.

A multi-survey analysis: context, definitions and methodology

Our study combines five case studies from France, which were originally disconnected but designed with similar goals, and which display consistent results about commercial fleet management and EV adoption. Investigations were aimed at obtaining direct information from EV users and stakeholders involved in the electro-mobility transition. Although the original case studies generally targeted both private users and fleet users (and among the latter, fleet managers), the present study centers on the sole category of fleet managers and their attitudes towards battery electric vehicles (BEVs) and plugin hybrid electric vehicles (PHEVs).

In total close to 50 interviews with fleet managers were conducted. All case studies were based on individual face-to-face interviews that were carried out using an exploratory approach, with a semistructured questionnaire. This allowed us to collect data and information on the managers' acceptance, conceptions and perceptions on EVs.

Definitions

Given that there is no widely accepted definition of what fleet management is [START_REF] Boutueil | Towards a sustainable transport system: Leveraging corporate car fleets to foster innovation[END_REF], we choose to give fleet management the widest definition possible, including all decisions involved in the acquisition process (e.g. selection of suppliers, selection of makes and models) as well as in the day-to-day operational management (e.g. reporting and monitoring on vehicle use and running costs) of corporate car fleets. The main rationale for this broad definition lies in the assumption that decisions relating to both acquisition and day-to-day operations are bound to be increasingly intertwined in the future, because of the growing use of reporting and other decision-support tools required for life-cycle cost-benefit analysis. However this paper focuses on the deployment of such cars and leaves aside the purchase decision in order to understand the day-to-day difficulties and constraints that frame the fleet manager practices concerning EV management.

The scientific literature underlines that decisions relating to alternative car purchases by companies are not always linked to a cost-benefit neither life-cycle cost analysis but more frequently to past experience [START_REF] Nesbitt | Myths regarding alternative fuel vehicle demand by light duty vehicle fleets[END_REF]: "Vehicle selection is often based on past experiences, with fleet operators sometimes being more brand-loyal than cost-conscious" (p.262). EV management follows, as we will see, the same experienced based process.

In the present analysis, we adopt Boutueil's definition (2015) of fleet managers, which includes inhouse corporate staff who are involved in the design and/or supervision of fleet management processes1 .

Case studies with comparable socio-organizational contexts

The technical setup of the five case studies is slightly different (see Table 1):  Case study A investigated the adoption of PHEVs in a wide range of companies and local authorities involved in a demonstration project for 4 years;  Case study B focused on different kinds of EVs (e.g. cars and vans) produced by the same manufacturer; we analyzed the domestication process by users (in a professional context) and how people in charge of the EVs in the companies had managed them.  Case study C focused on the interoperability of the public charging infrastructure and related to EVs of different brands, charging from various charging stations; this study compared professional and private users of EVs ;  Case study D explored the decision-making processes involved in corporate fleet management and analyzed the barriers to, and drivers of, the adoption of battery electric vehicles by corporate fleets;

 Case study E explored electric vans used by professional users in the transport sector.

With regard to the socio-organizational contexts, these investigations are comparable, since they look at how public and private institutions of all sizes (from SMEs to large industrial groups through local authorities) deal with the adoption of innovative vehicles in their fleets. Each organization defined its own policy on choosing and allocating EVs (assignment procedures, nominees or call for volunteers, etc.). Designated or volunteer staff were committed to use the vehicles over a long period.

Tableau EVs have been integrated into both large and small fleets. Among the entities which took part in the case studies, there are public institutions and large companies with fleets ranging from tens to thousands of vehicles. In these organizations, internal combustion engine (ICE) vehicles are usually acquired and / or leased and EVs complete the fleets. Some vehicles are pooled, some are assigned to specific services and some are assigned to designed people. The same options apply to EV fleet management.

Respondents

Respondents have different roles and responsibilities, with wide-ranging backgrounds according to the department they work for. For the present analysis we selected fleet managers and similar positions which include managers from the operations and maintenance division, logistics service, purchasing department. The sample includes facility managers for a public institution, on-site manager for a construction firm, etc. They are employed by agencies in the sector of energy, social welfare and municipal services, or in private companies in the field of construction, transport, retailing, etc.

Within the professional vans market, respondents are part of the goods collection and delivery sector, in particular postal operators, express deliveries companies and retail store deliveries. Some of them are early adopters of electric vans for last-mile operations, others were testing or considering testing electric vans.

Results

Our purpose here is to show the delicate balance on which the use of EVs in a professional context lays. Organisations (local authorities and companies) need to adapt to the EV constraints such as a limited battery range and high acquisition costs. Similarly to the implementation of other innovations, EVs modify the system of mobility practices of professional users and requires organisational creativity from the fleet managers. Our study concentrates on how fleet managers deal with EV characteristics: cost, battery range and acceptation from garage staff.

A car which is uneasy to manage: how to deal with range issues

Allocation and training

The EV is uneasy to manage as it requires:

-Training for the new drivers. Fleet managers are often in charge of training the new users on how to drive the EV (how to use an automatic gearbox, how to eco-drive) and how to recharge it. They also have to motivate employees who "do not want to give up their conventional cars". -Considering the limited range of this car. It means that they have to systematically assess the distances that the next user is going to drive. Taking this short range radius into account limits (or at least constrains) who they can give the next car to.

But in order to use EVs as efficiently as possible from economical and operational standpoints, they should not be used to short distances only. Fleet managers need to assess both the demand for mobility of employees and the optimal use pattern of each model.

Employees use EVs to travel short and middle range distances in all kinds of urban areas. The battery range of most EV models is barely over 150 km, so that this car is generally given for a short distance or a routine journey. The purposes reported included:

-Collection services and end deliveries in dense areas -Journeys between 2 sites of a company (for instance to go to a meeting or to deliver mail) -Commuting

As these purposes are taken into account, EVs are most frequently allocated to people making deliveries, mechanics, local property maintenance, construction site foremen, meter-readers, etc.

Allocating EVs requires indeed a beforehand reflexion on its optimum uses. But it causes additional tasks for the fleet managers.

Therefore, EVs are not used as all-purpose cars but as cars that are adapted to certain uses only: to say it quick, fixed daily routes or short distances. This functional specialisation relies on an accurate diagnosis of the needs of the supposed next user.

This diagnosis is more or less painstakingly done depending on whether it goes with a global car fleet rationalisation or not and which professional carries it out. As a matter of fact, « the lead purchasing manager would coordinate a network of contact persons responsible for procurement at a local level (…), most of whom would not be fleet specialists. » [START_REF] Boutueil | Towards a sustainable transport system: Leveraging corporate car fleets to foster innovation[END_REF] And some professions share a better field knowledge about the mobility patterns of employees than others. We found two successful configurations in our studies: the first one is about fleet managers who benefit from the statistics from software on mobility analysis2 and the second one is about some directors in very small businesses3 who perfectly know their employees' job.

EV allocations can have 2 different statuses:

 Allocation to a person. In this case there is a formal gradation in use rights: an official car can be used for a vaster range of purposes than a service vehicle which has been allocated to a profession within a department. However what really matters in the case of EVs is the possibility (or not) to get full-time access (no authorisation to ask for, keys within easy reach, etc.) and commuting rights. Even if there are 2 users in the same department, these conditions facilitate a real appropriation of the car. Personal allocation displaces battery range management and charging gestures from the fleet manager to the end-user but this status gives the latter all capabilities to assume them.  Allocation to a pool service. EVs are then shared between numerous employees and therefore require the fleet manager's intervention in order to allocate appropriately the car each time it is borrowed. Some companies consider this kind of allocation as a way to increase the use of cars -but the success of this model depends on the fleet manager's involvement.

A successful appropriation of EVs in the studied organisations relies on flexible procedures to access EVs, regardless their allocation status. The tasks of the fleet managers are either carried out in advance (a priori allocation to involved persons) or on day-to-day allocation in the case of pool cars.

In both cases, fleet managers are bound to be experts of employees' mobility. Anticipating professional journeys calls for a reflexive posture from fleet managers. Some of them accept it but others consider that "they are not car leasers". Moreover, the capacity to match technical abilities with social needs is often not recognised by organisations.

Similar adaptation is required in the case of fleet managers planning delivery routes with an electric van, which can have a reduced load capacity compared to its thermic counterpart. In case of carriers and last mile operators, using an electric van thus implies being willing to (partially) re-design delivery operations and re-think logistics platform localization [START_REF] Morganti | Evolution of EV/PHEV market Market trends and potential market for electric vans -4.1[END_REF].

Managing parking issues

Range issues imply a second task: make sure that EVs are recharged under the best conditions. First of all, it means that the organization needs to identify an appropriate charging and parking location, which has to be quite visible and close to the users and which has to respect safety issues. Secondly recharging cannot hinder the next user's journey.

This issue is quite important when EVs are allocated to a pool service as it implies a coordination between users. The users then follow the rules that fleet managers generally register in a formal protocol: shared EVs have to be systematically charged each time they come back to their parking spot. Some fleet managers program these buffers so that a delay is taken into account before any new lease.

Making the conditions of use more flexible

Fleet managers adopt flexible rules on EV use and they additionally authorise charging at home and in public stations. This initiative contributes to gaining new users' acceptance and reducing range anxiety issues. Moreover it proves that fleet managers understand the extent to which more relaxed rules (compared to the ones on thermic vehicles) could determine the success of an EV trial in their organisations. Doing so, they convince the reluctant employees to test EVs and they give them a chance to avoid range anxiety.

In freight transport companies, managers adopt new logistics measures such as setting up microplatforms near the high-density delivery areas (within a 20-30 kilometre range) to reduce the distance travelled by electric vans and to avoid range problems.

These actions show the resourcefulness of fleet managers in promoting the use of EVs.

Dealing with budgets

Financing EVs' implementation in companies modifies the balance of investment and running costs and generates a new assessment of total costs of ownership (TCO).

What costs?

The acquisition of an EV requires buying or leasing the car itself4 but also buying a new socket or charging wall-box to be installed on the company site. The latter expense is related to building cost and not included in the car TCO. Another difficulty is connected to the residual vehicle value (resale value) of EVs for which there is no second-hand market yet so that the TCO is difficult to establish.

The high predictability on how much EVs will cost partially compensates the uncertainty about their resale value. As a matter of fact, a frequent business model for EVs involves leasing the main battery of the car due to two main advantages: (i) The investment costs get lower as there is no need to buy the battery; and (ii) The lease is the guarantee that this battery will be replaced in case of any problems. Such an option is likely to encourage EV uptake among fleet managers and remove a barrier identified by Hutchins and Delmonte (2012, p.11).

Moreover, EVs are supposed to increase cost efficiency -in France a full charge generally costs less than 3 Euros. On the other hand, the potential savings may be hidden or difficult to assess because the cost of electricity or fuel is generally taken care of by departments other than General Resources. So it escapes the control of fleet managers who consequently overestimate the investment costs and miss the potential savings of such cars. As Nesbitt and Sperling already said in 1998 (p.263) "in order for fleets to recognize the potential economic benefits of using alternative fuel vehicles vis-à-vis conventional vehicles, the operating costs should be explicitly stated alongside the purchase price."

A budget under constraint According to the first field studies, EVs were extremely expensive because only prototypes were then available. Some fleet managers thus considered EVs as imposed by high management to promote a certain image of the company and simply could not see any economic gain in a situation where for instance they had to acquire a high standard electric car instead of two small conventional cars5 .

Moreover, as electric cars cannot cover all kinds of distance, this system consequently relies on the availability of others cars for high mileage coverage (Jarrigeon et al., 2013).

Lastly, pilot projects on EVs are often an opportunity for companies to test both leasing models for their fleets and to discuss further their car policy and mobility choices. This is a chance for them to rationalize their fleet and sometimes to reduce it.

Managing people

Most fleet managers are not only in charge of tracking mobility and following the progress of costs but also of leading teams including mechanics. The problem with EVs' implementation is that it lowers the skill perimeter of garage staff, as repairing a battery pack requires accreditation and training they are not familiar with. As Nesbitt and Sperling say (1998), "there is a trend away from inhouse maintenance" (p.262) and electric cars accentuate this trend. For companies which still have a proper garage, car leasing model thus shrinks the mechanics' power as defined by Crozier and Friedberg 6 (1977). There is indeed a general dynamic of externalization of support services and this dynamic benefits from the deployment of such innovations as they re-configure the routine patterns of the organization. The concomitance of EV implementation and externalisation of car maintenance is likely to be a sensitive issue for fleet managers who are in charge of these teams.

Moreover fleet management is an intermediary profession. Instructions are given through handmade protocols and driving guidelines.

For all these reasons, the appearance of EVs on the market puts car fleets under pressure. Being an expert of employees' mobility, summarizing car TCOs and mobilizing teams to accept this innovation: the multidimensionality of fleet management is reactivated by the implementation of EVs in companies and local authorities. But fleet managers are rarely recognised enough for all the additional tasks they perform.

Discussion

Relevant statements from sociology of concrete system of action view [START_REF] Crozier | The emergence of an electric mobility trajectory[END_REF] can be listed as a summary :

-Workers are well advised to depart from formal rules of organisations. For instance making the conditions of EV use more flexible increases the usage frequency of such cars. -Companies are not an example of pure industrial efficiency but are also regulated by experience and inventiveness. Eg. systematic charging resolves the need for anticipating a long charging time before a medium distance journey. -Fleet managers will not endorse the goal of helping EVs implementation if it represents cut down in their budgets or fleets or staff reductions. -Zones of uncertainty in organisations are related to loopholes that are also great opportunities. For instance the definition of what a service car is is unclear, so in fact empathetic fleet managers can let employees commuting with EVs.

There also are some relevant statements from practice theory perspective:

-The system of fleet management practices is modified by the implementation of EVs in organisations. The implementation of EVs in organisations requires. New skills, for instance the ones that are necessary to the battery range assessment; and to evaluate environmental benefits and make them more visible; new material arrangements: charging stations; accountability tools that have to be shared with other departments; and new significations for professional trips, work efficiency, mobility.

-Fleet managers thus become expert in professional practices and informally develop quite good sociological expertise.

Conclusion

Some EV characteristics represent relevant obstacles on the transition to electromobility. Notably, limited battery range and modified cost allotment become valid obstacles for companies that have to cope with them. Companies and organisations are progressively more aware of these constraints. However, the organisational changes associated with the adoption of EVs are sometimes poorly taken into account. Use of these cars requires the employees to adapt their mobility patterns and practices [START_REF] Pierre | Driving an EV: a new practice? How electric vehicle private users overcome limited battery range through their mobility practice[END_REF]. As showed in this paper, the burden of constraints involved in managing an EV shifts from users (employees) to the fleet managers, who assume the responsibility of facilitating the deployment of EVs in organisations.

Fleet managers face multiple difficulties concerning the implementation of EVs and they come up with solutions to solve them: give training in eco-driving, allocate EVs on the basis of an accurate mobility needs diagnosis, redesign delivery operations, make the conditions of use of these cars more flexible, ask the users to charge systematically, etc. All these tasks require additional work, that some fleet managers accomplish willingly and others prefer to avoid, depending on additional resources that they get for it. In this paper, we pointed out the contradictory significations and powerful constraints that complicate the performance of these tasks.

Fleet managers have multiple roles in organisations: users of EVs, garage leaders, cost managers, etc.

A deeper understanding of their position is needed, however we can state that their relation to EVs relies on this multitasking fulfilment and on their resources concerning global changes of the organisations such as fleet rationalisation. They thus obviously play an important but unexpected role in energy demand management.

  1. Overview of the five case studies

		Case study A	Case study B	Case study C	Case study D	Case study E
	General context	Pilot case (trial) in	Pilot case (trial) in 2012-	Mass deployment in	Mass deployment in 2012-	Mass deployment in
		2010-2013	2013	2012-2013	2013	2014 -2015
	EV types	PHEVs	Battery electric vans	Battery electric light	Battery electric light duty	Battery electric vans
			and sedan cars (same	duty vehicles	vehicles
			brand)
	EVs in use in corporate	80 vehicles	53 vehicles	approximately 80	Close to 500	80 vans and small trucks
	fleets
	Fleets involved in the	About 30	About 20	About 30	22 fleets of large	5 fleets
	case study				organizations (from 55
					vehicles to 40,000)
	Number of	16 including 6 fleet	13 including 9 fleet	5 (fleet managers only)	44 including 22 fleet
	interviewees	managers	managers		managers

This definition excludes external providers of fleet management services.

As Virginie[START_REF] Boutueil | Towards a sustainable transport system: Leveraging corporate car fleets to foster innovation[END_REF] explains in her Ph.D. dissertation: "Fleet managers use a wide range of reporting tools, from simple spreadsheets to very sophisticated fleet management software, the purpose of which is to store, monitor and report a range of fleet-relevant information on vehicle characteristics, driving licences, running costs (e.g. fuel, maintenance, tyres), maintenance (routine and scheduled), tax and insurance due dates, etc."

[START_REF] Nesbitt | Fleet purchase behavior: Decision processes and implications for new vehicle technologies and fuels[END_REF] distinguished fleets by the decision-making structures within the organization, taking into account the degree of formalization (the extent to which rules and procedures guide the fleet decision process) and centralization (the number of people involved in fleet decisions, and the decision-making autonomy). If we try to adapt this framework to our studies, we would say that the most successful configurations for EV management are both bureaucracy in big companies (high formalisation and disseminated decision process) and autocracy in small businesses (low formalisation and high centralisation of the decision processes). See also[START_REF] Hutchins | A study of the decision-making behavior of fleet managers in relation to electric vehicles[END_REF].

There are two options: either purchasing the car or leasing it. This latter model is more and more popular in organizations as it allows to forecast the expenses[START_REF] Boutueil | Les entreprises françaises face à l'automobilité et à la mobilité électrique : enjeux, mécanismes de décision et perspectives d'évolution[END_REF]. The implementation of EVs is sometimes a chance to test leasing models for small companies and local authorities.

Moreover, company fleets sometimes get interesting discounts when they buy a significant number of discontinued items (discounted vehicles). And this is only the case for ancient markets, i.e. combustion engine cars.

[START_REF] Crozier | The emergence of an electric mobility trajectory[END_REF] consider that power is the central issue of organisations and define it as the ability from individuals or groups to have an effect on others. One of the four power source is "la possession d'une compétence ou d'une spécialisation fonctionnelle difficilement remplaçable" (ib., p.72) such as mechanic skills.


Yoann Verger
email: yoann.verger@grignon.inra.fr

Keywords: B24, B51, P16 Sraa, rent, rate of prots, self-reproducing process, theory of

This comment from Fratini's article Rent as a share of product and Sraa's price equations corrects Fratini's demonstration that rent as a share of the product and rate of prots could both increase at the same time. By doing so, this comment underlines the specicity of Sraa's theory of value, and especially the need to only analyze systems of production where exchanges are needed to reproduce the system.

value

In a recent paper, [START_REF] Fratini | Rent as a share of product and sraa's price equations[END_REF] investigates rent as a share of the product.

He brilliantly shows how, in the Sraan framework, this view of rent can help to better understand the institutions governing the distribution of the national product (in the line of Adam Smith, Ricardo and Marx), instead of only considering rent per unit of land. However, while trying to show that, in some cases of joint production, the rent and the rate of prots could increase at the same time, he uses an example that is outside the scope of Sraa's analysis. After showing that the point he was trying to make can be demonstrated inside the scope of Sraa's analysis, I will try to underline the relevance of staying inside the boundaries of Sraa's analysis to defend the political project of Sraa.

First, Sraa already showed that, in some cases of joint production, the wage and the rate of prot could both increase:

The possibility that the price of a product may fall faster than the wage has some notable consequences. The rst is that the rule that the fall of the wage in any standard involves a rise in the rate of prots must now admit of an exception. (Sraa, 1960, 72).

The same reasoning can apply to the relation between the rate of prots and rent as a share of product. In a Sraan standard system of joint production, goods that are produced in surplus are in the same proportions they are used 1 as inputs. When the value of the surplus is set to unity (i.e. the numeraire is the standard commodity) and when the wage is kept constant to zero, it is possible to know the evolution of the rate of prots when the rent increases, even without knowing the prices. In this case, the maximum total rent is 1, i.e. the entirety of the surplus. In such system, at a certain level of the rent, the price of a product could increase more quickly than the rent, if this product is jointly produced with a good whose price increases more slowly than the rent.

If this good is chosen as the new numeraire, it is possible that, while the rent increases in terms of the old numeraire (the standard commodity), it decreases in terms of the new numeraire. As the rate of prots has a physical meaning, it will decrease, whatever the numeraire, if the rent increases in terms of the standard commodity.

Then, with an appropriate numeraire and at a certain level of the rent, a decrease of the rent can be followed by a decrease of the rate of prots, and the reverse will be true. If the numeraire is the standard commodity, however, this can never happen, and Sraa is right to claim:

A tax on a basic product then will aect all prices and cause a fall in the rate of prots that corresponds to a given wage, while if imposed on a non-basic it will have no eect beyond the price of the taxed commodity and those of such other non-basics as may be linked with it. (Sraa, 1960, 65).

This sentence almost conclude a chapter where the numeraire was always the standard commodity, and this may explain why Sraa does not specify that this sentence is only true if the standard commodity is the numeraire.

In order to show that the rent and the rate of prots can sometimes increase together, Fratini uses as an example a system where only two industries jointly produce the same two goods, commodity a and commodity b (Fratini, 2016, section 4, example 3, represented below):

q i1 (a) + l 1 → q o1 (a) + q 1 (b) q i2 (a) + l 2 → q o2 (a) + q 2 (b) (1)
While commodity a is used in both processes as input, commodity b is never used as input. Fratini calculates the rate of prots depending on the wage and the rent as a share of the product on commodity a, and he shows that, depending on the input coecients of commodity a and labor, it may happen that the rate of prots increases at all levels of the rent if the rent on commodity a increases, given a constant wage. The problem with this example is that at least one of the two processes must be self-reproducing. A process may be said self-reproducing if it produces enough commodities to reproduce itself without the need to exchange some commodities with other processes [START_REF] Dupertuis | Existence of the standard system in the multiple production case: a solution to the manara problem[END_REF]. In Fratini's example, commodity a is the only commodity input of the system, it must then be produced as output in a greater quantity than it is used as inputs, once the system is brought to a self-replacing state. Therefore, either one of the two processes produces more of the commodity a than it uses it as input, so that after an appropriate multiplication it can cover the needs of both processes, which means that this process is self-reproducing. Or each process produces more of commodity a than it uses it as input, which means that each process is self-reproducing. The numerical example developed by Fratini in his Appendix belongs to this second case:

2a + 20l → 10a + b 5a + 10l → 9a + b (2)
Sraa only deals with systems that can possibly be transformed, through appropriate multiplications, into self-reproducing systems:

This formulation presupposes the system to be in a self-replacing state; but every system of the type under consideration is capable of being brought to such a state merely by changing the proportion in which the individual equations enter it, (Sraa, 1960, 3, footnote).

However, inside a self-reproducing system, all processes must be non-self-reproducing. This is because prices are dened in the theory of Sraa as the exchange ratios that will allow the system to reproduce itself (and to distribute the surplus according to a given social rule):

There is a unique set of exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated (Sraa, 1960, 1).

If a process is self-reproducing, there is no need for this process to make exchanges with other processes in order to reproduce itself. The price of the commodity produced by this process and its rate of prots are then determined by the conditions of production of this process only.

Furthermore, if a non-self-reproducing process produces two outputs, the right method to nd the Sraan prices of each single output is to add an other non-self-reproducing process producing the same two outputs, as Sraa itself explains it (Sraa, 1960, 50, footnote 2). But, if a self-reproducing process jointly produces two outputs, it is not possible to dene the Sraan price of each single output. It is of course possible to calculate prices, if we add to this self-reproducing process an other process of production (either selfreproducing or not). But these prices cannot be the Sraan prices of the two joint products, as no exchanges are needed between both processes. These prices are not the exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated.

At this point, two questions arise. First what are Fratini's prices? These prices are the values that satisfy the equations, providing that a unique price is found for each commodity. In his example, Fratini nds a price for each single commodity, because he has two equations with two unknowns: but these prices are not Sraan prices, because at least one process is self-reproducing. Second can we construct Sraan prices from Fratini's example? Sraa (1960, 6) states: "we shall assume throughout that any system contains at least one basic product". Hence, Sraa's theory may well concern the determination of relative prices associated with a uniform rate of prots across sectors, but only for systems of single production that contains at least one basic product. I add to the previous restriction that, in case of joint production, the system of production must only contain one self-replacing subsystem, as the notion of "mutual dependence" associated with basic commodity in single production (Sraa, 1960, 7) 1 is lost if there is more than one self-replacing subsystem in joint production (see [START_REF] Dupertuis | Existence of the standard system in the multiple production case: a solution to the manara problem[END_REF]. In Fratini's example, there is a basic commodity, 2 but either one or both processes are self-reproducing, so there is no "mutual dependence" between them. In his numerical example, where both processes are self-reproducing, he does not have one circular system of production, but two side by side.

The implication of the lack of such conditions is the apparent impossibility to build a standard system (e.g. [START_REF] Manara | Sraa's Model for the Joint Production of Commodities by Means of Commodities[END_REF]Samuelson, 2008, in order to prove that a standard system can not be constructed in some cases of joint production, use systems of joint production with hidden self-reproducing processes). However this diculty is only apparent: following the method displayed in [START_REF] Dupertuis | Existence of the standard system in the multiple production case: a solution to the manara problem[END_REF], in order to construct the standard system, we will have to limit the system to the self-reproducing sub-system. If there is several self-reproducing sub-systems, several standard systems can be constructed.

But, as we already said, it is true that, if in the self-reproducing sub-system the number of commodities produced is higher that the number of processes, some prices will stay indeterminate.

The standard system is important for Sraa, as he can show that the maximum rate of prots is independent from the prices (it is a physical property of the system) and that, by using the standard commodity as the numeraire, the distribution also appears to be independent from the prices (i.e. it can be known prior to prices). Only in one case, it is not possible to calculate a standard system: it is the case where all industries produce non-basic commodities with the help of labour only (e.g. see [START_REF] Pasinetti | Structural economic dynamics: a theory of the economic consequences of human learning[END_REF] for a deep investigation of labor economy without capital). Interesting results can be found by analyzing such systems, but it must be underlined that such analyses move away from the 1 It is desirable at this stage to explain why the ratios which satisfy the conditions of pro- duction have been called 'values' or 'prices' rather than, as might be thought more appropriate, 'costs of production'.

The latter description would be adequate so far as non-basic products were concerned, since, as it follows from what we have seen in the preceding section, their exchange ratio is merely a reection of what must be paid for means of production, labour and prots in order to produce themthere is no mutual dependence.

But for a basic product there is another aspect to be considered. Its exchange-ratio depends as much on the use that is made of it in the production of other basic commodities as on the extent to which those commodities enter its own production (Sraa, 1960, 7).

2 Commodity a is a basic commodity, even following the denition given by Sraa after the introduction of joint production (Sraa, 1960, 60). kind of analysis developed by Marx and pursued by Sraa. They are interested in the description of a real capitalist system, and they try to highlight the possibility to decouple the problem of the distribution of wealth from the problem of value. This is why the possibility that an ultimate commodity is produced only by labour is explicitly rejected by Sraa (Sraa, 1960, Appendix D, 3).