Hakima Boulemche

Barkahem Anak

Amel Djedouani

Rachid Touzani

Michel François

Solenne Fleutot

Franck Rabilloud

Hakimaboulemche

Synthesis, X-ray crystallography, computational studies and catecholase activity of new zwitterionic Schiff base derivatives

Keywords: Schiff base, Zwitterionic form, X-Ray, Catecholase, Hirshfeld surface, DFT

come

Introduction

Schiff bases are important compounds owing to their wide range of biological activities and industrial applications [START_REF] Villar | Synthesis and cytotoxic activity of lipophilic sulphonamide derivatives of the benzo[b]thiophene 1,1-dioxide[END_REF][START_REF] Li | Artemisinin derivatives bearing Mannich base group: synthesis and antimalarial activity[END_REF]. They have also been used as ligands in coordination chemistry [START_REF] Kagkelari | Synthesis and structure of N-salicylidene-o-aminophenolato gallium(III) complexes[END_REF][START_REF] Ourari | Dioxygen activation with a cytochrome P450 model. Characterization and electrochemical study of new unsymmetrical tetradentate Schiff-base complexes with iron(III) and cobalt(II)[END_REF].Nsubstituted o-hydroxyimines have been reported to display thermochromism and photochromism in the solid state by H-atom transfer from the hydroxy O atom to the N atom, the features of photochromism are used in some application areas such as measuring and controlling radiation intensity, imaging systems and optical computers [START_REF] Karakurt | Molecular structure and computational studies on 2-((2-(4-(3-(2,5dimethylphenyl)-3-methylcyclobutyl)thiazol-2-yl)hydrazono)methyl)phenol monomer and dimer by DFT calculations[END_REF][START_REF] Hadjoudis | Photochromism and thermochromism of schiff bases in the solid state and in rigid glasses[END_REF]. In general, O-hydroxy Schiff bases exhibit two possible tautomeric forms, the phenol-imine (or benzenoid) and keto-amine (or quinoid) forms.

Depending on the tautomers, two types of intra-molecular hydrogen bonds are possible: O-H• • •N in benzenoid and N-H• • •O in quinoidtautomers. O-hydroxy Schiff bases have been previously observed in the keto form, in the enol form or in enol/keto mixtures [START_REF] Nazır | Intramolecular hydrogen bonding and tautomerism in Schiff bases. Structure of N-(2-pyridil)-2-oxo-1-naphthylidenemethylamine[END_REF][START_REF] Antanov | Tautomerism of 2-hydroxynaphth aldehyde Schiff bases[END_REF]. Another form of the Schiff base compounds is also their zwitterionic form [START_REF] Krygowski | Through-Resonance Assisted Ionic Hydrogen Bonding in 5-Nitro-N-salicylideneethylamine[END_REF][START_REF] Djedouani | Zwitterionic (E)-6-methyl-2-oxo-3-[1-(p-tolyliminio)ethyl]-2H-pyran-4-olate[END_REF][START_REF] Ouari | 1,1'-{(Hexane-1,6-diyl)bis[(azaniumylylidene)methanylylidene]}bis(naphthalen-2-olate)[END_REF][START_REF] Ouari | yl)bis[END_REF]. Zwitterions of Schiff bases have an ionic intramolecular hydrogen bond (N + -H• • •O -) and their N + -H bond lengths are longer than the standard interatomic separations observed in neutral N-H bonds (0.87 Å). The other ionic bonds in the zwitterions C-O -, is not a key indicator as distinctive as N + -H bond, because NH forms of Schiff bases in solid state can be regarded as a resonance hybrid of two canonical structures, the quinoidal and zwitterionic forms [START_REF] Ogawa | Aggregation controlled proton tautomerization in salicylideneanilines[END_REF].

Cu(II) complexes formed from Schiff base ligands have been important model compounds in studying the physical and chemical behavior of biological copper systems [START_REF] Reddy | Nuclease activity of mixed ligand complexes of copper(II) with heteroaromatic derivatives and picoline[END_REF]. As an important example, numerous biomimetic approaches were devoted to the synthesis of binuclear Cu(II) ion complexes with various ligands to reproduce catecholase activity [START_REF] Sreedaran | Synthesis, spectral, magnetic, electrochemical and catalytic studies of cyclam-based copper(II) and nickel(II) complexeseffect of N-substitution[END_REF][START_REF] Allam | Thermodynamic, spectroscopic studies and catechol oxidase activity of copper (II) complexes with amphiphilic dgalacturonic acid derived ligands[END_REF]. Notable progress has been made to mimic catecholase activity using copper complexes coordinated to multidentate Schiff bases ligands [START_REF] Djedouani | Catecholase Activity Investigations using in situ Copper Complexes Continuing Schiff Base Derivatives with a Theoretical Calculation[END_REF][START_REF] Mouadili | Biomimetic catecholase studies: using in-situ prepared complexes by 1,2,4-triazole schiff bases and different metal salts[END_REF][START_REF] Mouadili | Air Oxidation of catechol by in-situ copper (II) complexes with ligands containing benzyl groups[END_REF]. It is now well known that proteins containing copper (metal-protein) play a very important role in transport, activation, and metabolism of dioxygen in living organisms [START_REF] Zerrouki | Synthesis of new derivatizedpyrazole based ligands and Theircatecholase activity studies[END_REF].

In this paper, we present the full structural characterization and theoretical studies of new zwitterionic Schiff bases : 6-methyl-2-oxo-3-[1-(p-fluoriminio)ethyl]-2H-pyran-4-olate (L1), 6methyl-2-oxo-3-[1-(p-chloriminio)ethyl]-2H-pyran-4-olate (L2) and 6-methyl-2-oxo-3-[1-(pbromoriminio)ethyl]-2H-pyran-4-olate (L3). New copper (II) complex were prepared and evaluated for their catecholase activities at aerobic conditions. Experimental results are compared with theoretical results led in the framework of the density-functional theory.

Experimental

1. Materials and physical measurements

All chemicals were purchased from Sigma-Aldrich and were used without further purification.

Thin layer chromatography (TLC) was performed by using Merck silica gel (60 F254) plates (0.25 mm) and visualized under Ultraviolet light (UV). Melting points were determined with a digital melting point apparatus using capillary technique. Infrared (IR) spectra were recorded with a Shimadzu FTIR-8010M spectrometer between 400 and 4000 cm -1 (KBr disks). The 1 H RMN spectra were recorded on a Jeol GSX WB spectrometer at 270 MHz in CDCl3. The chemical shifts, δ, are given in parts per million (relative to TMS). The UV-Visible spectra were recorded in DMSO between 200-800 nm using JASCO V-650 spectrophotometer with quartz cells of 1 cm path length.

X-ray crystallographic study

X-ray single-crystal diffraction data were collected at 293Kfor L1-L2 and 150 K for L3 on a BrukerAPEX II CCD diffractometer equipped with a graphite monochromator using Mo Kα radiation (λ = 0.71073 Å). The structures were solved by direct methods using the SIR2002 program [START_REF] Burla | SIR2004: an improved tool for crystal structure determination and refinement[END_REF] and refined on F2 by full matrix least-squares [START_REF] Sheldrick | SHELX97 -Program for Crystal Structure Analysis[END_REF]. Unit cell refinement using all observed reflections and data reduction were performed using SAINT. All non hydrogen atoms were refined anisotropically and the hydrogens (except hydrogen atoms attached to N atom) were included in geometric positions.

The hydrogen atoms bound to N atom were located in difference Fourier map and their coordinates were refined with displacement parameters. The final difference Fourier maps showed no peaks of chemical significance.

Computational details

The ground state of the three compounds have been fully optimized within the Density Functional Theory method [START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF] (DFT) using the Gaussian09 program package [START_REF] Frisch | Gaussian Inc[END_REF].The exchange and correlation functional was modeled within the hybrid Becke's three parameters and the Lee-Yang-Parr function (B3LYP) [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF]. Atomic basis sets were 6-31+G(d,p) basis set [START_REF] Petersson | A complete basis set model chemistry. II. Open-shell systems and the total energies of the first-row atoms[END_REF].Vibrational frequencies were calculated to guarantee that the optimized structures are local minima. Such a level of approximation was previously shown to be quite adapted for a structural and electronic characterization of molecular complexes.

Catecholase activity measurements

following the appearance of o-quinone over time at 25°C (390 nm absorbance maximum, ε = 1600 L mol -1 cm -1 in methanol [START_REF] Calero | Oxidation and catalytic properties of a binuclear copper(i) complex with a meta-xylyl spacer ligand[END_REF]. The complexes were prepared in situ by successively mixing 0.3 mL of a solution (2. 10 -3 M) of CuX2, nH2O (X= CH3COO -, Br -, Cl -, NO3 -, or SO4 2-), with 0.15 mL of a solution (2. 10 -3 M) of ligand, then adding 2 mL of a solution of catechol at a concentration of 10 -1 M.

General procedure for synthesis of the Schiff base

To a hot ethanolic solution (15 mL) of dehydroaceticacid (0.01 mol) was added 0.01 mol of 4fluoro aniline for (L1),4-chloro aniline for (L2) or 4-bromo aniline for (L3). The resulting solution was refluxed for 3 hand the reaction was monitored by TLC (CH2Cl2: MeOH, 5:1). After standing 5 days for (L1) needles crystals were filtered off, washed with small amounts of cold ethanol.(L2) and (L3) were filtered and recrystallized from a mixture of ethanol and a few drops of distilled water,single crystals are obtained after two weeks. The reaction scheme is shown in schema 1.

Scheme. [START_REF] Villar | Synthesis and cytotoxic activity of lipophilic sulphonamide derivatives of the benzo[b]thiophene 1,1-dioxide[END_REF] The synthesis schematic for L1 (R=F), L2 (R=Cl) and L3 (R=Br).

Result and discussion

Analytical data

(E)-6-methyl-2-oxo-3-[1-(p-fluoriminio)ethyl]-2H-pyran-4-olate(L1):

A white crystals were obtained. Yield: 61%, m.p. 410 K. 1 H NMR (CDCl3), δppm: 2.15 (s, 3H, CH3); 2.55 (s, 3H, CH3acetyl); 5.75 (s, 1H,CHPyr); the aromatic protons appear as multiple signal in the 7.2-6.5 range;13.5 (s,HO-H…N ).Solubility: Soluble in MeOH, DMSO, DMF, CHCl3 and hot EtOH.

(E)-6-methyl-2-oxo-3-[1-(p-chloriminio)ethyl]-2H-pyran-4-olate (L2):

A white solid was obtained. Yield41%, m.p. 413 K. 1 H NMR (CDCl3), δ ppm: 2.15 (s, 3H, CH3); 2.57 (s, 3H, CH3acetyl); 5.74 (s, 1H, CHPyr);the aromatic protons appear as multiple signal in the 7.42-6.9 range; 15.3 (s, HO-H…N).Solubility: Soluble in MeOH, DMSO, DMF and hot EtOH.

3.1.3.(E)-6-methyl-2-oxo-3-[1-(p-bromoriminio)ethyl]-2H-pyran-4-olate(L3):

A light beige solid was obtained.Yield48%,463 K. 1 H NMR (CDCl3), δppm:2.14 (s, 3H, CH3); 2.63 (s, 3H, CH3acetyl);5.8 (s, 1H, CHPyr); the aromatic protons appear as multiple signal in the 7.2-7.7 range; 15.5 (s, HO-H…N).

Solubility: Soluble in MeOH, DMSO, DMF and hot EtOH.

Infrared spectra

Infrared spectra of the three compounds are found to be quite similar. A zwitterionic form was observed in the solid state for the three Compounds (see crystallographic data in the following paragraph).The IR spectra data of molecules taken from KBr pellet, are in agreement with the structure determined by the X-ray diffraction. The bands appearing around 3400 cm -1 are assigned to the O-…H-N + stretching [START_REF] Özkar | Crystal and molecular structure of bis(acetylacetone)ethylenediimine: intramolecular ionic hydrogen bonding in solid state[END_REF]. The ν(C=N) absorption bands are observed at 1555 and 1570 cm -1 for L1, L2 and L3 respectively as ArCH=Nar [START_REF] Gavranic | O hydrogen bonding, quinoid effect, and partial π-electron delocalization in N-aryl Schiff bases of 2-hydroxy-1-naphthaldehyde: the crystal structures of planar N-(α-naphthyl) and N-(β-naphthyl)-2-oxy-1-naphthaldimine[END_REF][START_REF] Freedman | I. A Spectroscopic Study of the Hydrogen Bond between Hydroxyl and Nitrogen[END_REF]. On the other hand, the bands observed between 1207 and 1275 cm -1 are assigned to νC-O (phenolic) frequencies [START_REF] Tan | Synthesis and characterisation of copper(II), nickel(II) and palladium(II) complexes of some schiff bases of dehydroacetic acid[END_REF][START_REF] Carugo | Influence of the complexation of copper(II) on the structure and reactivity of 4-hydroxy-6-methyl-3-[3-dimethylaminoacryloyl]-2H-pyran-2-one[END_REF]. The absorption peak around 1610 cm -1 is due to the CO stretching; the value appears to be lower than that for a typical C=O group (1712-1708 cm-1) and is indicate of the enolic form of the molecules, in which the proton is transferred from the oxygen atom to the nitrogen atom.

UV-Vis analysis

The UV-Vis absorption spectra show one bands at 326, 331, and 330 nm for L1, L2, L3 compounds respectively, which might be assigned to the π-π* transitions [START_REF] Emam | Synthesis, structural characterization, electrochemical and biological studies on divalent metal chelates of a new ligand derived from pharmaceutical preservative, dehydroacetic acid, with 1,4-diaminobenzene[END_REF].

Crystallographic studies of ligands

The main crystal parameters are reported in Table 1. The bond distances and angles are listed in Table 2. The numbering schema and a displacement ellipsoid plot of L1, L2 and L3 are showed in Fig 1 . (L1) is crystallized in a monoclinic system in P21/c space group and with a four unit per cell (Z = 4), (L2) crystallized in a triclinic system in P-1 space group and with a two unit per cell (Z = 2) and (L3) crystallized in anorthorhombic system in Pnab space group and with eight unit per cell (Z = 8). 2), indicating the zwitterionic character of the title compounds [START_REF] Petek | Z)-6-[(2-Fluorophenyliminio)methylene]-2,3dihydroxyphenolate[END_REF].

In the three compounds, the aromatic ring and dehydroacetic acid ring are in trans position with respect to the C=N bond, and the molecular configuration is determined by the presence of the intramolecular hydrogen bond O -...H-N + . The three molecules differ in the orientation of phenyl rings.

In L1 the dihedral angle between the two rings of aromatic and dehydroacetic acid is 37.35°, while it is 68.18° and 51.23°in the case of L2 and L3 respectively. The iminium atom H participates in a strong intramolecular hydrogenbond with the enolate atom O, which generates aS(6) ring motif [START_REF] Bernstein | Patterns in Hydrogen Bonding: FunctionalityandGraph Set Analysis in Crystals[END_REF].

Similar intramolecular hydrogen bonds were reported in the above-mentioned zwitterionic phenolates [START_REF] Huang | E)-2,4-Dichloro-6-[(2-hydroxyethyliminio)methyl]phenolate[END_REF][START_REF] Temel | Zwitterionic (E)-2-hydroxy-6-[(otolyliminio)methyl]phenolate 0.07-hydrate[END_REF]. This six-membered pseudocycle is almost planar, the maximum deviation from the mean plane being 0.018 Å for atom C4 in L1, and 0.109 for atom N in L2 and 0.021 in L3 for atom H7.

In the crystal, molecules of L1 are aligned head to foot along b axis, in columns parallel to [0 0 1] axis and the structure is stabilized by three kinds of C-H•••O interactions. This arrangement separates the equivalent groups in columns by 4.012 (1) Å (Fig. 4, Table 3).

Molecules of L2 exhibit one intermolecular hydrogen bond N5-H2…O3. In the crystal, molecules are aligned along c axis; forming layers that extend in zigzag parallel to the plane (b, c) (see Fig. 5). There are no other significant intermolecular contacts. In the crystal packing of L3, the structure is stabilized by four kinds of C-H•••O interactions alternating zigzag chains along the c axis (Fig. 6, Table 3).

Table 2

Selected bond distances (Å) and angles (°) for ligands. showing a sp 2 hybridization on the N(12) atom.

Computational Study

Frontier molecular orbitals (FMOs)

The frontier molecular orbitals (FMOs) play an important role in the electric proprieties. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is an indicator of the stability and optical polarizability of a molecule.

The Schiff bases display two possible forms of intermolecular hydrogen bonds: the phenol-imine (OH), and Keto-amine (NH) forms (fig. 5). The contour plot and energy of frontier orbitals HOMO and LUMO for the two forms are reproduced in fig. 5.

The keto-amine (NH) forms which were preferably compared with phenol-imine (OH) forms decrease the HOMO level and increase the LUMO level implying a more stability. The electronic structure for the phenol-imine (OH) shows an intra-ligand charge transfer from HOMO to LUMO, while the keto-amine (NH) forms have a charge transfer -* (fig. 5). Clearly the keto-amine form is in agreement with stability of three compounds.

Electronic absorption spectra

Theoretical UV-visible absorption spectra of L1, L2 and L3 using TDDFT are in clear agreement with experimental results (fig. 6). Calculated absorptions with wave length  (nm), oscillator strengths (f) and main transitions with their contribution are illustrated in table 5. L1 exhibits a strong absorption measured at 326 nm and theoretically obtained at 325 nm with a main contribution associated to HOMO-1→LUMO and related to -* transition (fig S1 in SI). The absorption band of L2 absorption wave length is found at 331nm, this band is calculated at 328 nm and mainly involved the HOMO→LUMO transition and is assigned to -* character. The L3 shows an experimental absorption at 330 nm which was calculated at 328 nm and attributed to HOMO→LUMO transition with a -* character.

The Hirshfeld surface analysis

The Hirshfeld analysis reveal the presence of intermolecular interactions(intercontact) in crystalline environment of the titled compounds. The normalized contact distance dnorm between molecules in 3D is a parameter that includes distances of any surface point to the nearest nucleus internal (di) and the nearest nucleus external to the surface (de) and the van der Waals radii of atoms (r vdw ) given by the equation:

d norm = d i -

Catecholase studies

The progress of the catechol oxidation reaction is conveniently followed monitoring the strong absorbance peak of o-quinone in the UV/Vis spectrophotometer (Scheme 2). The metal complex (prepared in situ from metal salt and the ligand) [START_REF] Kodadi | Synthesis of new tripodal ligand 5-(bis(3,5dimethyl-1H-pyrazol-1-ylmethyl)amino)pentan-1-ol, catecholase activities studies of three functional tripodalpyrazolyl N-donor ligands, with different copper (II) salts[END_REF] and a solution of catechol were added together in the spectrophotometric cell at 25°C [START_REF] Bouabdallah | Synthesis of new tripodal ligand: N,Nbis[(1,5-dimethylpyrazol-3-yl)methyl]benzylamine. Catecholase activity of two series of tripodal ligands with some copper (II) salts[END_REF][START_REF] Boussalah | Synthesis, structure and catalytic properties of tripodal amino-acid derivatizedpyrazole-based ligands[END_REF]. Formation of o-quinone was monitored by the increase in absorbance at 390 and 400 nm as a function of time. Table 6 gives absorbances of Cu(II) complexes generated in situ after 60 min by mixing metallic salts Cu(CH3COO)2, CuBr2, CuCl2, Cu(NO3) 2 and

CuSO4 and ligands L1-L3 (2/1) and catechol. The oxidation rates are shown in Table 7.

Scheme. 2 Catecholase reaction.

We note that the catalytic activity varies from a complex to the other one, the obtained results for Cu(CH3COO)2 salt are grouped in (Fig. 8) and the Vmax rates of the catechol oxidation were calculated in a time range of 5 min where the slope of the absorbance graph is maximal and collected in Table 6. In this part, we take one equivalent of ligand for two equivalents of metallic salt.

All copper complexes catalyze the oxidation reaction of catechol to o-quinone, but with oxidation rate values ranging from 0.04 µmol L -1 min -1 to 20.06 µmol.L -1 .min -1 . In fact, the first rate concerns the complexes formed from L2 and metallic salts CuBr2 and CuCl2 (weak catalysts) and the second one concerns the complex formed from L1and metallic salt Cu(CH3COO)2 (best catalyst) (Table 7).

The difference between the catalytic activities from a complex to another depends strongly on both the structure of the ligand and the action of the anion. Indeed, most ligands have a low absorbance with all the anions except in the case of acetate anion where the values of the absorbance are high (Table 6).

Table 6

Absorbance of the mixture of Cu(II) and cathecolafter 60 min(μmol L -1 min -1 ). The differences in activity observed during the oxidation reaction was found to be influenced by:

(a) The nature of the anion associated with the the anions that bind tightly with copper cannot be easily displaced by the substrate, thereby reducing the catalytic power as in the case of NO3 -, SO - 4, Cl -, Br -ions. In complexes with anions that form weaker bonds with the metal center, the substrate has no problem to coordinate to the metal because it can easily replace the weakly bound anions and consequently promotes the oxidation reaction of catechol with higher rate as in the case of CH3COO -.

(b) The nature of the substituent in the para position of the benzene ring : the ligand with the most electronegative substituent provides an important catalytic activity as the complexes of the ligands with substituent less electronegative, the electron attractor group can increase the complexing properties of the ligand [START_REF] Mouadili1 | Biomimetic catecholase activities by prepared in-situ complexes: development of a quantitative[END_REF][START_REF] Boyaala | Biomimetic oxidation of catechol employing complexes formed in situ with heterocyclic ligands and diferent copper(II) salts[END_REF].

Effects of the nature of anion and the ligand

In the CH3COO-case (Fig. 8), all ligands show high values of absorbance in time.In bromides, chlorides, nitrates, and sulfates (Fig. 9 -12), Cu-L1 complex seams the best oxidation catalyst with a highest value of rate (12.34 µmol L -1 min -1 ), whereas with the other ligands [START_REF] Thabti | Synthesis, X-ray crystal structures and catecholase activity investigation of new chalcone ligands[END_REF][START_REF] Bouanane | Synthesis, structural, catecholase, tyrosinase and DFT studies of Pyrazoloquinoxaline derivatives[END_REF] the rate values are located in the same gap but are still low within the range of 0.4 and 1 µmol L -1 min -1 (L2). The comparison between the catalytic activity of the complexes of copper (II) and the three four ligands L1, L2 and L3 (Table 6) shows that Cu-L2 complexes are observed to be the lowest active, except in the case of NO3 -anion.

Effects of the ligand concentration on the cathecolaseactivity

Evolution of catechol oxidation into o-quinone is followed by varying the ratio of equivalent ligand L1/metallic salt Cu(CH3COO)2. Three tests were carried out in ratio: 1/1, 2/1 and 1/2. The results indicate that the test with the ratio L2/Cu(CH3COO)2=3 leads to the higher oxidation rate value (20.06mmol L -1 min -1 ). For the ratio 1/1, the maximum value of the rate is 15.27mmolL -1 min -1 . For the ratio 2/1, the rate value have reached a maximum of 12.38mmol L -1 min -1 (Fig. 13).

Conclusion

We report here the synthesis of three new Schiff bases derivatives of dehydroacetic acid 6-methyl-

Fig. 2 Fig. 3 Fig. 4

 234 Fig. 2 Cell packing. H atoms have been omitted for clarity (a) and hydrogen bonding (b) for L1.

  . The calculated C-N and C-O bond distances for the three compounds which are most important of tautometric forms, are also in good agreement with experiment, since C(7)-N(12) and (C19)-O(31) bond distances are slightly longer than experimental values within 0.002-0.016 Å and 0.001-0.048 Å for L2 and L3 respectively. The calculated bond angles for the three compounds with B3LYP levels are all very similar to the experimental values with slight deviations within 0.6-7.18º. These results are in agreement with the expect delocalization in the molecule and confirmed by a bond angle C(7)-N(12)-C(14)129º

Fig. 5

 5 Fig. 5 The frontier molecular orbitals for the two possible tautomeric forms, the keto-amine (NH) L1, L2 and L3 the phenol-imine (OH) forms of the title Schiff base compounds L1', L2' and L3'.HOMO-LUMO gap is given.

  dnorm is negative or positive when intermolecular contacts are shorter or longer than r vdW respectively. The analyses of the Hirshfeld surface and fingerprint plots of the titled compound were obtained using the crystal Explorer 3.0 package[START_REF] Wolff | Crystal Explorer, Version 3.0[END_REF]. The overall two-dimensional (2D) fingerprint plot of contact O...H/H...O and N...H/H...N are illustrated in fig. 6.The intermolecular interactions of the O....H/H....O contact with a relative contribution of 21.9%, 25.5% and 25.9% for L3, L2 and L1 respectively have the most significant contribution to the total Hirsfeld surfaces. The spikes point out the dominant interactions for the O...H/H...O contact. The contact appears as a pair of sharp spikes where the (de,di) distributions correspond to de+di  2.4 Å, 2.5Å and 2.46 Å for L1, L2 and L3 respectively. These relative small values compared to the sum of the van der Waals radius (2.72 Å) reflect the relatively strong interaction between O and H.

Fig. 7

 7 Fig. 7 Two-dimensionalfingerprint plots of L1, L2 and L3 for O..H/H..O and N...H contacts.de and di represent the distances from the surface to nearest external and internal atoms. The blue color represents increasing numbers of surface contributors at individual de/di points.

Fig. 8

 8 Fig.8 Hirshfeld surfaces for visualizing the intermolecular contacts. The dnorm values are mapped onto the Hirshfeld surface using a red-blue-white colour scheme as follows: red regions represent closer contacts and a negative dnorm value; blue regions represent longer contacts and a positive dnorm value; and white regions represent the distance of contacts equal to exactly the vdW separation with a dnorm value of zero.

Fig. 9

 9 Fig. 9 Oxidation of catechol in presence of acetate.

Fig. 10 Fig. 11

 1011 Fig. 10 Oxidation of catechol in presence of bromide.

Fig. 12 Fig. 13

 1213 Fig. 12 Oxidation of catechol in presence of nitrate.

Fig. 14

 14 Fig.[START_REF] Reddy | Nuclease activity of mixed ligand complexes of copper(II) with heteroaromatic derivatives and picoline[END_REF] Catechol oxidation in methanol, in presence of formed L1 copper complexes with different concentrations.

2 -

 2 oxo-3-[1-(p-fluoriminio)ethyl]-2H-pyran-4-olate (L1),6-methyl-2-oxo-3-[1-(p-chloriminio)ethyl]-2H-pyran-4-olate (L2) and 6-methyl-2-oxo-3-[1-(p-bromoriminio)ethyl]-2H-pyran-4-olate (L3),with good yields. The X-ray structures of the three compounds have been investigated for the first time herein. The oxidation reaction of catechol is very efficient to give o-quinone by complexes of copper (II), obtained with the three ligands (L1-L3). Structural and electronic properties have been investigated at DFT/B3LYP level and the analyses of the Hirshfeld surface are in good agreement with the experimental data. Copper (II) complexes were generated in situ and our results show that all the complexes catalyze the aerobic oxidation of catechol to the corresponding o-quinone.

Table 1

 1 Crystallographic data and structure refinement details for L1, L2 and L3. View of the molecular structure of L1, L2 and L3 with the atom labeling.The structures reported here adopt a zwitterionic form, with the phenolic H atom having been transferred to the imino group. The H atom attached to N was located in a difference-Fourier map and freely refined. The resulting iminium and hydroxyl groups are linked by an intramolecular N-H…O hydrogen bond [0.90, 1.091 and 0.880 Å] for L1, L2 and L3 respectively, comparable with the similar zwitterions in the literature[START_REF] Djedouani | Zwitterionic 6-methyl-2-oxo-3-[1-(ureidoiminio)ethyl]-2H-pyran-4-olatemonohydrate[END_REF][START_REF] Wojciechowski | Crystal structure of Schiff base derivative of 2,2′-dihydroxybiphenyl-3-carbaldehyde with nbutylamine[END_REF]. The bond distances shown in Table2indicate that the C-

	Compound	L1	L2	L3
	Empirical formula	C14H12O3NF	C14H12O3NCl	C14H12O3NBr
	Formula weight, g/mol	261.25	277.70	322.16
	Crystal description	Needle	Needle	Prism
	Space group	P21/c	P-1	Pnab
	Crystal system	Monoclinic	Triclinic	Orthorhombic
	F(000)	544	288	1296
		Unit cell dimensions
	a/Å	4.0119(3)	7.5606(5)	9.6906(2)
	b/Å	23.6690(17)	8.7382(7)	9.9780(3)
	c/Å	12.8177(10)	10.2086(12)	26.7807(9)
	α/°	90	85.018(4)	90
	β /°	94.494(2)	79.311(3)	90
	γ/°	90	76.008(8)	90
	V/Å 3	1213.40(16)	642.45(10)	2589.50(13)
	Z	4	2	8
	Temperature/K	293(2)	293(2)	150(2)
	θrangefordata	1.72-25.69	2.03-25.58	3.03/27.36
	collection (°)
	Radiation	Mo Kα(λ= 0.71073)	Mo Kα(λ= 0.71073)	Mo Kα(λ= 0.71073)
	Dcalcd (g/cm -3 )	1.430	1.436	1.653
	µ(mm -1 )	0.111	0.300	3.178
	Range/indices (h, k, l)	-4 ≤ h ≤ 4	-8 ≤ h ≤ 8	-8 ≤ h ≤ /12
		-28 ≤ k ≤ 28	-10 ≤ k ≤ 9	-12 ≤ h ≤ 12
		-15≤ l ≤ 15	-12 ≤ l ≤ 12	-34 ≤ l ≤ /21
	Ref Nmb of reflections	118724	4176	11767
	measured
	Number of independent	2280	2248	2945
	reflections
	reflections with I > 2σ(I)	1503	1059	2309
	Number of parameters	209	173	174
	Refinement method	Full-matrix	Full-matrix	Full-matrix
		least-squares on F2	least-squares on F2	least-squares on F2
	Goodness-of-fit (GOF)	0.966	0.971	0.955
	R [F2 >2 σ (F2)]	0.0336	0.1082	0.0403
	wR(F2)	0.1311	0.1745	0.068
	Rint	0.0519	0.0673	0.0293
	Max / min δp (e /Å 3 )	0.290/-0.287	0.379/ -0.374	0.062/-0.308

bond length

[1.260(3)

, 1.274(5) and 1.260 (2) Å] respectively are intermediate between single and double carbon to oxygen bond lengths (1.362 Å, 1.222 Å)

[START_REF] Allen | Tables of bond lengths determined by X-ray and neutron diffraction. Part 1. Bond lengths in organic compounds[END_REF]

. The carbon-carbon bonds connecting the enol and imine groups exhibit intermediate distances between a single and a double bond (Table

Table 3

 3 Distances (Å) and angles (°) of hydrogen bond for L1, L2 and L3.

	D-H…A	d(D-H)	d(H…A)	d(D-A)	D-H-A
	L1
	N1-H12… O3	0.91(3)	1.72(3)	2.545(3)	150(3)
	C12 -H1… O2	0.92(3)	2.49(3)	3.236(3)	139(2)
	C10 -H5… O2	0.94(3)	2.30(3)	2.762(4)	109(2)
	C10 -H6… O3	1.04(4)	2.40(4)	3.311(4)	145(3)
	L2
	N005-H2… O003	1.0900	1.7400	2.535(5)	126.00
	L3
	N7-H7…O18	0.8800	1.7600	2.528(2)	144.00
	C3-H3…O16	0.9500	2.5700	3.472(3)	158.00
	C9-H9B…O16	0.9800	2.3100	2.787(3)	109.00
	C9-H9C…O18	0.9800	2.4900	3.252(2)	134.00
	C14-H14…O16	0.9500	2.5800	3.524(3)	172.00

Table 4 .

 4

	Bond lengths (Å) and angles (°) for L1, L2 and L3.Experimental data are given in parentheses (in
	bold).X designs the halogen atom (X=Br,Cl and F).
	Bond length (Å)	L1	L2	L3
	X(1)-C(2)	1.357 (1.359)	1.755 (1.731)	1.900 (1.900)
	C(7)-N(12)	1.422 (1.422)	1.420 (1.436)	1.419 (1.417)
	C(14)-C(19)	1.341 (1.324)	1.341 (1.351)	1.341 (1.321)
	C(19)-C(25)	1.464 (1.442)	1.464 (1.435)	1.464 (1.451)
	C(19)-O(31)	1.258 (1.210)	1.258 (1.212)	1.258 (1.259)
	N(12)-H(13)	1.042 (0.904)	1.042 (1.043)	1.042 (0.879)
	Angle (º)
	C(7)-N(12)-H(13)	118.30 (118.90)	118.17 (124.90)	118.13 (115.14)

H(13)-N(12)-C

[START_REF] Reddy | Nuclease activity of mixed ligand complexes of copper(II) with heteroaromatic derivatives and picoline[END_REF]

112.51 (110.44) 112.42 (114.37) 112.41 (115.10) C(7)-N(12)-C(14) 129.16 (130.63) 129.38 (124.90) 129.45 (129.75) C(19)-C(25)-O(31) 123.26 (128.09) 123.24 (130.42) 123.23 (123.60) The DFT-optimized parameters (bond lengths, angles) are given in Table 4. They are in good agreement with the experimental data. The calculated bond distance C(19)-C(25) is slightly longer than experimental values within 0.013-0.029 Å for the three compounds

Table 5 :

 5 TD-DFT calculated excitations approximate assignments for L1, L2 and L3.

		λ Expt.	λ Cal.	Oscillator	Assignment	Contribution
		(nm)	(nm)	Strength		(Coeff %)
	L1	326	325	0.132	HOMO-1→LUMO	39.60
	L2	331	328	0.246	HOMO→LUMO	45.22
	L3	330	328	0.303	HOMO→LUMO	52.22

Fig. 6 Experimental and simulated electronic absorption spectra of L1, L2 and L3.

Table 7

 7 Oxydation rate of cathecoloxydation in methanol (µmol.L -.min).

	Ligand/metallicsalt	Cu(CH3COO)2 CuBr2	CuCl2	Cu(NO3)2	CuSO4
	L1	1.928	1.418	0.945	0.3619	0.948
	L2	1.6937	0.0386	0.0387	0.0961	0.2678
	L3	1.348	1.312	0.292	0.554	0.574

Acknowledgements

Th eauthors acknowledge the Algerian Ministry of Higher Education and Scientific Research, and the Algerian Directorate General for Scientific Research and Technological Development for support of this work.


Stephan Marette
email: marette@agroparistech.fr.

John Beghin
email: beghin@unl.edu.

Anne-Célia Disdier
email: celia.disdier@psemail.eu.

Eliza Mojduszka
email: eliza.mojduszka@usda.gov

Can foods

Keywords: C91, D12, Q18, Q16 New plant engineering techniques (NPETs), Gene editing (GE), Consumer information, Willingness new plant engineering techniques (NPETs), gene editing (GE), consumer information, willingness to pay, food innovation, industrial organization, apple C91, D12, Q18, Q16

come

Introduction

New Plant Engineering Techniques (NPETs), such as gene editing (GE), are a group of recent biotechnologies allowing to accurately target deoxyribonucleic acid (DNA) manipulation of various organisms at a relatively low cost by silencing, suppressing, adding, or altering genetic material without introducing foreign genes. 1 Various applications of those techniques already exist and many others are actively explored for their promising potential in human and animal medicine, as well as in agriculture (Erpen-Dalla Corte et al., 2019; Herrero et al. 2020; NAS, 2016; Ormond et al., 2017; Qaim, 2020; and Zhao et al. 2019). For example, in horticulture, GE and other NPETs have path-breaking potential to alter fruits and vegetables by improving the strength of their production, by increasing their resistance to biotic stresses, and by favoring their appearance and/or their nutritional quality (e.g. improved starch content in potatoes or higher lycopene content in tomatoes, Erpen-Dalla Corte et al., 2019). For arable crops like cereals or legumes, NPETs are essential for strengthening plants' characteristics to endure prolonged droughts or bypassing pesticides resistance, acute problems likely to cripple yields and ultimately supply security. Animal applications are addressed in Zhao et al. (2019).

However, this potential revolution in agricultural and food production innovation may be facing major headwind, especially in countries where a significant proportion of consumers are reluctant to purchase "anything produced with biotechnologies." 2 Under this considerable uncertainty in the marketplace, several questions are paramount and require answers. Will consumers and policymakers treat NPETs-based novel foods the way they had treated GMOs? What are the consequences for R&D investments relying on GE or other NPETs and producer strategies in terms of innovations' adoption, as well as the potential social benefits resulting from these innovations? Will such innovations be speeded up by increasing problems with many diseases and pests, such as the Fusarium fungus affecting Cavendish bananas (Crop Biotech Update, 2021), and the ringspot virus, which has whipped 1 NPETs also include other techniques such as RNA interference (RNAi) used to silence or suppress specific gene function in plants in a targeted way. These techniques do not rely on the traditional gene splicing of older Genetically Modified Organisms (GMOs). The framework applies to most NPETs although we focus on gene editing in the application. 2 Policymakers and regulatory delays could also be a major impediment in many countries, especially those in which GMOs faced very stringent and slow regulatory approvals and countries treating NPETs as traditional GMOs (Purnhagen and Wesseler, 2020).

out traditional papayas in Hawaii (Gonsalves et al., 2007)? The papaya case represents a tangible case of the collapse of a conventional crop leading to greater consumer acceptance of GMO-based food innovation (the resistant papaya). Environmental issues such as climate change or water scarcity could also facilitate these innovations.

Our paper provides answers to the above questions and contributes to the current debate on new biotechnologies by studying the link between consumers' preferences and firms' incentives for R&D of new foods through GE and other NPETs, or through conventional hybridization methods. We analyze the social value of food innovations utilizing a simple Industrial Organization (IO) model that combines the cost of food innovations (with different technologies, NPETs or traditional hybridization) with consumers' willingness to pay (WTP) for those innovations. Our analysis relies on three main components. First, the WTP is conditioned on the level of acceptance or rejection of the technology used to innovate. The framework highlights the role of consumer acceptance of technology and their information levels regarding the technology underlying the novel food. Consumer acceptance or reluctance implies a potential cost of ignorance and regret if consumers are not informed on the technology embodied in the new food before they buy it. Second, the model accounts for the uncertain and costly nature of R&D processes for traditional hybridization and NPETs. The model allows identifying each preferred technology (NPETs or traditional hybridization) that emerges under varying assumptions and their respective economic welfare outcomes. Third, the framework is also suitable for analyzing a collapse scenario in which the existing conventional food item (the default option for consumers) disappears and must be replaced by the new food. Consumers can no longer revert to the conventional food, making the new food the unique choice available to consumers. Welfare implications of such a collapse scenario are evaluated.

We follow with an application of the model to a case study of a hypothetical development and introduction of new apple varieties into the market. The application builds upon the results of two experimental surveys of consumers' preferences in France and the US for novel apples, relative to conventional apples (Marette et al., 2021). The experiments use hypothetical and fictitious choices in a lab and different technology messages (on traditional hybridization and GE as representative case of NPETs), to estimate the WTP3 of 162 French and 166 US consumers for new apples, which do not brown upon being sliced or cut. 4 Messages center on the social and private benefits of having the new apples relative to conventional ones.

In these surveys, consumers in France and the US exhibit similar preferences with respect to biotechnology. Many, but not all consumers, in both countries discount the apple improvement obtained through GE techniques, relative to traditional hybridization-based innovation. However, there is a significant group of consumers knowingly accepting the new GE apple. This group of accepting consumers is relatively larger in the US than in France, strongly suggesting that the acceptance of GE foods is possible in a significant segment of the population (at least in some countries).

Based on these consumers' WTPs, we derive the demand for the new apples and associated consumer surplus, as well as ex ante (e.g., before the actual introduction of the new variety of the good) estimates for the welfare impacts of GE apples onto the market, by taking into account both R&D cost of innovation and probability of innovation success. Our simulations suggest that GE may be socially beneficial if full information on the technology is provided to consumers and if the probability of success under GE is significantly higher than under the traditional hybridization. In the case of partial or no information, consumers discounting the GE apples would buy them unknowingly, experiencing regret losses relative to their true valuation of the GE apples. Thus, in this context, traditional hybridization remains the socially optimal innovation technique.

Our paper provides several contributions to the literature evaluating WTP for novel foods based on NPETs techniques and their emergence. First, recent studies identify significant discounting of GE and other NPETs foods by consumers compared to conventional foods, which is reminiscent of past reluctance to GMO food (Bunge and Dockser Markus, 2018; Caputo et al., 2020; De Marchi et al., 2019 and 2020; Edenbrandt et al., 2018; Hudson et al., 2015; Lin et al., 2019; Marette et al., 2021; Muringai et al., 2019; Shew et al., 2018; and Yunes et al., 2019). See Bredahl, 1999; and Lusk, 2011 for earlier studies on attitudes towards GMOs. We go one-step further by providing a conceptual framework to analyse the social desirability, thus value, of NPETs-based food innovations and their potential emergence and success in the marketplace.

Second, the application to apples leverages the recently elicited WTPs into the proposed framework. A welfare analysis uses the WTPs to calibrate the model of food innovations under competing technologies (traditional hybridization, GE as representative of NPETs). The approach accounts for the fixed cost of R&D and the probability of innovation success under both technologies.

The proposed framework is applicable to other food novelties that could emerge with similar technologies or other disruptive technologies contributing to a sustainable food supply (see Herrero et al., 2020, for a list of these technologies).

Third, we analyse the situation of a potential agronomic collapse of conventional foods to evaluate if the emergence of NPETs-based foods can be facilitated under this extreme case scenario.

We draw some ex ante policy implications, before any actual realized outcomes. This inclusion of probabilities of innovation and a collapse case scenario is new and differs from previous contributions to the literature on experimental methods (Lusk et al., 2005a; Lusk and Marette, 2010; Rousu et al., 2007; and Rousu et al., 2014). In those papers, the introduction of new goods is certain and the innovation "predictable" and effectively existing, while our paper introduces R&D uncertainty and sunk costs into the analysis.

The remainder of the paper is organized as follows. Section 2 discusses new genetic technologies for food innovations in agriculture, as a potential solution for addressing risks related to complete collapses (or disappearance) of conventional food crops. Section 3 develops the simple IO model of R&D investment combined with the consumer demand for the new food varieties and consumer surpluses leading to the welfare analysis. Section 4 presents the application of the model to apples and summarizes the hypothetical experiments' results used to derive the consumer demands and welfare valuations. The main results of the application follow and the extension to the collapse of conventional apples is also studied. In the conclusions, we discuss potential extensions of our research approach and some implications for regulatory policies.

NPETs technologies for food

In this paper, we focus on the case of quality enhancement of food brought about by NPETs and rely on a hypothetical case of improved apples. The innovation consists in editing the genetic sequence of the apple to neutralize or delete the gene responsible for browning. More specifically, we refer to the CRISPR-Cas9 technique, 5 which has become an engineering tool that makes it easier and more precise to modify DNA sequences. This process clearly differs from traditional GMOs since no external gene is introduced in the new good.

Beyond the hypothetical cases, the actual commercialization of new fruits and vegetables based on GE or other NPETs is limited. Non-browning mushrooms obtained with GE and non-browning potatoes obtained with RNAis have been patented but not yet commercialized (Jalaluddin, et al., 2019).

Currently only the Arctic© apple and the Simplot Innate® potatoes are sold in Canada and the US on a limited basis and with caution. 6 Innovations and varietal improvement in agriculture are slow and costly processes. For example, it takes around 20 years of R&D for getting a new apple variety. Besides, consumers may react negatively to innovations (Glenna et al., 2007). Consequently, producers and private innovators often prefer newly augmented traditional methods, such as the Marker Assisted Selection (MAS) that combines genetic knowledge and classical hybridization into so-called selective breeding, even if such techniques remain quite expensive (Wannemuehler et al., 2019). GE and other NPETs innovations in food are mainly driven by public research institutes or by marketing orders with checkoff program 5 CRISPR stands for Clustered Regularly Interspaced Short Palindromic Repeats. The Nobel Prize in Chemistry 2020 was awarded jointly to E. Charpentier and J.A. Doudna for the development of this new and promising method for genome editing. 6 In 2019, production of Arctic apples reached 4000 short tons for the U.S. market (mostly for expanded sales in foodservice). In 2020, production increased to 6500 tons. In retail, there were three sizes of bags with pre-cut apples (10oz, 5oz, and 2oz) available for sale and two varieties (Arctic Golden and Arctic Granny).

funding agricultural research, or with public involvement like the one led by Washington State University for designing new apples. These public organizations of R&D potentially mitigate the reluctance of innovators and producers by maintaining conditions under which new goods could emerge. This is important because of crops' agronomic fragility, pesticide resistance and outbreaks, and even collapse of the conventional variety of the good. Biotechnology appears as potential solution for preventing these risks (Crop Biotech Update, 2021; Le Page, 2019; and NAS, 2016). Examples of major outbreaks include cocoa with the swollen-shoot virus, tomatoes with the brown rugose virus, and bananas with the Fusarium fungal disease (Tropical Race 4). Regarding papayas, a GMO variety was introduced over twenty years ago and saved the entire Hawaiian industry from the ringspot virus (Gonsalves et al., 2007). Now the GMO papaya is ubiquitous and fully accepted by consumers in Hawaii. The papaya case motivates the analysis of a collapse scenario.

NPETs can appear as an important revolution in the field of fruit and vegetables for improving the strength of their production and/or the quality of goods including the context of possible collapse.

However, this public R&D should also consider the potential reluctance of many consumers for new goods created with GE and other NPETsas in the past for GMOs. Consumers' acceptance influencing private and social profits could be estimated ex ante via experiments, namely before the actual introduction of a food on a market.

An IO model integrating experimental results

We develop a simplified model incorporating IO considerations and consumers' valuation of novel foods. Our model accounts for the probability of having new goods resulting from R&D investments. This is consistent with a benevolent regulator deciding how to invest in R&D. The proposed model allows for a simplified estimation of potential market effects with one or two goods, which is a proxy for market adjustments with many imperfect substitutes. For simplicity, we consider decisions based on welfare measures focusing on surpluses of consumers and public investment decisions in R&D to maximize consumer welfare. Extensions to the basic model are proposed in the subsections 4.5 and 4.6 and in Appendix C.

A three-stage game

The market equilibrium is determined as a 3-stage game summarized in Figure 1. The equilibrium is solved by backward induction (i.e., subgame Nash equilibrium). Assumptions of the game are detailed in Figure 1.

Figure 1. Stages of the IO model

In Stage 1, the benevolent regulator in charge of innovation decides whether to choose one type of innovation, namely hybrid or NPETs, denoted by N={HY, NPETs}. If the innovation is selected, the economy incurs a sunk expenditure FN, associated with the R&D investment, leading to a probability 𝜆 𝑁 of getting the new good as revealed in Stage 2. The innovation does not emerge with a probability

(1 -𝜆 𝑁 ). Traditional hybridization is characterized by FHY and 𝜆 𝐻𝑌 , and NPETs is characterized by FNPETs and 𝜆 𝑁𝑃𝐸𝑇𝑠 . It is assumed that FNPETs > FHY and 𝜆 𝑁𝑃𝐸𝑇𝑠 > 𝜆 𝐻𝑌 , which means that sunk costs and probabilities of innovation are positively correlated. 7 Sunk costs are incurred when investments are made in the first stage and cannot be recovered (Sutton, 1991). To select the innovation, the regulator considers expected welfare defined by the sum of consumers' surpluses minus the sunk costs of R&D.8

In Stage 2, the outcome of the innovation investment previously decided in Stage 1 becomes known. If the innovation is successful, with a probability of success 𝜆 𝑁 , new goods (hybrid or NPETS) are offered on the market. Conversely, if the innovation fails, with a probability (1 -𝜆 𝑁 ), only the conventional goods are sold on the market.

In Stage 3, the exchanges occur. Consumers know the characteristics of the sold good(s), except for the information about the type of innovation. Two cases are considered. First, consumers are fully informed about the underlying technology. Second, they are not or only partially informed on the technology and face costs of ignorance and regret. Market prices of goods are exogenously given for simplicity.

We now turn to equilibria at different stages, by starting, according to the backward induction principle, with Stage 3 and the way consumers' demand is determined.

Stage 3: Demands and surpluses under different configurations

Consumers' demands depend on the estimations of their surpluses that relate to their WTP. To convert consumers' WTP into demand curves, we assume that each consumer purchases one unit, providing the largest surplus approximated by the difference between WTP and the market price (Roosen and Marette, 2011; Rousu et al., 2014). Choices can be real or inferred, and hypothetical, depending on the type of survey and goods being considered.9

For the estimation of purchases in Stage 3, the available goods sold on the market are given and depend on the innovation investment made in Stage 1 and its realization in Stage 2. Consumers individually choose either, to purchase or not to purchase one unit of the goods, without mixing the two types of goods if both conventional and new goods are offered. The unit of the conventional good is sold at a price P (observed or relevant at the time of the experiment/survey) and the new good is assumed to be sold at the same price PN = P, for simplicity. The WTP for the new good is denoted by 𝑊𝑇𝑃 𝑁 𝑘 𝑚 and the WTP for the conventional good is denoted 𝑊𝑇𝑃 𝐶 𝑘 𝑚 for an informational message m on the technology and a consumer k. Informational messages m cover the technologies {HY, NPETs} and the case of no information provided on the technology.

Without innovation investment in Stage 1, or if the innovation fails to provide the new goods in Stage 2, the consumer k (with k=1,…,K) can choose between two outcomes in Stage 3: conventional good and none, with a utility normalized to zero. This case corresponds to the reference baseline of any experiment. Consumer k chooses a single unit of the conventional good, when this good brings a positive surplus, given by the difference between the WTP and the market price (and no good otherwise). Thus, the consumer surplus (SC) leading to the purchasing decision of a good is given by

𝑆𝐶 𝐶 𝑘 0 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐶 𝑘 0 -𝑃, 0} . (1)
There is no information to be revealed since no new technology appeared.

With innovation investment in Stage 1, and if this innovation is successful in Stage 2, the consumer can choose between three outcomes in Stage 3: new good, conventional good and none. For a message m on the novelty component, consumer k chooses the purchasing alternative that generates the highest utility; her surplus becomes

𝑀𝑎𝑥{𝑊𝑇𝑃 𝐶 𝑘 𝑚 -𝑃, 𝑊𝑇𝑃 𝑁 𝑘 𝑚 -𝑃, 0} . (2)
The new good is selected if 𝑊𝑇𝑃 𝑁 𝑘 𝑚 -𝑃 ≥ 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐶 𝑘 𝑚 -𝑃, 0}, and not selected otherwise, for turning to the other options depending on the comparison between 0 and 𝑊𝑇𝑃 𝐶 𝑘 𝑚 -𝑃.

Two subcases can be considered here: i) with full information about the innovation technology and ii) without (or just partial) information about the technology. Under the first configuration, the consumer is fully informed on the innovation process and there is no ignorance cost or regret effect.

Thus, the surplus for consumer k is described by equation ( 2) with a valuation for each technology (HY and NPETs) and with their respective "full-information" messages. Directly from equation (2), we derive consumer surplus under the full information message (denoted by the superscript fi)

𝑆𝐶 𝐻𝑌 𝑘 𝑓𝑖 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐶 𝑘 𝑓𝑖 -𝑃, 𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑓𝑖 -𝑃, 0} (3a)
and

𝑆𝐶 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑓𝑖 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐶 𝑘 𝑓𝑖 -𝑃, 𝑊𝑇𝑃 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑓𝑖 -𝑃, 0}. (3b)
The second configuration with no (or only partial) information about the type of innovation technology leads to a decision based on equation ( 2) that subsequently the consumer could regret once that full information is revealed on the technology. Some consumers would make different decisions with the full information provided ex ante. 10 Therefore, the costly ignorance effect linked to the lack of full technology information needs to be accounted for by a benevolent regulator in the computation of the "complete" surplus. For a consumer purchasing a specific good, the effect of ignorance is given by the WTP for the good with full information minus the WTP related to the purchase. This allows to measure the difference between the "ideal" choice under full information and the "actual" choice without (or partial) information.

If goods sold are generated by hybrid methods, the complete consumer surplus accounting the absence of information about the technology (denoted by the superscript ni) along with the potential cost of ignorance after information revelation is

𝑆𝐶 𝐻𝑌 𝑘 𝑛𝑖 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐶 𝑘 𝑛𝑖 -𝑃, 𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑛𝑖 -𝑃, 0} + 𝐽 𝐶 𝑘 [𝑊𝑇𝑃 𝐶 𝑘 𝑓𝑖 -𝑊𝑇𝑃 𝐶 𝑘 𝑛𝑖 ] + 𝐽 𝐻𝑌 𝑘 [𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑓𝑖 -𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑛𝑖 ], (4)
where 𝐽 𝐶 𝑘 (respectively 𝐽 𝐻𝑌 𝑘 ) is an indicator variable related to the effect of ignorance, taking the value of 1 if consumer k is predicted to have chosen the conventional (respectively new hybrid) good in the absence of information.

If goods sold are NPETs-generated goods and following the previous notation, the complete consumer surplus under no technology information and accounting for the potential cost of ignorance ) for hybrid-and NPETs-generated goods under no (or partial) technology information.

Stage 1: Choice of investment in R&D and expected welfare

The innovation investment in Stage 1 is decided based on expectations of events and market equilibria related to Stages 2 and 3. Stage 2 determines the realization of the investment resulting in a new good.

For innovation investments N={HY,NPETs}, the innovation agency has a probability 𝜆 𝑁 to get the innovative good leading to a welfare with new goods, and the innovation does not emerge with a probability (1 -𝜆 𝑁 ) leading to the welfare without innovation. Sunk expenditures FN are associated with R&D investments and the authorization of new goods. They are incurred by the innovation agency and withdrawn from the welfare of consumers.

Under full information about technology and if the regulator chooses to invest with the technology N={HY,NPETs}, the expected welfare takes into account the probabilities 𝜆 𝑁 and (1 -𝜆 𝑁 ). For the hybrid investment, the overall expected welfare (W) summed over all the consumers with their average consumption is given by

𝑊 𝐻𝑌 𝑓𝑖 = [𝜆 𝐻𝑌 𝐸(𝑆𝐶 𝐻𝑌 𝑓𝑖 ) + (1 -𝜆 𝐻𝑌 ) × 𝐸(𝑆𝐶 𝐶 0 )] × 𝐸𝑋𝑇 -𝐹 𝐻𝑌 , (6)
with EXT being an extrapolation parameter equal to the number of consumers multiplied by expected average consumption over a year. For the NPETs investment, the overall expected welfare is

𝑊 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 = [𝜆 𝑁𝑃𝐸𝑇𝑠 𝐸(𝑆𝐶 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 ) + (1 -𝜆 𝑁𝑃𝐸𝑇𝑠 ) × 𝐸(𝑆𝐶 𝐶 0 )] × 𝐸𝑋𝑇 -𝐹 𝑁𝑃𝐸𝑇𝑠 . (7)
In the absence of information about technology, the corresponding welfare measures are

𝑊 𝐻𝑌 𝑛𝑖 = [𝜆 𝐻𝑌 𝐸(𝑆𝐶 𝐻𝑌 𝑛𝑖 ) + (1 -𝜆 𝐻𝑌 ) × 𝐸(𝑆𝐶 𝐶 0 )] × 𝐸𝑋𝑇 -𝐹 𝐻𝑌 , (8)
and

𝑊 𝑁𝑃𝐸𝑇𝑠 𝑛𝑖 = [𝜆 𝑁𝑃𝐸𝑇𝑠 𝐸(𝑆𝐶 𝑁𝑃𝐸𝑇𝑠 𝑛𝑖 ) + (1 -𝜆 𝑁𝑃𝐸𝑇𝑠 ) × 𝐸(𝑆𝐶 𝐶 0 )] × 𝐸𝑋𝑇 -𝐹 𝑁𝑃𝐸𝑇𝑠 . (9)
Finally, without any innovative investment and any new good, the expected welfare with conventional goods only is

𝑊 𝐶 0 = [𝐸(𝑆𝐶 𝐶 0 )] × 𝐸𝑋𝑇.
For a given context of information (fi, ni,0), the comparison of ex ante welfares determines the regulator choice. For instance, for the case under full information, the regulator chooses the strategy resulting from 𝑀𝑎𝑥{𝑊 𝐻𝑌 𝑓𝑖 , 𝑊 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 , 𝑊 𝐶 0 } , which depends on surpluses and parameter values.

Interestingly, the welfares comparison may lead to inequalities helping to define optimal strategies.

The inequality 𝑊 𝐻𝑌 𝑓𝑖 > 𝑊 𝐶 0 is equivalent to 𝜑 𝐻𝑌 < 𝜆 𝐻𝑌 [𝐸(𝑆𝐶 𝐻𝑌 𝑓𝑖 ) -𝐸(𝑆𝐶 𝐶 0 )] , with 𝜑 𝐻𝑌 = 𝐹 𝐻𝑌 / 𝐸𝑋𝑇, being the sunk cost per unit of sold good. In other words, this is a sunk cost by sold unit without being passed onto consumers into the market price. The same parameter will be used for 𝜑 𝑁𝑃𝐸𝑇𝑠 = 𝐹 𝑁𝑃𝐸𝑇𝑠 /𝐸𝑋𝑇. The relevant inequalities will conduct to the determination of the optimal policy, now applied to the apple case.

Application to apples

Summary of the apple experiments

We now apply the framework to a case study of novel apples. We first summarize the results from two recent experiments on WTP for apples under different technology messages (Marette et al., 2021). 11 We then expand and build upon these results by deriving consumer demands and performing a welfare analysis of the potential emergence of the new apple innovation.

These hypothetical experiments were undertaken in France (Dijon) in December 2019 and the US Midwest (Ames, IA) in early March 2020. The number of surveyed consumers was equal to 162 in France, and 166 in the US. Successive rounds of WTP elicitation were conducted (see Figure A1 in Appendix A). An initial round (the baseline) focused on the conventional apples without informative message (message #0). Then, both conventional and new apples were presented in following rounds and consumers were asked to value conventional and new apples with improved attributes (nonbrowning and reduced bruising) under three different messages. These messages were as follows:

-The first message mentioned the innovation slowing the browning process without specifying the technology generating the innovation (corresponding to message ni);

-The second message delivered full information and specified traditional hybridization as the underlying technology (message fi for hybrid technology);

-The third message also provided full information and indicated gene editing (GE) as the source of the innovation (a specific case of NPETs) (message fi for GE). 12 Pictures of goods were presented, and no specific apple variety reference was indicated. A multiple-price list (payment card) was used for eliciting WTP of consumers for 1kg of apples in France and 1 pound in the US, for both conventional and new apples. During each round, consumers were asked to choose whether (or not) they will buy the good for prices varying from €1.60 to €3.30 for 1 kg of apples in France and from $0.70 to $2.40 for 1 pound in the US (the quantity gap is justified by differences in consumption habits between these two countries). For each round and each good, the WTP was determined by taking the highest price consumers were willing to pay (namely, the highest "Yes" checked off in the list). If a consumer never replied "yes" to each line of the multiple-price list, the selected WTP was supposed to equal 0.

These rounds of information lead to WTPs for new apples denoted by 𝑊𝑇𝑃 𝑁 𝑘 𝑚 (N=HY, GE), and for conventional apples denoted 𝑊𝑇𝑃 𝐶 𝑘 𝑚 for an informational message m={0, ni, fi for HY, fi for GE} and consumer k.

Experiment results show strong heterogeneity in consumers' WTP for both the conventional and new apples in both countries. To highlight this heterogeneity and compare the two countries, we normalize the WTP expressed by a consumer for the new good by the WTP he expressed for the conventional one for a given message. For an informational message m and a consumer k, the ratio is thus (𝑊𝑇𝑃 𝑁 𝑘 𝑚 /𝑊𝑇𝑃 𝐶 𝑘 𝑚 )x100. Figure 2 presents the unitless ratios for informational message ni (only mentioning the benefits from the new good but not the underlying technology) and message fi for GE (detailing the GE innovation as a specific case of NPETs). We abstract from the ratios for the traditional hybridization (with message fi for HY) because they were nearly similar to those under message ni. The graph on the left presents results for France, while the graph on the right reports results for the US. In each graph, observations related to consumers are on the X-axis, and ratios on the Yaxis. Ratios are sorted by increasing order.

For both countries and curves, three groups of consumers can be distinguished: those who do discount the innovation (left part of curves with ratios lower than 100), those who are indifferent between both goods (central part of curves with ratios equal to 100), and those who value the new nonbrowning GE good with a positive premium (right part of curves with ratios higher than 100).

The impact of full information on GE technology on consumer WTP can be seen by the comparison between the blue curve (after message ni) and the red curve (after message fi for GE). The provision of GE information leads to a significant decrease in WTP expressed for the new good. A larger number of surveyed consumers discount the innovation with a negative premium. The decrease in premia is noticeable in the US and substantial in France. This result questions the acceptance of the GE innovation by some consumers, particularly in France.

For both countries and curves, three groups of consumers can be distinguished: those who do discount the innovation (left part of curves with ratios lower than 100), those who are indifferent between both goods (central part of curves with ratios equal to 100), and those who value the new nonbrowning GE good with a positive premium (right part of curves with ratios higher than 100). The impact of full information on GE technology on consumer WTP can be seen by the comparison between the blue curve (after message ni) and the red curve (after message fi for GE). The provision of GE information leads to a significant decrease in WTP expressed for the new good. A larger number of surveyed consumers discount the innovation with a negative premium. The decrease in premia is noticeable in the US and substantial in France. This result questions the acceptance of the GE innovation by some consumers, particularly in France.

However, in both countries there is also a significant group of consumers with a positive premium (ratios higher than 100) when fully informed about the GE innovation process (the right part of the orange curves), and a priori accepting the controversial technology. This group of accepting consumers is relatively larger in the US than in France. Moreover, in the US, a few consumers give very high value to the GE innovation (extreme right of the orange curve). This group of accepting consumers is likely to make the adoption of GE possible and potentially socially desirable when full information about the GE technology is provided.

The values shown in Figure 2 become the basis for the surpluses computed in the next subsection. The heterogeneity in consumer preferences (with pro-and anti-GE) particularly matters for understanding market adjustments and consumers' surpluses.

Simulations

Some additional assumptions are necessary before conducting simulations to select the socially optimal innovations. Consumers' surpluses derived from equations (1) to ( 5) are obtained by comparing their WTP and market prices. To set prices, we rely on observed prices in supermarkets at the time of the experiments and use the average observed price 𝑃 𝐶 for the conventional apples equal to €2.10 per kg in France and $1.20 per pound in the US. 13 For simplicity, we keep assuming 𝑃 𝑁 = 𝑃 𝑐 = 𝑃 for the new good. 14 For allowing comparisons between both countries, the average surpluses for 1 kg with the French experiment are converted in a value of 1 pound (kg 1= LBs 2.2) in $, by multiplying the French average surplus by (1.10/2.20), with €1 equal to $1.10 on March 1, 2020 at the time of the second experiment. We now turn to simulations' results.

Estimated surpluses

Table 1 presents the average surpluses estimated for each country and for the different configurations as described in Stage 3 of Figure 1 and presented in equations ( 1)-( 5), with GE being the specific NPETs technology.

Table 1 shows that for each configuration, the average surpluses are higher in the US than in France. For each country, surpluses with the new apples coming from the innovations are generally higher than the surpluses under the absence of new apples, except the case with GE under no 13 These average prices are not in the middle of the price interval of the multiple-price lists for allowing higher valuations related to the innovation process. 14 Prices could be different and endogenously determined, by considering a retailer choosing a price for the new good (with the price of the conventional apple being given) based on the WTP and assuming some ability to mark prices up.

technology information (message ni in the experiment, GE apple variety). Still the situation without information about the process of innovation leads to a surplus lower than the surplus under full information for the equivalent good (messages fi for HY and fi for GE). This result comes from the cost of regret in the absence of information on technology, which is included in the total consumer surplus. The surpluses with hybrid apples are higher than the respective surpluses with GE apples, since consumers are more enthusiastic about the hybrid technology than its GE counterpart. The discounting of the GE technology implies significant regret costs under the ni message, when consumers would only learn ex post about the technology. This explains why GE without technology information (message ni) leads to a much lower surplus ($-0.11 for France and $0.34 for the US) than the configuration where only the conventional good is available in the market ($0.11 for France and $0.53 for the US). The negative surplus for France ($-0.11) is explained by the very high effect of ignorance leading to costly regrets.

In both countries, the surpluses with GE and full technology information (message fi, GE variety) are higher than those without the new good (message 0, conventional variety), but lower than the surpluses with hybrid apples (message fi, HY variety). However, the innovation with GE under information provision can be favored because of higher probability of innovation success for GE than for traditional hybridization. These probabilities are now considered in ex ante welfare analysis to understand the R&D investment decision.

Socially optimal innovation investments

We now derive ex ante welfare values in Stage 1 of the game, based on the consumers' WTP and related surpluses reported in Table 1. The comparison of ex ante per-unit welfare measures permits the selection of the socially optimal innovation strategy. We look at the potential investment choices maximizing per-unit welfares and leading to possible emergence of innovation with a probability 𝜆 𝑁 for N={HY,GE}, with 𝜆 𝐺𝐸 > 𝜆 𝐻𝑌 , meaning that GE accelerates the innovation and the likelihood of success.

We start with the configuration under no technology information, in which the social objective is given by 𝑀𝑎𝑥{𝑊 𝐻𝑌 𝑛𝑖 , 𝑊 𝐺𝐸 𝑛𝑖 , 𝑊 𝐶 0 }. The comparison of per-unit welfares leads to simulations presented in Figure 3 3 panel (a) shows that the hybrid investment is socially optimal for relatively low levels of per-unit sunk cost. For relatively high-values of per-unit of sunk cost, there is no innovation investment and no emergence of the new good. Interestingly, the optimal hybrid investment linked to one unit of apples leads to a larger area in the US compared to France, because the per-unit surpluses 15 Comparisons of welfares were performed using Mathematica software.

in Table 1 are higher in the US than in France. The sunk cost per unit of good 𝜑GE =FGE /EXT coming from the GE investment is represented on the Y-axis. On each chart, the constraints are derived from welfare comparisons for reaching max {𝑊 𝐻𝑌 𝑛𝑖 , 𝑊 𝐺𝐸 𝑛𝑖 , 𝑊 𝐶 0 }. For France, the equation 𝜑 𝐺𝐸 = 0.03 𝜆 𝐺𝐸 is given by the equality 𝑊 𝐻𝑌 𝑛𝑖 = 𝑊 𝐶 0 . For 𝑊 𝐻𝑌 𝑛𝑖 > 𝑊 𝐶 0 , the inequality 𝑊 𝐻𝑌 𝑛𝑖 > 𝑊 𝐺𝐸 𝑛𝑖 is systematically verified, and for 𝑊 𝐻𝑌 𝑛𝑖 < 𝑊 𝐶 0 , the inequality 𝑊 𝐶 0 > 𝑊 𝐺𝐸 𝑛𝑖 is systematically verified, which leads to the choices of the chart on the left. For the US, the same is observed with 𝜑 𝐺𝐸 = 0.13 𝜆 𝐺𝐸 .

This result suggests that return to innovations would be higher in the US than in France, providing larger R&D incentives in the US. This effect is amplified by the larger number of US consumers embodied in the US extrapolation parameter EXT appearing in welfare equations ( 8) and (9). For both countries, the GE investment under no technology information does not emerge, because the cost of regret undermines the positive valuation of the novel apples. As shown in Table 1, the average per-unit surplus with GE under no technology information is lower than the one without new apples and with only conventional apples, eliminating any incentive to invest with GE. except for the expected surpluses under different information contexts (see Table 1). Figure 3 panel (b) shows that, under full information, the GE investment is socially optimal for relatively low level of per-unit sunk cost 𝜑GE. As the per-unit surplus with the GE under full information is relatively high and close to the hybrid one (Table 1), the GE is socially beneficial since the probability of success is higher than the one with the hybrid investment (with 𝜆 𝐻𝑌 = 0.6 𝜆 𝐺𝐸 ). In France, the GE investment dominates the hybrid investment for these relative success probabilities. 16 Moreover, because of consumers' preferences (Table 1), the traditional hybridization is preferred in the US for medium values of the sunk cost fHY, since this sunk cost is lower than the one for GE with 𝜑HY = 0.8 𝜑GE. When the sunk costs of investments rise high enough, no investment is selected.

Beyond these simulations, the comparison of Figure 3 panels (a) and (b) shows that the emergence of GE is clearly linked to the context of information about the innovation technology.

However, information about GE-based innovation might be difficult to grasp for consumers in actual situations, because of imperfect recall, labels/messages proliferations, and the complexity of the scientific knowledge leading to misunderstandings and confusions (Yokessa and Marette, 2019). This issue is larger than novel food as most goods consumed (cars, phones, computers, online services, etc.) embody complex technologies and production processes beyond the grasp of many consumers. 16 For 𝜆 𝐻𝑌 ≥ 0.7 𝜆 𝐺𝐸 , the hybrid investment replaces the GE investment in France.

Extension with a collapse configuration

We now investigate the risk of a collapse with the possible disappearance of the conventional product.

Section 2 explored the acute issue of crop vulnerability. To account for this effect, we introduce 𝜓, the collapse probability of the conventional good following a disease, in Stage 2 of the game (see Section 3.1). The collapse does not happen with the probability (1 -𝜓). The probability 𝜓 is taken into account in Stage 1 by the benevolent regulator.17 In such case, the conventional good disappears from equations (1) to (5); while (1 -𝜓) is the probability of having the conventional good on the market as in equations ( 1) to (5) (see Appendix B for the detailed equations and Table B1 for the per-unit surpluses under this collapse case scenario).

New ex ante welfare values in Stage 1 integrating the probability of a collapse are computed based on the consumers' WTP and related per-unit surpluses (Table B1 in Appendix B). The comparison of ex ante welfare measures (B3) to (B6) in Appendix B leads to the selection of the socially-optimal strategy. The simulations are shown in Figure 4, for France and the US (under full technology information only, for simplicity). A given level of per-unit sunk-cost is assumed with 𝜑GE = $0.03. On each chart, the probability 𝜆 𝐺𝐸 of getting the GE innovation is represented on the X-axis and the probability 𝜓 of collapse of conventional apples is represented on the Y-axis.

Figure 4 shows the respective influence of both probabilities 𝜆 𝐺𝐸 and 𝜓. When the probabilities of successful innovation 𝜆 𝐺𝐸 and 𝜆 𝐻𝑌 = 0.6 𝜆 𝐺𝐸 are relatively low, the innovation investment is not selected (left side of each chart), because of low social benefits from new apples relative to the sunk cost 𝜑GE = $0.03. Conversely, a relatively high value for the probability of collapse 𝜓 (even with a low value of probabilities of innovation 𝜆 𝐺𝐸 ) leads to the selection of innovation investments. The hybrid investment is socially optimum for medium values of 𝜆 𝐺𝐸 (middle of each chart). On the other hand, for high value of 𝜆 𝐺𝐸 (right side of each chart and bounded by 𝜆 𝐺𝐸 = 1), the GE investment clearly dominates because of the likely emergence of the innovation. Thus, the GE strategy is reinforced with the risk of a collapse. Note that this important significance of the GE investment also exists under no technology information for the US with small areas, but not for France because of negative values of surplus from Tables 1 andB1 for GE under no technology information.

Extension with costly regrets limited to a subgroup of consumers

We now explore the effect of ignorance under no technology information (see equations ( 4) and ( 5)).

In our analysis, the ignorance effect integrates differences in WTP under various contexts of information provision and concerns all consumers. In the real world (e.g., in stores outside the lab) however, regrets due to the ignorance effect are likely to only be costly for very concerned consumers. 18 To address this bias that may affect our analysis and identify consumers really concerned in practice by the innovation process (natural such as traditional hybridization vs. based on biotechnologies such as GE and other NPETs), we rely on the exit questionnaire answered by surveyed consumers during the experiment. This questionnaire provides clues regarding food habits and the level of concerns in real world contexts. In particular, a strong consumption of organic fruits and vegetables is likely to indicate a significant concern regarding information about NPETs such as GE, as many of these consumers try to shun GMOs via organic choices.

From the exit questionnaire, we isolate consumers with a regular and exclusive consumption of organic fruits and vegetables and create a new dummy variable equal to 1 for those consumers (and 0 otherwise). This dummy variable is multiplied to 𝐽 𝐶 𝑘 and 𝐽 𝑁𝑃𝐸𝑇𝑠 𝑘 in 𝑆𝐶 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑛𝑖 given by equation ( 5).

In other words, the effect of ignorance really matters for those concerned consumers only, while others are indifferent to it outside the lab. Applying the new dummy variable to the US case only (and with GE as a specific case of NPETs) for simplicity, leads to an increase in the expected surplus for the GE innovation under no technology information from Table 1, with a shift from 𝐸(𝑆𝐶 𝐺𝐸 𝑛𝑖 ) = 0.34 to a new value 𝐸(𝑆𝐶 𝐺𝐸 𝑛𝑖 )′ = 0.59, reflecting the lower number of consumers really affected by regrets. This new value integrated in equation ( 5) leads to a higher acceptance of the GE technology under no technology information.

Figure 5 shows the social optimum R&D choice for the US under this new configuration.

Results reported in the left chart suggest that GE may be socially beneficial when consumers' losses from regrets are limited to a subgroup of very concerned consumers, and when the probability of success with the GE is significantly higher than the one for traditional hybridization (𝜆 𝐻𝑌 =0.3 𝜆 𝐺𝐸 ),

and for low values of the sunk cost. However when the probability of success of hybrids gets closer to that of GE (right chart, with 𝜆 𝐻𝑌 =0.6𝜆 𝐺𝐸 ), GE does not emerge as socially optimal as it was already the case in Figure 3 panel (a).

We consider further extensions in Appendix C, extrapolating our results to the whole country.

We also discuss how to incorporate a supply chain with seedlings, apple producers, and retailers. In addition, prices for novel apples could be endogenized. Some dynamic elements could also be considered with multiple periods and consumers becoming more accepting of biotechnology as in the papaya case. The model could be extended to international trade with the associated regulatory issues for biotech goods to cross borders.

Conclusions

In this paper, we emphasized the important role of consumers' preferences, along with R&D spending, and uncertainty in the resulting success of innovative foods in the marketplace. We developed and utilized a simple IO model for R&D investment in food innovations based on NPETs and traditional hybridization methods, to identify which technology emerges under various parameter characterizations and associated economic welfare outcomes. Our simulations show that information delivered to consumers matters for determining social benefit outcomes resulting from innovations based on NPETs and hybridization. Performed simulations also suggest that NPETs, such as GE, may be socially beneficial when consumers are informed about the technology, or when they experience limited regret losses (thus, when not informed, before their purchases take place). Otherwise, the innovation based on traditional hybridization is socially optimal, which is particularly true when the values of the probabilities of success under NPETs and hybridization are relatively similar. Finally, the reluctance for NPETs-based novel foods by some consumers makes the adoption of this technology uncertain, particularly in France.

We further explore a series of potential and easily implementable extensions, in Appendix C, to flesh out the developed and utilized approach beyond the essence of consumers' WTP, sunk cost of R&D processes, technology information and probabilities of success of those technologies. The collapse may (or not) occur in Stage 2 of the game (see section 4.5). In Stage 1, the regulator anticipates the risk of collapse by integrating the probability 𝜓 with the surplus detailed in the previous paragraph, and the absence of collapse by integrating the probability (1 -𝜓) with the related surplus detailed in equations (1) to (5). The regulator also accounts for the probability of innovation success (𝜆 𝑁 ) and the probability of innovation failure (1-𝜆 𝑁 ), depending on the type of investment (see sections 3.1 and 3.2). Thus, the expected welfare measures computed in Stage 1 integrate the probability of different events.

Under full information and for the hybrid investment, the overall expected welfare of the economy is given by

𝑊 ̅ 𝐻𝑌 𝑓𝑖 = (1 -𝜓)[𝜆 𝐻𝑌 𝐸(𝑆𝐶 𝐻𝑌 𝑓𝑖 ) + (1 -𝜆 𝐻𝑌 ) × 𝐸(𝑆𝐶 0 )] × 𝐸𝑋𝑇 + 𝜓𝜆 𝐻𝑌 𝐸(𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑓𝑖 ) × 𝐸𝑋𝑇 -𝐹 𝐻𝑌 , (

Results from the experiment with apples

The simulations under the collapse case based on the experiment with apples lead to the results reported in Table B1, with GE being the specific NPETs technology (as indicated in the subscripts). These per-unit surpluses under the collapse case and the ones detailed in Table 1 under the absence of collapse are integrated in welfare equations (B3) to (B6), leading to Figure 4.

helping and refining the classical technique of plant hybridization. These alternative techniques could be also taken into account in the analysis with new and specific probabilities 𝜆 𝑁 of getting new goods.

A meta-analysis isolating the WTP for different foods generated with various technologies (Lusk et al, 2005b) may also be used for replicating consumers' attitudes toward new foods, when R&D programs are launched. Other technologies of interest are mentioned in Herrero et al. (2020). (8) The configuration with or without information about the technology could be endogenous, meaning that the regulator decides whether or not to perfectly inform consumers about the process of innovation, namely traditional hybridization or NPETs, by incurring additional cost, entailing a campaign of information and/or a label. 20 These costs could be taken into account in a cost-benefit analysis accounting for R&D and markets adjustments.

(9) Additionally, the sunk costs FNPETs and FHY and the probabilities 𝜆 𝑁𝑃𝐸𝑇𝑠 and 𝜆 𝐻𝑌 could be evaluated with interviews, questionnaires and financial analyses. Their evaluations could increase the credibility of any ex ante analysis searching to define the social benefit related to new food innovations.

(10) In the model, we only focused on a per-country situation, similar to a quasi-autarky situation. However, countries may import/export with the sensitive question of the new goods authorization. Trade could be a powerful way to boost success probabilities by benefiting from more sales, lower prices coming from competition and foreign R&D investments increasing the diversity of goods. The international regulatory aspects regarding new and innovative goods appear as an important 20 According to the FDA Labeling Cost Model, administrative costs (in 2017 dollars) per UPC for minor, major and extensive labeling changes range from $341 to $2,971, $776 to $5,993, and $1,039 to $7,632, respectively. The fixed costs (documentation and generation of records) associated with labeling range from $35 to $113 per UPC. In addition, costs of printing and applying new labels may be incurred and range from $288 to $814 per UPC. Finally, administrative and signage costs to grocery stores (retail display sign costs) range from $20 to $200 per sign. Coordinating a regulatory mandated label change with changes that are already occurring for other business reasons (e.g. change in marketing or need to restock label supply) can dramatically lower costs. Firms only incur additional printing costs if the regulatory mandate requires acceleration of printing and/or the disposal of existing label stock. (RTI International, 2015).

question.

Figure 2 .

 2 Figure 2. WTP expressed for the new GE apples relative to the WTP expressed for the conventional apples.

  panel (a), with the French configuration presented on the left chart and the US configuration presented on the right chart. On both charts, the probability 𝜆 𝐺𝐸 of getting the GE innovation is represented on the X-axis. The sunk cost per unit of sold good for the GE investment, 𝜑 𝐺𝐸 = 𝐹 𝐺𝐸 /𝐸𝑋𝑇, expressed in $, is represented on the Y-axis. Specific parameter values (𝜆 𝐻𝑌 = 0.6 𝜆 𝐺𝐸 , 𝜑HY = 0.8 𝜑GE) are used both for France and the US. The parameters related to the hybrid technology are implicitly represented, since in the simulations, 𝜑HY = b𝜑GE and 𝜆 𝐻𝑌 = 𝑟 𝜆 𝐺𝐸 , with r,b<1.15

Figure

  Figure 3 panel (a) shows that the hybrid investment is socially optimal for relatively low levels

Figure 3 .

 3 Figure 3. Social choices maximizing the per-unit welfare in France and in the US

Figure 3

 3 Figure 3 panel (b) reports the simulations coming from a configuration under full information

Figure 4 .

 4 Figure 4. Risk of collapse and socially optimal choices in France and in the US

Figure 5 .

 5 Figure 5. Social choices maximizing the per-unit welfare in the US under no technology information

  B3)with the expectation E(.) and EXT being an extrapolation parameter equal to the number of consumers multiplied by average consumption over a year.Under full information and for the NPETs investment, the overall expected welfare of the economy is given by𝑊 ̅ 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 = (1 -𝜓)[𝜆 𝑁𝑃𝐸𝑇𝑠 𝐸(𝑆𝐶 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 ) + (1 -𝜆 𝑁𝑃𝐸𝑇𝑠 ) × 𝐸(𝑆𝐶 0 )] × 𝐸𝑋𝑇 + 𝜓𝜆 𝐻𝑌 𝐸(𝑆𝐶 ̅̅̅̅ 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 ) × 𝐸𝑋𝑇 -𝐹 𝑁𝑃𝐸𝑇𝑠 .(B4)The corresponding welfare measures for the hybrid and NPETS investment under no technology information are as follows𝑊 ̅ 𝐻𝑌 𝑛𝑖 = (1 -𝜓)[𝜆 𝐻𝑌 𝐸(𝑆𝐶 𝐻𝑌 𝑛𝑖 ) + (1 -𝜆 𝐻𝑌 ) × 𝐸(𝑆𝐶 0 )] × 𝐸𝑋𝑇+𝜓𝜆 𝐻𝑌 𝐸(𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑝𝑖 ) × 𝐸𝑋𝑇 -𝐹 𝐻𝑌 , investment and without any new good, the expected welfare with conventional goods only is 𝑊 ̅ 𝐶 0 = (1 -𝜓)[𝐸(𝑆𝐶 0 )] × 𝐸𝑋𝑇.

( 7 )

 7 The regulator may simultaneously promote both technologies for boosting chances of innovation. One solution would consist of having classical hybridization in one research center and NPETs in another research center. If both programs are simultaneously decided and launched, the probability of innovation would be 𝜆 𝐻𝑌 𝜆 𝑁𝑃𝐸𝑇𝑠 + (1 -𝜆 𝑁𝑃𝐸𝑇𝑠 )𝜆 𝐻𝑌 + (1 -𝜆 𝐻𝑌 )𝜆 𝑁𝑃𝐸𝑇𝑠 .

Table 1 . Average surplus for one pound of apples in US$ under the different configurations

 1

	France

  Noteworthy, we look at a collapse scenario by altering the choice set for consumers in which the conventional food is no longer available, Despite limitations resulting from stylized WTP elicitations and IO approaches, our methodology can be replicated for R&D related to all sorts of food novelties and other potentially disruptive technologies as pointed out byHerrero et al. (2020). The case of apples demonstrates the feasibility of the approach and suggests it could be applied in varying configurations. The consumers' acceptance influencing private and social profits could be estimated ex ante via experiments before the effective introduction of a novel food on a market. Welfare estimates would help to guide public debates about the future of foods generated by new and sometimes controversial technologies. 𝐽 𝐻𝑌 𝑘 is an indicator variable related to the effect of ignorance, taking the value of 1 if consumer k is predicted to have chosen new hybrid good after the message with no technology information (denoted by the superscript ni). If goods sold are NPETs-generated goods and following the previous 𝐽 𝑁𝑃𝐸𝑇𝑠 𝑘 is an indicator variable related to the effect of ignorance, taking the value of 1 if consumer k is predicted to have chosen NPETs-generated good after the message with no technology information (denoted by the superscript ni).

		𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑘 𝑛𝑖 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑛𝑖 -𝑃, 0} + 𝐽 𝐻𝑌 𝑘 [𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑓𝑖 -𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑛𝑖 ],		(B1)
	where notation, the complete surplus becomes
	𝑆𝐶 ̅̅̅̅ 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑛𝑖	= 𝑀𝑎𝑥{𝑊𝑇𝑃 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑛𝑖	-𝑃, 0} + 𝐽 𝑁𝑃𝐸𝑇𝑠 𝑘 [𝑊𝑇𝑃 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑓𝑖	-𝑊𝑇𝑃 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑛𝑖	] ,	(B2)
	where

Table B1 . Average surplus for one pound of apples in US$ under the collapse case with no conventional apples on the market

 B1

		France
	Configuration: no apples	𝐸(𝑆𝐶) = 0
	Configuration: only new apples (after the innovation success)
		Hybrid variety	GE variety
	No information (message ni) Full information (message fi)	𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑛𝑖 = 0.15 𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑓𝑖 = 0.17	𝑛𝑖 = -0.15 𝑆𝐶 ̅̅̅̅ 𝐺𝐸 𝑆𝐶 ̅̅̅̅ 𝐺𝐸 𝑓𝑖 = 0.11
		The US
	Configuration: no apples	𝐸(𝑆𝐶) = 0
	Configuration: only new apples (after the innovation success)
		Hybrid variety	GE variety
	No information (message ni) Full information (message fi)	𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑛𝑖 = 0.69 𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑓𝑖 = 0.70	𝑛𝑖 = 0.30 𝑆𝐶 ̅̅̅̅ 𝐺𝐸 𝑆𝐶 ̅̅̅̅ 𝐺𝐸 𝑓𝑖 = 0.52

Even if hypothetical WTP are likely to be upward biased, some contributions downplay risks of biases for marginal WTP related to a quality characteristic or the impact of additional information. By comparing hypothetical and nonhypothetical responses,[START_REF] Lusk | Are Choice Experiments Incentive Compatible: A Test with Quality Differentiated Beef Steaks[END_REF] showed that marginal WTP for a change in quality/characteristic is, in general, not statistically different across hypothetical and real (consequential) payment settings.

 4 The fictitious situation is inspired by the Artic© apple, which uses RNAi rather than GE to suppress the gene responsible for browning and bruising in apples. Arctic apples have been approved in the US and Canada. They are sold through food service as well as very limited number of retail establishments in some US states.

Few empirical cases suggest an opposite relationship for the cost, with FNPETs < FHY and 𝜆 𝑁𝑃𝐸𝑇𝑠 > 𝜆 𝐻𝑌 . This configuration is not studied in this paper, but it is likely to lead to the welfare dominance of the NPETs if consumers are not too averse to this new technology.

Profits in the supply chain are addressed in the extension section.

The consumers' surplus with the integration of the possible cost of ignorance regarding the innovation process is fully compatible with the value of information defined under welfare theory[START_REF] Foster | Measuring welfare effects of product contamination with consumer uncertainty[END_REF][START_REF] Teisl | Measuring the welfare effects of nutrition information[END_REF].

The experiments and the estimated WTPs are reported in details in[START_REF] Marette | A Comparison of EU and US consumers' willingness to pay for gene-edited food: Evidence from apples[END_REF].

A fourth message noted GMO as the biotechnology used to generate the innovation. Given the overwhelming discounting of the new apple under that technology, it was clear that GMO apples would not emerge as an acceptable innovation. We therefore exclude this last round of WTP elicitation in the present paper.

This is a simplifying assumption making the regulator able to predict the probability of accident. In many configurations, the collapse cannot be predicted in Stage 1 and cannot directly influence the R&D investment with the timing for the innovation to emerge that is very long (20-25 years). Despite the absence of a clear probability, a R&D policy can be implemented for having an option value with new foods if a collapse happened.

The lab creates a focalization bias towards specific questions related to food innovation which some consumers will forget outside the lab.

The authors acknowledge financial support through a cooperative agreement from the Office of the Chief Economist at USDA, the projects DIETPLUS ANR17-CE21-0003 and ANR-17-EURE-0001 funded by the French National Research Agency (ANR) and the M. Yanney Chair at UNL. Without implicating them, we thank Shawn Arita, Anastasia Bodnar, Michael Coe, Fan-Li Chou, Karina Gallardo, Sharon Sydow, and Chengyan Yue for discussions.

Surpluses if the conventional good collapses

With the collapse of conventional apples, only the innovative apples are sold on the market, and the previous surpluses can be rewritten by withdrawing all the options linked to the conventional good (and by adding a bar above surplus and welfare expressions to differentiate them). The equation ( 1) now leads to a surplus equal to zero under the absence of innovation and collapse. Equation (2) becomes 𝑀𝑎𝑥{𝑊𝑇𝑃 𝑁 𝑘 𝑚 -𝑃, 0} with the disappearance of the conventional good. From equations (3a) and (3b), the surpluses under full information on technology are now 𝑆𝐶 ̅̅̅̅ 𝐻𝑌 𝑓𝑖 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝐻𝑌 𝑘 𝑓𝑖 -𝑃, 0}

and 𝑆𝐶 ̅̅̅̅ 𝑁𝑃𝐸𝑇𝑠 𝑓𝑖 = 𝑀𝑎𝑥{𝑊𝑇𝑃 𝑁𝑃𝐸𝑇𝑠 𝑘 𝑓𝑖 -𝑃, 0} . From equations (4) and (5), the surpluses under no technology information can also be rewritten. If goods sold are generated by hybrid methods, the complete surplus is

Appendix C. Other extensions of the approach

In the previous sections, we considered ex ante welfares based on several simplifications. To focus on the main economic mechanisms at work, we kept the mathematical aspects as sparse as possible by using simple assumptions. Our analysis could accommodate alternative situations using the following extensions.

(1) In the previous section, we focused on per-unit welfare for facilitating comparisons, which is a limitation. Extrapolations of surpluses were made with the parameter EXT allowing to get the welfares over one year for the whole country and all apples. For instance, in 2018, the average apple consumption per inhabitant in France was equal to 6.95 kg/year. 19 Multiplying this quantity by the 67,064,000 inhabitants in France leads to an extrapolation parameter EXT = 466,532,174 and significant social welfare estimates. Thus, the overall surplus over a year for the whole population is calculated by integrating this parameter EXT in equations ( 6) to ( 9). Despite the fragility of extrapolations, they provide clues for identifying potential benefits compared to R&D sunk costs.

(2) Our analysis abstract from production and supply chain. We could integrate cost functions for producers of apples, retailers and seedling industries. To do so, equation ( 6) could be rewritten for example, as follows:

for the technology HY, and by denoting Π 𝑓𝑖 (𝐻𝑌) (resp. Π 𝑓𝑖 (𝐶)) the profits for the supply chain offering new goods (resp. conventional goods) under the innovation regime. Profit Π 0 (𝐶) denotes the profits for the supply chain offering conventional goods without introduction of novelty in the market.

Different types of models could be used for determining profits using demand calibrated with price elasticities, and or experimental results for the characteristics influencing that demand (Marette et al., 2008). Alternatively to this profit characterization, marketing orders bringing together farmers and 19 See https://rnm.franceagrimer.fr/bilan_campagne?pomme.

Universities could also be studied with a per-unit paid by farmers for financing the R&D and impacting the price of apples.

(3) Prices of conventional and new goods are exogenously given both in our model and in the empirical application. Endogenous adjustments of prices could be also made by considering profits presented in equation ( 10).

(4) We considered just one period of exchanges. Several periods of exchanges with different probabilities of success in the innovation could be envisaged. For two periods of exchanges (for simplicity), the probability 𝜆 𝑁 of having innovation immediately at the first period or (1 -𝜆 𝑁 )𝜆 𝑁 at the second period leads to an "overall" benefit including the discount factor between the two periods equal to 𝛿 (and with N={HY,NPETs}). Extending equations ( 8) and ( 9) with a fourth additional stage in the model integrating a second period of exchanges with similar parameters regarding the market configurations, the net welfare for a society investing in R&D at Stage 1 is defined by

This equation can be expanded through multiple time periods.

(5) In a dynamic context, consumers may update their preferences and WTP when GE apples are introduced (with GE as specific case of NPETs). After a certain period of time, particularly if the safety of new apples could be established, consumers may revise their WTP for GE apples upwards, making the market introduction easier than the one underlined in previous simulations. For the consumers discounting GE, the revision of beliefs may lead to update WTP for new apples and bring those values closer to WTP for conventional apples. Moreover, WTP may be evaluated with other methodologies, including field experiments in supermarkets when the new apples are effectively introduced and sold.

(6) Other methods for fruit and vegetables improvements exist and could be added in the analysis, leading to more goods and regulatory options to evaluate. For instance, there are classical GMOs such as the resistant papaya now sold on the US market (see section 2). Alternatively, Marker Assisted Selections and DNA-assisted selective breeding methods tend to partially use the GE for