Anagha Sasikumar

Anouar Belhboub

Camille Bacon

Alexander C Forse

John M Griffin

Clare P Grey

Patrice Simon

Céline Merlet
email: merlet@chimie.ups-tlse.fr

Mesoscopic simulations of the in situ NMR spectra of porous carbon based supercapacitors: Electronic structure and adsorbent reorganisation effects †

In situ NMR spectroscopy is a powerful technique to investigate charge storage mechanisms in carbonbased supercapacitors thanks to its ability to distinguish ionic and molecular species adsorbed in the porous electrodes from those in the bulk electrolyte. The NMR peak corresponding to the adsorbed species shows a clear change of chemical shift as the applied potential difference is varied. This variation in chemical shift is thought to originate from a combination of ion reorganisation in the pores and changes in ring current shifts due to the changes of electronic density in the carbon. While previous Density Functional Theory calculations suggested that the electronic density has a large effect, the relative contributions of these two effects is challenging to untangle. Here, we use mesoscopic simulations to simulate NMR spectra and investigate the relative importance of ion reorganisation and ring currents on the resulting chemical shift. The model is able to predict chemical shifts in good agreement with NMR experiments and indicates that the ring currents are the dominant contribution. A thorough analysis of a specific electrode/electrolyte combination for which detailed NMR experiments have been reported allows us to confirm that local ion reorganisation has a very limited effect but the relative quantities of ions in pores of different sizes, which can change upon charging/discharging, can lead to a significant effect. Our findings suggest that in situ NMR spectra of supercapacitors may provide insights into the electronic structure of carbon materials in the future.

Introduction

Electrochemical double-layer capacitors (EDLCs) or supercapacitors have gained importance in recent times as the demand for reliable clean energy sources has increased. They store energy through the formation of an electric double layer at the electrode/electrolyte interface via ion adsorption, resulting in desir-able properties such as high charge/discharge rate and long cycle life. Porous carbons are widely used as electrode materials in supercapacitors due to their high surface area for adsorption, high electrical conductivities, low-cost and inert nature [1][2][3] . The electrochemical properties of porous carbons are highly dependent on both their local and longer range structure. Despite this, a detailed understanding of the underlying molecular mechanisms and structure-properties relationships that are crucial for improving device performance is lacking. Several experimental and theoretical efforts have been put forward in this aspect although the structural complexity of the porous material raises multiple challenges.

The development of in situ characterization techniques has facilitated the study of supercapacitors under working conditions and has provided valuable insights about charging mechanisms and the structure of the electrode-electrolyte interface. In situ electrochemical quartz crystal microbalance (EQCM) has been used to monitor ion fluxes under an applied potential and identify factors influencing it such as the average pore size or the electrolyte nature. [4][5][6] Scattering techniques such as small-angle X-ray scattering (SAXS) or small-angle neutron scattering (SANS) have helped in probing the structure of the carbon electrode as well as ion adsorption and desolvation during the course of charging/discharging. [7][8][9] Nuclear Magnetic Resonance (NMR) spectroscopy stands out among these experimental techniques as, owing to its nucleus specificity and sensitivity to local chemical environments, it provides detailed information about the behaviour of electrolyte ions in porous carbon electrodes. The ability to distinguish species that are adsorbed to the electrode surface (in-pore) from those in the bulk and to quantify them has assisted in comprehending the charging mechanisms of supercapacitors. [10][11][12] Up to now, in-pore electrolyte species are always observed to be shifted to lower frequencies relative to bulk species on account of the presence of a local magnetic field originating from the circulating electrons in the carbon electrode (ring currents). This ring current shift can be approximated by calculating Nucleus Independent Chemical Shifts (NICS).

Several studies have suggested that the difference in chemical shift between in-pore and bulk species, noted ∆δ , can be used to determine structural characteristics of the porous carbon. [13][14][15][16] Theoretical studies by Forse et al. 13 , using Density Functional Theory (DFT) on model aromatic molecules, have explored the effect of structural factors such as carbon pore size and curvature in the carbon structure on the resulting NICS. In general, the closer the ions are to the surface, the more negative the NICS is. Xing et al. 15 have used similar calculations to estimate the average pore size and pore size distribution of activated carbons. Forse et al. 14 have shown that the shift between the bulk and inpore species also brings information regarding the local ordering of the carbon atoms. It is worth noting though that ion and solvent dynamics can also affect the in-pore chemical shift 17 making the experimental results more challenging to interpret in depth.

In situ [10][11][12]18 and ex situ 19,20 NMR experiments of organic electrolytes have revealed changes in intensity and chemical shift of the in-pore resonances with charging. On the application of a potential, a number of studies showed that in-pore resonances moved to higher chemical shifts irrespective of the polarity of the electrode. These variations are believed to arise from the reorganisation of the in-pore ions, the alteration of the ring currents in the carbon electrode during charging, or a combination of both. An in situ NMR study of NaF aqueous electrolyte in nanoporous carbons has shown a reverse trend, with in-pore resonances moving to lower chemical shifts as the potential increases, for some of the nuclei studied and potentials applied. 21 In this case, the influence of the speciation (and in particular hydration number) makes the microscopic picture more complex and this system is not studied here as the focus is on organic electrolytes. DFT calculations on charged aromatic molecules have shown that the NICS varies from negative values close to the surface for neutral molecules to positive values for charged molecules, independently of the positive or negative charge imposed. 18 This is consistent with the experimental observation in terms of the qualitative variation of the shift but the magnitude of the effect is not understood to date. DFT calculations, while being powerful tools to estimate the NICS, only consider simplistic carbon structures and surface charges and do not allow for ion dynamics in complex mesostruc-tures to be readily taken into account.

In this study, we simulate in situ NMR spectra by using a lattice simulation model 22,23 in order to quantify the chemical shifts and explain the previously observed trends in detail. The mesoscopic model employed here was previously used to model ion diffusion, NMR spectra for neutral carbons and capacitive properties of supercapacitors. It combines inputs from experiments, molecular dynamics simulations (MD) and DFT calculations to predict an NMR spectrum in a very computationally efficient manner. In particular, data from gas adsorption experiments can be used to model carbon particles with the appropriate pore size distribution and data from simulations allow for the assessment of the relative importance of ion reorganisation, included through free energy profiles extracted from molecular simulations, and NICS modification, following DFT calculations, at different potentials. We investigate the NMR spectra obtained experimentally for a range of electrolyte species in a YP-50F activated carbon and examine the relative importance of free energies and NICS on the resulting chemical shift of in-pore species. The model shows good agreement with experimental results and suggests that the shifts caused by ring currents dominate those that result from ion reorganisations.

Methods

Overview of the lattice model

The lattice simulation method used in this work allows ions diffusing inside porous electrodes as well as their NMR spectra to be modeled. 22,23 Using this method it is possible to simulate the chemical shift difference between the bulk electrolyte species and the in-pore electrolyte species (∆δ = δ in-poreδ bulk ) at two different scales: (i) a slit pore having a well defined pore size and (ii) a carbon particle with a realistic pore size distribution. A schematic representation of these two models is given in Figure 1.

The system under consideration is mapped onto a threedimensional lattice consisting of discrete sites separated by a distance a. Each site is assigned an "accessible" or "non accessible" character depending on whether it corresponds to a position in the fluid or in the carbon. ∆t is the time a particle, here an ion or solvent molecule, takes to diffuse over a distance a. The ion diffusion is described by executing kinetic Monte Carlo moves on the lattice. To conduct a simulation, one has to assign: (i) the positions of the inaccessible sites if any; (ii) the free energies for ions (or solvent molecules) on each lattice site, E i ; (iii) the resonant frequencies corresponding to ions (or solvent molecules) on each lattice site, w i . The free energy, E i , accounts for the quantity of adsorbed species at a given site i and is defined using ionic densities from molecular dynamics simulations. The diffusion of ions between lattice sites is then associated with the free energy difference between these sites. The transition probability from a site i to j is given by:

P(i, j) = exp( -(E j -E i ) k B T ) if E j > E i 1 if E j ≤ E i (1)
Resonant frequencies account for the shielding environment of a site and are defined using DFT calculations directly (for the slit pore model) or through a combination of molecular simulations and DFT results (for the particle model). For an ion at a particular site, the resonance frequency is expressed as the difference between the Larmor frequency of the ion at that site and in the bulk liquid. During the course of its motion, the ion explores sites of different frequencies. For all the nuclei under consideration, the NMR signal is calculated as follows:

G(t) = e i ∑ n n =1 ω i (n .∆t)∆t (2)
where < ... > denotes an average over all ions considered, ω i is the Larmor frequency at site i, and n designates a given time step.

Parametrisation of the model for simulating NMR spectra of ions in a single slit pore

A slit pore can be described by a lattice with two parallel planes of obstacles representing the pore walls surrounding an accessible volume. In this work, the pore is aligned perpendicular to the zaxis. The free energies and chemical shifts are assumed to be invariant in x and y directions, and periodic boundary conditions are applied, thus requiring only a single site in these directions.

The considered slit pore has a pore width of 20 Å and was mapped onto a lattice of size 1 × 1 × 41 with a lattice parameter a set to 0.5 Å. This pore size was chosen as i) it is representative of a range of activated carbons 17,24 and ii) it allows for the study of ion reorganisation at the local scale, inside a pore, thanks to the existence of several layers of ions at different distances from the carbon surface.

To assign free energy values to the lattice sites, free energy profiles for anions obtained from MD simulations performed at fixed potentials ranging from -2 V to 2 V in 1-butyl-3-methylimidazolium tetrafluoroborate dissolved in acetonitrile ([BMI][BF 4 ] in ACN, 1.5 M) [25][26][27][28] are used. A single electrolyte is studied for this slit pore representation as the chemical shift changes on this local scale are not directly comparable with exper-imental values. The aim here is to illustrate the qualitative trend on an example as opposed to providing a comparison with measured values. Note that a coarse-grained approach 25,29,30 was used to model the molecular species, in particular a single sphere represents the BF - 4 anions (see Supplementary Information †). The free energy profiles reflect the adsorption behaviour of ions at various potentials. As can be seen in Figure 2a, a decrease in free energy at the minimum around 4 Å indicates a stronger adsorption of anions at the positively-polarised pore surface. On the contrary, the application of a negative potential results in the desorption of anions from the surface (see Supplementary Information †). Each site is then assigned an energy value appropriate to its distance from the site to the pore wall.

As done in a number of previous works, NICS profiles are determined by performing DFT calculations of NICS in the proximity of aromatic molecules using the Gaussian 09 software. 13,15,[31][32][33][34] Circumcoronene is used as the main model molecule to calculate the chemical shifts as it provides good agreement with the NICS evaluated experimentally for a mesoporous carbon material (CMK-3) and an organic electrolyte. 22,35 Interestingly, circumcoronene is also the molecule used in the model of Xing et al. 15 to determine the average pore size and pore size distribution of porous carbons from NMR experiments. This model provided average pore sizes in good agreement with those obtained from gas adsorption isotherms, when applied to NMR data for aqueous solutions in contact with activated carbons 17 . The NICS profiles were estimated for a neutral molecule or ions with a ±1e charge which corresponds to a surface charge of ±16.3 µC cm -2 . The actual surface charge at the potentials under consideration in real supercapacitors is far less than this. 30 Hence we intrapolate the NICS profiles to obtain chemical shifts for a particular surface charge corresponding to the potential under consideration (Figure 2b). Details of the DFT calculations and charges considered for all potentials, extracted from molecular simulations, are given in Supplementary Information †.

Parametrisation of the model for simulating NMR spectra of ions in a carbon particle

To represent a realistic carbon particle, a lattice of size 20×20×20 is used, where each lattice site is a slit pore with well defined pore size. This lattice size was previously shown to provide reliable results for NMR spectra calculations. 22 The model allows the pore characteristics (pore width and pore surface) as well as the quantity of adsorbed ions (through free energies) and the resonant frequency to be specified. The pore width is defined following the pore size distribution obtained experimentally through gas adsorption studies on the YP-50F activated carbon material. 36 The pore width is defined as the distance between the centers of the carbon atoms in both the present model and in the QSDFT model used to analyse the gas adsorption experiments. For the pore surface, which corresponds to the area of the flat carbon surfaces surrounding the liquid in the model (see Figure 1), a lognormal distribution centered around the area of circumcoronene, with a mean value of -0.1 and a standard deviation of 0.25, is used. Different pore surfaces are a way to represent different local graphitization degrees in real porous carbons. The choice of the distribution was again based on the good agreement it provides with the experimental results obtained by Borchardt et al. 35 and Cervini et al. 17 . Both pore size and pore surface distributions are shown in Supplementary Information †, along with results on the use of different pore surfaces.

The quantity of adsorbed ions in a given slit-pore is obtained from ionic density profiles from MD simulations at various potentials. [26][27][28][37][38][START_REF] Pádua | fftool[END_REF] 25,29,30 while the other electrolytes are simulated using all-atom models. [START_REF] Canongia Lopes | [END_REF][41][42][43] Molecular simulations details are given in Supplementary Information. Figure 3a shows the integrated densities of BF - 4 in [BMI][BF 4 ] for various pore sizes. The adsorption/desorption of anions at different applied potentials is clearly visible on this plot.

Chemical shifts of an ion inside a pore are calculated using both NICS and free energy profiles. Specifically, the average chemical shift is a weighted average of the NICS profile across the pore (see previous work for details 22 ). These shifts are largely dependent on the model molecules chosen in the DFT calculations (i.e. coronene, circumcoronene, and dicircumcoronene, corresponding to different pore surfaces) and on the surface charge (Figure 3b). Since a distribution of pore surfaces is considered, the average chemical shifts corresponding to a particular pore surface at an applied potential were determined by intrapolating the NICS profiles calculated using model molecules coronene (36.2 Å 2 ), circumcoronene (98.1 Å 2 ) and dicircumcoronene (191.1 Å 2 ), with the surface charge corresponding to the applied cell voltage.

Testing the relative importance of ion reorganisation and ring currents at various potentials

In this study, the aim is to understand the underlying principles behind the voltage-dependence of the chemical shift of inpore resonances by assessing the influence of ion reorganisation, through free energies, and ring currents, through NICS. The contribution to the global shift of the local ion reorganisation (or the variation in quantities of adsorbed ions in different pores for the particle model) between 0 V and a given applied cell voltage was evaluated by considering i) NICS profiles (or average chemical shifts for the particle model) calculated for a neutral surface and ii) free energies (or integrated ion densities for the particle model) for the respective potentials. By contrast, the contribution of altered ring currents was assessed by i) considering NICS profiles (or average chemical shifts) calculated for a charged surface and ii) disregarding the change in carbon-ion distance (or quantity of adsorbed ions inside the pore) while charging by considering free energies (or integrated ion densities) at 0 V.

Results and discussion

In situ NMR spectra of ions adsorbed in a single slit pore

In order to assess the relative importance of (i) ion reorganisation at the electrolyte/electrode interface and (ii) charge dependent ring currents, on the chemical shift variation observed in in situ NMR experiments, 19 F NMR spectra were simulated and average chemical shifts for BF - 4 anions confined inside a slit pore with respect to those in the free electrolyte ([BMI][BF 4 ] in ACN, 1.5M), ∆δ slit 19 F, were calculated. Average chemical shifts obtained for fixed potential differences between -2 V and 2 V are shown in Figure 4. For the total chemical shift, an approximately linear variation to higher frequencies is observed on the application of a potential, independently of the polarity of the pore. For a voltage of 1.5 V across the electrochemical cell, a difference of +2.1 ppm and +3.6 ppm was observed for positive and negative pores respectively compared to 0 V. This is in the same range as that observed experimentally for a similar electrolyte, ([NEt 4 ][BF 4 ] in ACN, 1.5 M), in contact with YP-50F activated carbon, where 19 F chemical shifts changes of +3.7 ppm and +4.4 ppm were ob-served for positive and negative electrodes respectively 10 . While the actual values are different, which is unsurprising due to the crudeness of the slit pore pore model, the larger chemical shift change for negative potentials observed experimentally is reproduced by the lattice model. When looking at the relative contributions of ring currents and ion reorganisation in the pores, it is very clear that most of the total shift is due to variations in the ring currents. With an applied potential, the ions experience different positions in the pore leading to different ring currents as the NICS depends on the ioncarbon distance. It is important to note that the ring currents and ion reorganisation contributions are not additive because the average chemical shift results from a convolution of the NICS and free energy profiles which vary differently as a function of the distance to the carbon surface. The chemical shift change due to the NICS is always to more positive chemical shifts irrespective of the electrode polarity as suggested by DFT calculations, owing to the accumulation of electrons/holes on the pore surface rendering paratropic ring current effects. It is worth noting that the absolute changes in NICS are smaller on the positive side than on the negative side. While the contribution due to the NICS varies proportionally to the applied cell voltage, the ion reorganisation contribution is more constant. The reorganisation leads to a negative chemical shift change for a positively charged pore and to a positive chemical shift change for a negatively charged pore. This is due to a stronger adsorption of BF - 4 anions on a positively charged surface, leading to a shorter carbon-anion distance on average (and a larger ring current effect), and the reverse phenomenon on a negatively charged surface.

In situ NMR spectra of ions adsorbed in a carbon particle

To get closer to experimental conditions, the lattice model was then used with a representation of a carbon particle, which in-cludes its pore size distribution taken as the one of YP-50F, and a pore surface area distribution, which follows a log-normal distribution centered around the area of circumcoronene. The chemical shifts of in-pore BF - 4 anions relative to their bulk counterparts, ∆δ 19 cle model are very similar to the ones observed for the slit pore. In particular, the chemical shift change observed with an applied potential is mainly due to variations in the ring currents, while the effect of ion reorganisation is limited. It is worth noting that the chemical shift changes observed between 0 V and 1.5 V are much larger than for the slit pore, more precisely +5.1 ppm for the positively and +8.0 ppm for the negatively charged particles compared to +2.1 ppm and +3.6 ppm for the slit pore model. The larger ∆δ values compared to the slit pore are expected as the pore size distribution of YP-50F (see Supplementary Information) shows mostly pore sizes below 2 nm (the pore size used for the slit pore model) leading to larger chemical shifts for adsorbed ions relative to the bulk. The experimental values for [NEt 4 ][BF 4 ] in ACN, +3.7 ppm and +4.4 ppm, are between the values obtained with the slit-pore and the particle models 10 . Nevertheless, as the electrolytes are not exactly the same, it is hard to comment on these differences. As for the slit pore model, the absolute changes in shifts on the positive side are smaller than on the negative side, which is believed to be mainly due to the charge dependence of the NICS, even though for this system both NICS and ion reorganisation are cooperative.

To investigate the predictive power of the model in more depth, additional simulations were conducted with another organic electrolyte for which experimental results are published, namely [PEt 4 ][BF 4 ] in ACN, and with a neat ionic liquid.

While the neat ionic liquid studied in this work, [EMI][TFSI], is not the same as the previously reported on ex-perimental one, [Pyr 13 ][TFSI] (1-methyl-1-propylpyrrolidinium bis(trifluoromethanesulfonyl)imide), they share a common anion and provide lattice simulations results for a system where ionic correlations are not screened by a solvent and the approach, adopted here, of extracting free energy profiles from molecular dynamics simulations could potentially lead to dramatically wrong results. In particular, the quantity of ions adsorbed in Fig. 6 Comparison of average chemical shifts for anions adsorbed inside YP-50F carbon particles relative to the bulk electrolyte obtained through experiments 6,20 and lattice simulations.

small pores could be largely underestimated leading to very small ∆δ values compared to experiments. Indeed, if ions are only present in relatively large pores, the average ion-carbon distance is overestimated and the simulated ∆δ is underestimated. The comparison between lattice simulations and experimental results for anions is shown in Figure 6. The agreement between lattice simulations and experiments is good, especially for positive potentials. For negative potentials, the lattice simulations seem to overestimate the chemical shift change with potential. It is remarkable that for experiments or simulations, the chemical shift variation with potential, i.e. the slope of the profiles, is very similar for all electrolytes, consistent with a variation mainly due to ring currents. This effect has actually been seen experimentally on a larger range of electrolytes than the one explored here. 44 According to the results obtained here, the coarse-grained or allatom representation of the ions and molecules in the molecular simulations do not lead to significant changes. The ion adsorption can still have an effect on the actual chemical shift as can be seen in particular at 0 V.

To understand the discrepancy between experiments and simulations for negative potentials, a more detailed study of the [PEt 4 ][BF 4 ]-ACN electrolyte was carried out. Figure 7a shows the average chemical shifts for anions and cations adsorbed inside YP-50F carbon particles relative to the bulk electrolyte ([PEt 4 ][BF 4 ] in ACN, 1.5 M) obtained through experiments 6 and lattice simulations. For the PEt + 4 cations, while the chemical shifts are underestimated by the lattice model, the variation with the potential follows closely that seen experimentally. For the BF - 4 anions, while the agreement is very good on the positive side, the trend observed on the negative side diverges from the experimental one and becomes very similar to the one of PEt + 4 cations. Interestingly, below -0.5 V, the lattice model gives almost identical results for BF - 4 and PEt + 4 indicating that the environments visited by these two ions were very similar. The excellent agreement between the trends with the applied potential difference observed experimentally and with the model is even clearer on Figure 7b, where chemical shifts are plotted with respect to the values at 0 V. This suggests that discrepancies between the simulations and experiments are due to inaccuracies in the representation of ion adsorption rather than in the DFT NICS calculations.

It is important to note that while the lattice model also includes a determination of total quantities of adsorbed ions, this is not the appropriate quantity to understand the average chemical shift observed as the chemical shift depends on the distribution of ions in different environments, here different pore sizes. The quantities of adsorbed ions relative to the ones at 0 V are shown in Figure 8. Considering the crudeness of the model, where the carbon particle is represented as a collection of slit pores, the overall agreement with experiment is very good. Indeed, the order of magni-Fig. 8 Comparison of relative quantities of adsorbed ions determined from the lattice model and from experiments 6 for the same electrolyte at various applied potential differences with respect to the values at 0V. tude of the relative changes is well captured by the model. This plot shows, however, that the overall chemical shift does not follow the same trend as the quantity of in-pore ions. In particular, while the agreement between experiments 6 and simulations is better on the negative side, the agreement for the chemical shifts is better on the positive side. One striking feature is that the lattice model seems to overestimate the variations in quantities of adsorbed ions, especially for anions at the positive electrode. In this work, anions and cations adsorption have been considered in separate lattice simulations which can lead to an overestimation of the ion adsorption as the total ionic volume in the pores is underestimated.

The environments explored by the ions are highly dependent on the surface densities of the ionic species obtained from molecular simulations results. Figure 9a shows the surface densities for BF - 4 and PEt + 4 ions at positive and negative electrodes for a potential difference of 1V. Apart from BF - 4 at the positive electrode, the approach adopted here predicts that the surface density is zero for pores below 10 Å. As the pore size distribution of YP-50F (see inset of Figure 9b) shows that this carbon contains a majority of pores of around 8.5 Å, these low surface densities are expected to impact the actual shifts, especially as smaller pores lead to higher chemical shifts. From the lattice simulations results, it is possible to extract the distributions of ions in pores of different sizes. The distributions corresponding to a potential difference of 1 V are shown in Figure 9b. The pore distributions for BF - 4 at the positive electrode follow quite closely the pore size distribution. This situation corresponds to a case where the agreement between simulations and experiments is excellent. It is interesting to note that for pores larger than 20 Å, the relative quantities of ions are larger than the probabilities from the pore size distribution. This is expected as larger pores contain more ions. The distributions for BF - 4 at the negative electrode and for PEt + 4 at both electrodes indicate lower number of ions in pores below 10 Å. The chemical shifts for all these situations will therefore be underestimated compared to experiments. Overall, the discrepancy between ex- periments and simulations in some cases, and the distributions of ions in pores of different sizes suggest that: i) the reorganisation of ions in a pore of a given size has a limited effect on the chemical shift, ii) the presence or not of ions in small pores has a large effect. Indeed, ions in small pores experience large chemical shifts in absolute values which lead to noticeable features in the experiments. In addition, the fact that the best agreement is obtained for cases where the ions are present in the pores below 10 Å confirm that experimentally these pores are accessible to the ions, as expected from the large capacitances measured for this activated carbon.

To confirm that the lattice model underestimates the quantity of adsorbed ions in small pores, additional molecular dynamics simulations were performed for [PEt 4 ][BF 4 ]-ACN (1.5 M) in contact with a porous carbon having an average pore size of 8.6 Å 45 , i.e. close to the most common pore size observed in the PSD of YP-50F (8.5 Å, see Figure 9b). The distributions of ions in different pore sizes and the details of the molecular simulations are given in Supplementary Information †. In contrast to the lattice model predictions, cations and anions both enter pores with a size below 10 Å spontaneously in the molecular simulations. The actual density calculated with the lattice model for pores of 8.5 Å is 1.24 10 -4 ions Å -3 for BF - 4 and 1.21 10 -6 ions Å -3 for PEt + 4 . From the molecular simulations, the density is much larger, equal to 4.97 10 -4 ions Å -3 for both anions and cations. This comparison can help explain the discrepancy between lattice simulations and experiments and shows the limit of the lattice model to predict quantities of adsorbed ions in small pores for which the use of free energy profiles extracted from simulations of an electrolyte at a planar surface is not adequate. Future works will explore the possibility of extracting three dimensional ionic densities from molecular simulations or using other theoretical methods such as molecular density functional theory. 46 The presence of functional groups on the carbon surface, not taken into account in this work, and potentially leading to significant effects, [47][48][49][50][51][52] could also be included in the future. An alternative way to exploit the lattice model would be to extract the distribution of ions in pores of different size by identifying which distribution leads to the best fit with the experimental results.

Conclusion

In this work, we have used a lattice simulation method to generate in situ NMR spectra for various electrolyte species under a range of applied potentials. With this theoretical approach it was possible to quantify the relative importance of free energy, i.e. the ion adsorption and reorganisation, and the NICS, i.e. carbon ring currents, to the overall chemical shift. We have established that changes to the ring currents occurring in the carbon material during charging have a larger influence on the chemical shift changes. Comparisons of our model results with experimental data show that the lattice model is able to predict the variation of the chemical shifts with applied potential very well. Nevertheless, the model fails to predict the actual shift in some cases, probably as a consequence of using molecular dynamics results corresponding to electrolytes adsorbed at planar surfaces separated by distances considerably larger than the solvated ions to extract free energy profiles. The use of a realistic porous carbon electrode in molecular dynamics simulations and DFT calculations could lead to a better agreement and will be investigated in future works. Lastly, our finding that changes in ring currents dominate the observed chemical shift changes confirms that in situ NMR spectra provide information on the electronic structure of carbon materials, providing motivation to explore this further in future studies of different carbons.

Fig. 1

 1 Fig. 1 Schematic representation of (i) a single slit pore and (ii) a particle in the lattice model. The discrete sites in the lattice are separated by a distance a.

Fig. 2

 2 Fig. 2 (a) Free energy profiles for BF - 4 anions in [BMI][BF 4 ]-ACN (1.5M) at the positive electrode for various applied potential differences. (b) NICS values at various distances obtained from DFT calculations using circumcoronene as model molecule. NICS values for intermediate surface charges are intrapolated from the results of the DFT calculations (see Supplementary Information for details †).

  Several electrolytes are considered for this more realistic model of the carbon particles to allow for a direct comparison with experiments: 1-butyl-3methylimidazolium tetrafluoroborate in acetonitrile ([BMI][BF 4 ]-ACN, 1.5M), tetraethylphosphonium tetrafluoroborate in acetonitrile ([PEt 4 ][BF 4 ]-ACN, 1.5M) and the neat ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([EMI][TFSI]). In MD, the [BMI][BF 4 ]-ACN electrolyte is again represented by a coarse-grained model

Fig. 3

 3 Fig. 3 Integrated density profiles (a) and average chemical shifts of BF - 4 with respect to the bulk electrolyte ([BMI][BF 4 ] in ACN, 1.5M) (b) as a function of pore width calculated for various potentials and model molecules (coronene, circumcoronene, and dicircumcoronene corresponding to different pore surfaces).

Fig. 4

 4 Fig. 4 Average chemical shift for BF - 4 anions adsorbed inside a 2 nm carbon slit pore relative to the bulk electrolyte and contributions of ion reorganisation and ring currents, obtained through the lattice model for [BMI][BF 4 ] (1.5 M in ACN). The ion reorganisation and ring currents contributions are assessed by fixing the free energies and NICS to their values at 0V in specific calculations.

Fig. 5

 5 Fig. 5 Average chemical shift for BF - 4 anions adsorbed inside carbon particle relative to the bulk electrolyte and contributions of ion reorganisation and ring currents, obtained through the lattice model for [BMI][BF 4 ] (1.5M in ACN). The ion reorganisation and ring currents contributions are assessed by fixing the surface densities and average chemical shifts to their values at 0V in specific calculations.

Fig. 7

 7 Fig. 7 (a) Comparison of average chemical shifts for anions and cations adsorbed inside YP-50F carbon particles relative to the bulk electrolyte ([PEt 4 ][BF 4 ] in ACN, 1.5 M) obtained through experiments 6 and lattice simulations. (b) Same as (a) but given with respect to the values at 0V.

Fig. 9

 9 Fig. 9 Integrated ionic density profiles for [PEt 4 ][BF 4 ]-ACN at 1V (a) and corresponding distributions of the ions in the pores obtained with the carbon particle model (b).

[1][2][3][4][5][6][7][8][9][10]

J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreements no. 714581 and no. 835073). This work was granted access to the HPC 1-10 J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

resources of CALMIP supercomputing center under the allocations P17037 and P19003, and of TGCC under the allocations A0070911061 and A0080910463 made by GENCI. This work was also supported by a UKRI Future Leaders Fellowship to Alexander C. Forse (MR/T043024/1). The authors acknowledge Dimitrios Kilymis, El Hassane Lahrar and Dongxun Lyu for useful discussions.

Data availability

The program used to do the lattice simulations is available, along with a manual, on github (https://github.com/cmerlet/LPC3D). The data corresponding to the plots reported in this paper, as well as example input files for the mesocopic model, are available in the Zenodo repository with identifier 10.5281/zenodo.5097581.

Conflicts of interest

There are no conflicts to declare.

Notes and references


Maria Sayu Yamamoto

Camille Benaroch

Aline Roc

Thibaut Monseigne

Fabien Lotte

Should frequency band selection algorithms include neurophysiological constraints?

Should frequency band selection algorithms include neurophysiological constraints?

Maria Sayu Yamamoto 1,3,* , Camille Benaroch 1,2 , Aline Roc

Introduction:

In order to build a reliable BCI, it is useful to calibrate the BCI system considering the characteristics of each user's ElectroEncephaloGraphy (EEG) [1]. A concrete approach is to select user-specific frequency bands based on data. Our previous work suggested a correlation between online BCI performances and the selected user-specific frequency bands [2]. In particular, users with the highest performance were the ones for whom the selected frequency bands' width was larger than 3.5Hz, and selected frequency band mean belonged to α-lowβ (5-16 Hz). However, it did not reveal whether the selected user-specific frequency band in α-lowβ causes higher performance or if users with higher performance have their user-specific frequency bands in α-lowβ range. In this study, we developed a frequency band selection algorithm to select user-specific frequency bands only from α-lowβ range and investigated how the online BCI performance change [3]. Methods and Results: We conducted a Motor Imagery (MI) BCI experiment with the same protocol as our previous work [4] with 12 healthy users who performed left or right hand MI. Their user-specific frequency bands were selected restrictively between 5-20 Hz and the minimum width was set as 3.5Hz. Then the average online BCI accuracies were compared with control users who have selected user-specific frequency band between 8-30Hz and without restriction for width from our previous study in [4]. The comparison results showed no significant difference (p=0.26) in online BCI performance. We will still continue this investigation with several users but this current result may suggest the users with higher performance can modulate their α-lowβ range activity well and their user-specific frequency bands belong to α-lowβ range as a result.

1,2 , Thibaut Monseigne 1 , Fabien Lotte 1,2 1

  Inria Bordeaux Sud-Ouest, Talence, France; 2 LaBRI (CNRS / Univ. Bordeaux / Bordeaux INP), Talence, France; 3 Tokyo University of Agriculture and Technology, Tokyo, Japan

	*200 avenue de la Vieille Tour, 33405 Talence cedex, France. E-mail: yamamoto18@sip.tuat.ac.jp


Lise Arena

Until the post-war period, there was no established form of industrial economics at Oxford, despite a signi cant number of scholars interested in the study of industrial structures and rms.

, noting that 'these volumes mark the explicit recognition of the theory of the rm as an integral division of economic analysis upon which rests the whole fabric of equilibrium theory' (Boulding 1942: 791).

L. Arena

Introduction

Industrial economics is usually de ned as the study of the structure of markets, the economic performance of industries, the behaviour of both and the manner in which they interact. e discipline did not emerge as a separate subject area until the inter-war period in the United States and in England. 1 Embryonic forms of industrial economics can be found in earlier economic theories, with the earliest example in the United Kingdom probably being e Economics of Industry by Alfred and Mary Paley [START_REF] Marshall | e Economics of Industry[END_REF]. Four decades later, a number of US economists, including Frank [START_REF] Knight | Risk, Uncertainty, and Pro t[END_REF] and John Maurice [START_REF] Clark | Studies in the Economics of Overhead Costs[END_REF], had succeeded in introducing some central concepts, such as speci c forms of imperfect competition and the role of uncertainty and risk in the context of innovation.

While industrial economics focuses on the aggregate analysis of sectors and industries, the theory of the rm is primarily concerned with the internal organisation of rms and rm behaviour. Until the end of the nineteenth century, questions relating to rm organisation were subsumed within the 1 As Hay and Morris remarked in their internationally known textbook on the subject, 'people have been interested in the economic behaviour and performance of industries since the beginning of the industrial revolution, but the delineation of a speci c area of economics under the title of industrial economics is a phenomenon of the last forty years' (Hay and Morris 1979: 3).

L. Arena (*) CNRS-Université Côte d'Azur Research Institute GREDEG, Nice, France e-mail: lise.arena@univ-cotedazur.fr theory of prices and value and were, at best, concerned with sector-or industry-level analysis (see [START_REF] Marshall | e Economics of Industry[END_REF]: rms were "empty boxes" governed by cost curves [START_REF] Clapham | Of Empty Economic Boxes[END_REF]). e concept of the internal organisation of a rm remained neglected, especially after Pigou and Robertson's highly abstract neoclassical analysis e ectively eliminated the Marshallian concern with the actual workings of the rm [START_REF] Pigou | ose Empty Boxes[END_REF]. In a well-known survey of the theory of the rm, Kenneth Boulding (1942: 791) attributed early developments in the eld to 'extensive transformations' in the basic theory of value in the 1930s. 2 At the same time, empirical studies, which were increasingly concerned with the separation of ownership from management (see [START_REF] Berle | e Modern Corporation and Private Property[END_REF], highlighted the separate existence of rms from markets, and the importance of their internal forms of organisation for overall economic performance.

Since the inter-war period, industrial economics and the theory of the rm have constituted a signi cant part of applied microeconomics. is chapter seeks to provide a better understanding of Oxford's contributions to the emergence and the institutionalisation of industrial economics as an academic discipline. It falls into four main parts: "Premises", triggered by David Macgregor's contribution and the Oxford Economists' Research Group (OERG) ; "Roots", illustrated by the research on the Courtauld Inquiry and Philip Andrews' contribution (1943Andrews' contribution ( -1947)); "Institutionalisation", evidenced by the creation of the Journal of Industrial Economics (1952Economics ( -1968)); and "Transformation", exempli ed by the shift of the discipline towards industrial organisation (1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991). Despite the prominent position of its researchers in their respective elds, Oxford's leading role in the emergence of industrial economics is not attributable to any speci c school of thought it produced, as could be argued was the case at Cambridge. Rather, the Oxford case stands out because of its contribution to the emergence and development of institutions that are still internationally central to the discipline.

2

Premises: From Macgregor's (Isolated) Contribution to the OERG in the Analysis of Industrial Firms discipline were fostered by a relatively obscure economist, David Hutchison Macgregor, who was involved in the creation of an informal group of Oxford economists known as the Oxford Economists' Research Group (OERG).

Macgregor and Embryonic Industrial Economics

is section considers the life and work of Macgregor who published a substantial amount on the theory of the rm and contributed to the development of Oxford industrial economics. Macgregor studied economics at Cambridge where he obtained a BA in 1901. ere, he became 'one of Marshall's favourite students and became quite attached to his method, i.e. to the use of theory tempered by empirical investigation' (Lee 1989: 23). In particular, it was argued that if Macgregor 'used Marshallian methods that was because, testing them as far as he could against the facts of ordinary life they seemed to him the best available' (Andrews 1953: 348). During his stay at Cambridge, Macgregor prepared his Industrial Combination, which was published in 1906 and resulted in him being elected a Fellow of Trinity College, Cambridge, in 1904. According to Lee's biography of Macgregor, at this time he was 'employed as a university lecturer in general economics and was paid, unocially, by Marshall for the work' (Lee 2008: 3). In 1908, Macgregor left Cambridge to become Professor of Political Economy at the University of Leeds.

Macgregor's Report of Travels (1913) expressed his interest in studying forms of industrial organisation in di erent countries, such as China, Japan, India, Russia and the United States. In particular, Macgregor 'had in view specially the relation of foreign nations to the great industrial changes which occurred in England nearly a century and a half ago-changes to which we owe the nature and the problems of our present industrial life' (ibid.: 8). In 1919, Macgregor moved to Manchester where he became Stanley Professor of Political Economy He stayed there for only two years, as in 1921, Edgeworth vacated the Chair at Oxford, and according to Young and Lee (1993: 12), although Macgregor 'did not formally apply for the Drummond', the 'electors o ered it to him'. Immediately after his appointment, Macgregor engaged in extensive research concerned with a wide range of economics topics, such as: unemployment [START_REF] Macgregor | Public Authorities and Unemployment[END_REF]; consumption [START_REF] Macgregor | Consumer's Surplus: A Reply[END_REF]; agriculture [START_REF] Macgregor | e Agricultural Argument[END_REF]; and family allowances [START_REF] Macgregor | Family Allowance[END_REF]. He also pursued his research interests in industrial economics and prepared the nal revision of his 1906 book. In addition, towards the end of the 1920s, Macgregor published his research on cartels and other industrial combinations (Macgregor 1927a[START_REF] Macgregor | Joint Stock Companies and the Risk Factor[END_REF][START_REF] Macgregor | e Coal Bill and the Cartel[END_REF] and became interested in proposals for the rationalisation of industry (Macgregor 1927b). From 1925 until 1937, he was joint editor of the Economic Journal, with John Maynard Keynes. 3 Macgregor's concern with an empirical approach to economics was re ected by the statistical investigations conducted in his various articles. Although his intellectual orientation and personality made him, to some extent, an isolated gure, he still contributed to the development of the theory of the rm and industrial economics at Oxford, both at the teaching and research level. Macgregor's analysis did not follow the usual methods of pure maximisation and equilibrium concepts. Rather, he was more interested in the growth of rms and the way that they were able to reproduce themselves. His main idea was that new competition came about from skilled businessmen who had learnt the trade, who promoted existing relations with customers and suppliers and who used their savings (and personal connections) to start their own businesses.

By the mid-1930s, Macgregor had published Enterprise Purpose & Pro t (1934)-concerned with the behaviour of rms over the trade cycle under risk and uncertainty-where he 'used the formations of new joint stock companies to represent the course of enterprise' to discover that 'variations of this index precede variations of both prices and employment' (Todd 1935: 544). To him, variations in nancial and stock market conditions re ected variations in company formations. Hence, the concept of strategic behaviour is implicitly used at the heart of Macgregor's contribution: once a rm has entered into competition and is established in the market, it then follows long-term policies, such as stable prices, balanced with more short-term ones, such as decisions to expand.

Despite his research, Macgregor's message did not take hold at Oxford at the time, his contribution eclipsed by the then evolving mainstream of microeconomics. is situation made him, as recently argued by Warren Samuels, 'an "applied" economist in a new world dominated by "pure" economics' (Samuels 2008: 150). 4 Yet, he could not be completely ignored by mainstream economists due to his steady ow of books and journal articles principally published in the Economic Journal and more occasionally in Economica until 3 Further information about this can be found in Macgregor's correspondence with Roy Harrod. See in particular Letter 119R, Macgregor to Harrod, 18 September 1926(Besomi 2003: 74); Letter 150, Harrod to Macgregor, 7 July 1928 (ibid.: 95);Letter 337, Keynes to Harrod, 30 December 1933 (ibid.: 259); Letter 456R, Macgregor to Harrod, 12 July 1935 (ibid.: 397). 4 is view is also reinforced by Maurice Allen who argued that ' [Macgregor] was in the old-fashioned Marshall tradition and had … little interest in rigorous analysis that came into vogue in the later years of his life. In my view, he was none the worse for that. I should say that in his books … and in his teaching he gave students a sounder understanding of the problems of the economy of his time than contemporary dons give them at present … It seems to me that … the value of his contribution was underestimated because the newer trends (fashions?) in economics passed him by' (Allen in Lee 2008: 1).

L. Arena

the mid-1930s. Furthermore, Industrial Combination still constituted an early signi cant account of industrial economics, which was reprinted on several occasions and was used as an economics textbook by subsequent generations of students inside and outside Oxford.5

2.2

The Role of the OERG in the Analysis of Industrial Firms

Despite his isolated position, Macgregor became an 'active and enthusiastic member' of the OERG shortly after its creation (Andrews 1953: 346) Oxford economists-who were already developing the work of the Oxford Institute of Statistics (OIS)-took the opportunity to approach the Rockefeller Foundation. In 1937, the nancial assistance given by the Foundation to Roy Harrod enabled the Group to grow, in two years, from a relatively small number of participants to more than nineteen members.

e meetings of the OERG were quite informal and their studies basically consisted of sets of inquiries or research projects which usually took about eighteen months and which were based upon questionnaires. ese questionnaires were sent in advance and then formed the basis for after-dinner interviews with businessmen who were invited to come to Oxford to dine and spend an evening answering members' questions. Intensive questioning and discussions often took place until the small hours of the morning. A record was kept of what was said at each meeting and sent back to the guest, allowing him to alter his comments. is procedure was considered to be a completely new methodology at the time and broke with traditional deductive methods.

While the topics studied within the Group were diverse and not only focused on rms and industries, its most notable research concerned the in uence of interest rates on investment, and the pricing policies of rms. It was found that investment decisions taken by businessmen were in uenced very little by changes in the rates of interest. Regarding pricing policies, many of the businessmen participants claimed to set prices according to the "full-cost" principle, that is, calculating the average cost of production and then adding a margin. In October 1938, the Group published its results in the rst issue of Oxford Economic Papers. Indeed, a key purpose of the journal was to make public the empirical research being carried out by the OERG and the OIS.

In 1939, the OERG published papers on pricing, in particular the famous Hall-Hitch exposition of the full-cost principle. It was the rst time that theorists had examined actual business practice. ey used questionnaires for a sample of thirty-eight rms, with the results showing that a signi cant proportion of these companies did indeed set their prices according to full-cost. Typically, a company would make an ex-ante estimate of its output for the coming year, then determine average cost (direct costs, e.g. labour, materials, energy, per unit of product) and then add to it percentage margins for pro tthe "mark-up". e rms in question insisted that this pricing mechanism was a "rule of thumb" and could result in maximum pro ts by accident only. Hence, the results of the survey appeared to con ict with the received doctrine of the time. In other words, this exercise tested the conventional assumption of maximisation in terms of equalisation of marginal cost and marginal revenue. In fact, Hall and Hitch justi ed the full-cost principle by arguing that 'producers cannot know their demand or marginal revenue curves' (Hall and Hitch 1939: 22). us, the evidence obtained from the businessmen showed that they did not and could not use marginal revenue and cost (i.e. any forms of marginalism) to set prices. Rather, it indicated 'that they [were] thinking in altogether di erent terms' (ibid.: 18).

After the publication of the articles in Oxford Economic Papers, 6 the Group was full of intellectual vitality and raring to take their research forward, but when the War started in September 1939, members were dispersed, disrupting the OERG, which became inactive for the duration of hostilities. 7 e conventional wisdom on the post-war OERG is that it had a limited e ect on Oxford economics in terms of in uence and direction of research. 6 ese publications were reprinted in Oxford Studies in the Price Mechanism in 1951 edited by Wilson and Andrews. 7 One of the di culties for scholars in collecting archival evidence from this period is the lack of documentation. e rumour, which was still circulating many decades later, was that concerns about a Nazi invasion and con dentiality issues led Harrod and Andrews to burn the les which contained the entire proceedings of the Group in the boilers of Christ Church College, Oxford.

L. Arena

According to some of its former members, the OERG tried to resurrect itself after the War, but the drive and interest that existed before 1939 had gone. Nevertheless, the Group did reform, and some new members played an active part in its reconstruction. Roy Harrod took the chair and was accompanied by some new and some old members, listed in Appendix 2. As can be seen in this Appendix, Frank Burchardt, Hubert Henderson and Edward Hugh-Jones still attended meetings, along with Philip Andrews, who became the new Secretary of the Group and was assisted by Elizabeth Brunner, one of the very few female members.

During the post-war period, the members of the OERG were more concerned with researching the internal organisation of the rm. Work on pricing had been completed before the War and the post-war Group began to look at issues such as productivity and factors a ecting capital expenditure (Andrews and Brunner 1950: 197). Between 1950 and the end of the OERG, four main themes were studied: pricing policy of exporters when the exchange rate altered; relationships between rms; business investment; and the sources of growth. Papers looking at the last of these were published in the March 1964 number of Oxford Economic Papers [START_REF] Leyland | Growth and Competition[END_REF][START_REF] Richardson | e Limit to a Firm's Rate of Growth[END_REF][START_REF] Richardson | e Growth of Firms[END_REF].

At the beginning of the 1960s, the links that had been developed with businessmen were still growing, especially with the help of Harrod, Richardson, Leyland and Andrews, and the reputation of Oxford itself. Meanwhile, in November 1962, Roger Opie became Secretary of the Group in place of Norman Leyland. At the same time, however, the Group's members started showing some loss of interest in its work and the decision to try to increase membership and invite new economists was taken. is did not work, however, and by the summer of 1964 the Group started to seriously question its relevance. A meeting in 1965 examined forecasts and business decisions, this turning out to be the last gathering of the OERG.

3

Roots: From the Courtauld Inquiry to the Publication of Manufacturing Business (1943)(1944)(1945)(1946)(1947)(1948)(1949) e outbreak of War transformed economics research at Oxford and provided some new war-related research topics for the OERG and the OIS. is new range of issues soon became institutionally based and gave rise to new developments within the University, such as the Nu eld College Post-War Reconstruction Survey (1941)(1942)(1943)(1944) which led to the Courtauld Inquiry (1943)(1944)(1945)(1946)(1947). Later on, the publication of Manufacturing Business by Philip Andrews in 1949 ushered in a new period of institutionalisation.

3.1

Courtauld Inquiry (1943)(1944)(1945)(1946)(1947) In 1937, the philanthropist, Lord Nu eld, expressed his desire to fund the creation of a new postgraduate residential college at Oxford which would be devoted to the study of both engineering and accountancy. While the form of the o er proposed by Nu eld did not match the University's desire, it was still seen as a major opportunity to provide some coherence within social studies at Oxford. Nu eld's o er was discussed between Alexander Dunlop Lindsay (Vice-Chancellor of Oxford) and the economist William Beveridge (then Master of University College), the latter clearly disapproving the idea of Nu eld's project on the grounds that it was not sensible to focus exclusively on the type of research being suggested (Taylor 2008). Eventually, Lindsay convinced Nu eld to fund a college just concerned with social studies, to the exclusion of engineering.

In May 1940, the Warden of Nu eld, Harold Butler, proposed to the College Committee a project which would look at the problems of post-war economic and social reconstruction. At this stage, G.D.H. Cole and Lindsay (also members of the Committee) suggested that Butler's proposal was too focused on a post-war context, and should rather deal with the changes then taking place in the economy, such as the e ects of the redistribution of population. During the following months, Cole and Lindsay went in search for nancial support for their project from the government. By April 1941, funding had been secured, and under Cole's enthusiastic direction, work began on examining the economic and social prospects of Britain's main industrial regions (Young and Lee 1993: 142). Over the next two years, Cole invested the majority of his time and energy in this e ort. However, the purpose of this Social Reconstruction Survey was soon being criticised by senior members of the University and by some of Cole's colleagues at Nu eld who questioned its practicality.

e "failure" of the Survey did not help with the promotion of social studies at Oxford. Shortly before Cole's resignation in 1944, he received a letter in March 1943 from Samuel Courtauld, Visiting Fellow at Nu eld and wealthy textile industrialist, expressing his doubts about the dictum "bigger is better". Courtauld o ered to partially nance an investigation which would aim to collect evidence among rms and their accountants on the issue of the growth AU2 L. Arena of rms. In 1943, it was decided that a six-month pilot investigation should be undertaken. is became known as the "Courtauld Inquiry" and was placed under a special committee called the "Courtauld Committee" within the College Committee at Nu eld. 8 e theoretical investigation-concerned with the optimum size of a rm-was conducted by Josef Steindl, J.R.L. Schneider and Arthur Bowley and worked out of the OIS.

In May 1944, the rst report of the Courtauld Committee was sent to Courtauld who particularly liked the statistical investigation conducted by Andrews, 'because it dealt with Courtauld's data obtained from the [Courtauld] accountants' (ibid.: 149). As a result, Henry Clay, who had taken over from Butler as Warden of Nu eld in 1945, agreed with Courtauld that Andrews should continue his statistical investigation. e latter went one step further, proposing to Clay and Courtauld that he expand his study to the clothing and shoe industries. Over the next two years, Andrews, along with the help of the OIS, carried out this additional investigation with the assistance of his collaborator, Elizabeth Brunner. Although Courtauld died in 1947, funding for the project went on until 1949 and led Andrews to publish his results in Manufacturing Business.

Phillips Andrews' Contribution and the Publication of Manufacturing Business

Manufacturing Hall and Hitch, however, as shown earlier, followed a more empirical critique and sought to demonstrate that the assumption of short-run pro t maximisation which formed the basis of Pigou's interpretation clearly contradicted the pricing practices of businessmen.

In addition to this theoretical background, it is relevant to recall that Manufacturing Business emerged from the initial Courtauld Inquiry and was 8 Archival documents about the Courtauld Inquiry can be found in the Andrews and Brunner Archive held at the London School of Economics (LSE). See, in particular, Box 56, which contains an interesting note on the relative e ciency of small and big businesses; Box 58, which contains some documents about big and small business; Box 60, which contains a report to the Courtauld Committee written by Andrews in 1945;and Box 63. also an attempt to provide some "practical" tools and empirical evidence for the few existing theories on the internal organisation of the rm. Andrews made clear his theoretical inspiration: is mention of a wider experience gives me an opportunity to pay a tribute to a major element in my education as an industrial economist-my association with the pre-war Oxford Economists' Research Group … It was the work of this Research Group that developed so strongly the conviction that the behaviour of business men was consistent, and that, accordingly, even though, on many points, it might not seem directly explicable by generally accepted economic theory, there was hope that one would arrive at a consistent theory by studying individual businesses. (Andrews 1949: xv) In the volume, Andrews used an approach based on observed industrial realities at the expense of elementary mathematical formalism. Andrews' rst objective was to illustrate the combination of both deductive and inductive approaches, and to emphasise their complementarities. us, accordingly, Manufacturing Business was largely concerned with the complex facts of business life, expressed by a detailed investigation of speci c rms and industries.

At the same time, however, Andrews tried to develop analytical foundations to go with Hall and Hitch's empirical results. In fact, he was strongly in favour of an integrative approach, combining the full-cost principle (reshaped as "normal cost") with a revival of the Marshallian framework. Andrews' main idea was that in his analysis of the short run, Marshall could clearly be interpreted with the help of marginal tools. His analysis of the long period was, however, considered to be incompatible with these tools and their individualistic foundations. 9 Andrews' interpretation of Marshall's theory in particular stressed the existence of long-run supply curves, including economies of scale.

e expansion of a rm's operations over the long run could not be supported by a marginal approach, which only admitted increasing average costs across such a time period.

Andrews' expression of normal costs in the long run was, to a large extent, in uenced by Marshall's long-period theoretical framework, and especially by his concept of the representative rm. By contrast with the marginal interpretation of the representative rm, which considered this concept as an equilibrium rm, Andrews considered it as a rm which represented the reality of industry. He made it clear in the following note: is [concept of the representative rm] was his [Marshall's] new semi-historical concept which he brought into his analysis. In Book IV, Ch. XIII, p. 317 when he refers to the long period, he talks about normal expenses of production and says that for these we must refer to the representative rm, not to any particular competitive rm. (Andrews' Lecture Notes IV, 2 December 1968, Andrews and Brunner Archive, LSE: 3; underlining in original) Hence, Andrews refused to see Marshall's contribution to economics as a 'static marginalist equilibrium theory'10 extended to the long run. Marshall's representative rm was rather an industrial concept and 'in e ect he [Marshall] is saying that we must refer the industrial supply curve to industrial conditions and not disaggregate it to purport to get long run marginal cost curves for individual businesses'.

us, the content and methodology of Manufacturing Business was a direct attack on the marginalist theory of the rm.

From Manufacturing Business emerged a series of further work on industries which led, in turn, to the establishment of industrial economics as an academic discipline at Oxford.

Creation of the Journal of Industrial Economics

As a response to the wave of interest in empirical studies of industries described earlier, the rst issue of the Journal of Industrial Economics in 1952 represented the con rmation of industrial economics as a stand-alone discipline. e aim of the Journal was to drive the new discipline forward, not only based upon industrial facts, but also supported by general theoretical assertions:

en in 1952 he [Andrews] founded the Journal of Industrial Economics. Did not mean just the old economics of industries. e new term for a new subject was not established then as it is now … searching about whether we could use the term and not be misunderstood. It is very de nitely not just an "applied" subject. e heart of it is the study of the individual business unit and the decision-making process-investment, pricing, etc.-and also of course the relationships between businesses, which brings in the study of industrial structure, restrictive practices and environment generally. (Talk given by E. Brunner to Frank Friday Group (c.1961), Andrews and Brunner Archive, LSE, Box 529: 1-2) e rst issues of the Journal were largely concerned with industrial matters, often supported by case studies. For instance, the rst article of the rst issue, which was written by Edward Mason, mainly focused on the speci c case of the raw products industry in the United States [START_REF] Mason | An American View of Raw Materials Problems: e Report of the President's Materials Policy Commission[END_REF]). In the same issue, Fred Stones wrote about 'Price Policy in a Nationally Administered Industry' [START_REF] Stones | Price Policy in a Nationally Administered Industry[END_REF] while Robert Shone considered 'Steel Price Policy' [START_REF] Shone | Steel Price Policy[END_REF]). e making of business decisions-particularly those studied by Frank Friday in the rst issue with his paper on ' e Problem of Business Forecasting' [START_REF] Friday | e Problem of Business Forecasting[END_REF]-was also a central issue for the Journal.

The Information-and Knowledge-Based Approaches to the Firm: Contributions by Richardson and Malmgren

Less than a decade after the emergence of the Journal of Industrial Economics, a new trend in the economics of industry and competition emerged with the contributions made by two Oxford economists: George Richardson and Harald Malmgren, both students of John Hicks. e development of the Richardson-Malmgren view of the behaviour of industrial rms was not a coincidence or an unintended consequence of their respective work, but on the contrary was largely in uenced by the intellectual context of Oxford in the late 1950s and early 1960s. Indeed, Richardson and Malmgren were not aware of each other's work until quite late on. e Richardson-Malmgren approach stressed the role of information and knowledge in explaining industrial behaviours. Several remarks can be made about the similarities between both authors.

George Richardson contributed to a new strand of thinking in the eld of industrial economics, stressing the role of information in the evolution of rms. Richardson opened Information and Investment (1960) with a critique of the concept of perfect competition and of the Walrasian general economic equilibrium (GEE) theory.

is stressed the fundamental importance of information and knowledge and led to Richardson's more general critique of the suppression of the co-ordination problem in neoclassical microeconomics. In fact, according to Richardson, informational factors within the rm are essential, mainly because 'no direct connection can exist between objective conditions and purposive activity; the immediate relationship is between beliefs about relevant conditions and planned activities which it may or may not prove impossible to implement' (Richardson 1959: 224;italics in original). us, Richardson's critique of GEE theory was made on the basis of the existence of informational factors. Company performance largely depends on what Richardson called the "market conditions" in the GEE. is includes both "primary" conditions (concerned with technical production possibilities and the current state of consumer preferences) and "secondary conditions" meaning the 'relevant projected activities' of other economic agents (ibid.: 229). As Richardson puts it, '[ rms'] mutual interdependence clearly presents, for entrepreneurs, a barrier to obtaining the necessary secondary information, and, if we are to hope to show how a system can work, we cannot escape the obligation to explain how the barrier is overcome ' (ibid.: 230). is concept of mutual interdependence providing more information to the rm represents the rationale behind the emergence of co-ordination.

Harald Malmgren worked on very similar issues but seems not to have been aware of Richardson's work until he was very far advanced in writing his thesis.11 He spent much time discussing period analysis with his supervisor, John Hicks, after the publication of Value and Capital (1939). In line with Richardson's argument, Malmgren's work on the concept of time periods led to insights regarding the importance of new ows of information in the process of decision-making and located informational factors at the heart of his theory of industries. In fact, Malmgren argued that rms entered into co-operation to stabilise the expectations of managers and could therefore reduce transaction costs (as also argued by Richardson). Malmgren's contribution was original and constituted a rst attempt in paving the way to a new kind of industrial organisation, mainly based on organisational and rm theory. His contributions favoured a multi-disciplinary approach, incorporating ideas not only from economics, but also from organisational theory, game theory and information theory.

e desire for realism expressed by the co-ordination approach to industrial economics does not, however, imply that Richardson's and Malmgren's contributions were purely empirical. On the contrary, their publications remain theoretically grounded, especially regarding their insights on the importance of co-ordination and individual interactions in a decision-making process. A modern theorist of the rm, reading their texts for the rst time, may be tempted to link their examination of decision-making to early game theory in that they consider the importance of strategic interactions. However, this interpretation would be misleading as Richardson and Malmgren made it clear that, even though they were aware of game theory, they did not explicitly employ it in their research.

Richardson's work could not be framed in terms of game theory mainly because, in his framework of investment co-ordination, before "placing their bets", entrepreneurs are rst trying to improve the information they have about other agents, since the actions of others necessarily in uence the outcomes of their own choices (Earl 1998: 18). In other words, Richardson was much more interested in the way that agents search for and collect information than by their strategic choices per se. Similarly, in his DPhil thesis, Malmgren made clear his rejection of game theory. Indeed, he argued that the solution to strategic interactions could only depend on the initial nature of the information available to each competitor and, therefore, on the degree of communication between these competitors. In this respect, Malmgren rejected the "theory of games" approach, 'which ordinarily requires perfect information', and which realistically 'turns out to be a non-zero-sum game' with an indeterminate solution (Malmgren 1961: 253).

e novelty of Richardson's and Malmgren's approaches to Oxford industrial economics was mainly due to their success in providing an alternative framework to GEE theory, which remained predominant at Oxford after having been revived by the publication of Hicks' Value and Capital, twenty years before. e Richardson-Malmgren co-ordination view of the rm, as it stood, also o ered an alternative to contemporary developments in game theory, which were mainly concerned with strategic choices and much less with the nature of information and knowledge at an individual level.

5

Transformation: From Industrial Economics to Industrial Organisation (1979Organisation ( -1991) ) Two Oxford economists in uenced the general orientation of the subject of industrial economics at Oxford during the last part of the twentieth century. Donald Hay's and Derek Morris' roles in Oxford economics are often associated with their landmark textbook, Industrial Economics: eory and Evidence, which is considered as important historical evidence regarding the evolution of industrial economics. e increasing weight of new microeconomics at Oxford is seen as highly in uential in the theoretical generalisations made by the discipline, which moved further away from the hitherto empirical approach to the rm.

A Comparison of the Successive Editions of Industrial Economics: Theory and Evidence-A Shift from Industrial Economics to Industrial Organisation

e rst edition of Hay and Morris' textbook on industrial organisation in 1979 constituted a landmark in the development of the subjects of industrial economics and industrial organisation in the United Kingdom. It served as a basis for teaching even decades after its publication and, as such, exempli ed the orientation taken by the discipline at Oxford and more generally in England. In the Preface of the book, Hay and Morris made the objective of their volume explicit:

In recent years Industrial Economics has emerged as a major area of economic analysis both in terms of theoretical and empirical research and in terms of the number of courses at undergraduate and graduate level. is book, stemming originally from lecture and seminar series at both levels, is designed for those pursuing such courses. (Hay and Morris 1979: v) is rst edition was a standard textbook in which industrial economics was described as a eld in which debates and controversies were ongoing. It tried to provide students with synthetic overviews of di erent approaches. In their Introduction, Hay and Morris outlined the di culty in nding a single de nition of industrial economics and raised two particular matters related to it: the disagreements on both theoretical and empirical issues and the confusion over the scope, concepts and methodology of the subject.12 ey made it clear that industrial economics had emerged as a distinct approach from the traditional theory of the rm. In particular, they claimed that:

First, there is an important sense in which the traditional theory of the rm represents a long detour in the history of the study of rms' economic behaviour. Second, the development of industrial economics can partly be seen as a consequence of several inadequacies and faults of analysis in the theory of the rm. ird, while the latter provides a main foundation for the study of industrial economics, several important in uences from outside have given a totally di erent character to industrial economics. (Ibid.: 4) Nevertheless, while Hay and Morris' approach to rms and industries rejected the standard version of the theory of the rm, their contribution to the subject still constituted a break from the Oxford tradition of industrial economics, as shaped by Andrews and the Journal of Industrial Economics of the 1950s. is judgement is reinforced by comparing the rst edition (1979) with the second edition, published in 1991, under a slightly di erent title, Industrial Economics and Organisation: eory and Evidence. e 1979 edition referred only twice to Andrews' normal cost theory.

e rst reference appeared in a chapter dedicated to "pricing behaviour" in which Manufacturing Business was mentioned only for its empirical evidence on pricing. e book was depicted as a series of empirical investigations, which supported the validity of the cost-pricing principle and tried to incorporate this into a theory of competition. It is clear, however, that in the authors' minds, Andrews' book only constituted new evidence to support the 1939 Hall and Hitch article on pricing. As regards Marshall, Hay and Morris adopted a very cautious approach while arguing that Post-Marshallians had lost a part of Marshall's message in dedicating too much work to purely empirical studies. Finally, they indicated their support for an approach to industrial organisation that would, once again, combine empirical and theoretical aspects, as Marshall had done.

e second edition of Hay and Morris' textbook con rmed these comments. Andrews was again mentioned infrequently, with Manufacturing Business only being considered among various empirical contributions, its theoretical aspects being completely neglected. Marshall received more or less the same treatment as he did in the rst edition. e main di erence between the editions was in the ebbing of controversy within the eld of industrial organisation between 1979 and 1991, mainly because of the increasing domination of game theory in the theory of imperfect competition and strategic interaction. Interestingly, the change in title between the two editions did not merit comment or explanation from the authors. However, the second edition indicated a shift away from empirical studies towards formalisation, which had initially emerged in the United States. Overall, the publication of Hay and Morris' textbook depicted the waning in uence of Marshall and to the empirical approach to the rm.

Developments in Applied Microeconomics and Their Influence on Industrial Organisation (1950s-1980s)

e development of industrial organisation by Hay and Morris was conducted in harmony with advances in general microeconomics. At Oxford, microeconomics was taught at undergraduate level in Philosophy, Politics and Economics (PPE) and at graduate level in the BPhil in Engineering Science and Economics and in the BPhil in Economics. e rst microeconomics lecture addressed to PPE students was introduced as late as 1968 and was taught by Peter Oppenheimer. Before then, studies of rms' behaviour were encapsulated in the " eory of the Firm", "Structures of Industry", "Industrial Organisation", " eory of Prices", "Welfare Economics" and the " eory of Demand". 13 From 1968, microeconomic theory was taught by Oppenheimer and George Richardson to PPE students; by Christopher Allsopp, Nicholas Dimsdale and Laurie Baragwanath to BPhil students in Engineering Science and Economics; and by Richardson, James Mirrlees, Max Corden and occasionally by John Hicks to BPhil students in Economics. 14 e rst lectures in the theory of games were introduced in the Hilary term of 1954. is increasing amount of teaching of microeconomics, applied microeconomics and game theory con rms the new orientation taken by industrial organisation, suggested by the successive editions of Hay and Morris' textbook, and re ected a general tendency in the mid-1970s and early 1980s towards developing more deductive and normative approaches in the discipline.

When Andrews and Brunner left Oxford in 1968, David Stout was left in charge of the BPhil seminar on industrial economics before he, in turn, left Oxford in the early 1970s. Derek Morris then became its organiser and pushed the seminar in a di erent direction. For instance, in 1974 the seven weeks of the rst term were structured as follows:

1.

e principles and signi cance of company accounts 2.

e pro t-maximising hypothesis 3. Price formation 4. Game theory and oligopoly 5. Mergers and concentration 6.

e organisational structure of the modern corporation 7. Multinational corporations A closer look at the reading lists for each topic shows that Week 2 includes references to [START_REF] Berle | e Modern Corporation and Private Property[END_REF], [START_REF] Marris | e Economic eory of 'Managerial' Capitalism[END_REF] and [START_REF] Williamson | e Economics of Discretionary Behaviour: Managerial Objectives in a eory of the Firm[END_REF], as contributions to the extension of the pro t-maximising hypothesis without referring at all to Hall and Hitch or to any work made by the OERG at Oxford. It has been argued elsewhere that Marris and Williamson developed approaches to the rm supported by concepts of optimum and equilibrium, far from Andrews' interpretation of industrial economics [START_REF] Arena | Post-Marshallian Approaches to Firms and Competition: e Cases of J. Robinson[END_REF].

As a comparison with the rst-term topics examined by the seminar, the programme for the Michaelmas term of 1957 was concerned with industrial economics as de ned by Andrews:

1. Pro ts in accountancy and in economic theory 2. Empirical cost functions and their theoretical implications 3. Competition and the conditions of entry 4. Competition and the structure of markets 5.

e growth of the rm and the concentration of industry 6. Oligopolies is Oxford orientation could be contextualised within a broader picture. e introduction of the theory of contestable markets by [START_REF] Baumol | Contestable Markets and the eory of Industrial Structure[END_REF] was indeed considered a generalisation of the theory of perfectly competitive markets in which the determination of industry structure was made endogenous. According to Baumol, 'in the limiting case of perfect contestability, oligopolistic structure and behaviour are freed entirely from their previous dependence on the conjectural variations of incumbents and, instead, these are L. Arena generally determined uniquely … by the pressures of potential competition' (Baumol 1982: 2;italics in original).

e concept of "potential competition" that is central to the theory of contestable markets had already been referred to by Marshall and Walras before it was systematised by Baumol and his colleagues as the key to their theory of industrial structures. e new research programme in industrial organisation also highlighted the need to understand economics not only as the production of theoretical knowledge but also as policy. e formulation of a competition policy as needing to maintain the threat of potential competitors in order to ensure the e ciency of new entries/exits contrasted with the structureconduct-performance paradigm which was clearly more concerned with the stabilisation of structures through insiders' behaviour. is new line of reasoning enlarged the validity conditions of theories of perfectly competitive markets questioned by some industrial economists, especially with the introduction of multi-product rms based on di erentiation.

In addition, new models of strategic interaction were also seen as an alternative to standard microeconomics and as a contribution to industrial organisation, as shown in [START_REF] Hay | Industrial Economics and Organization: eory and Evidence[END_REF]. Price strategies were now studied in the context of duopolies and oligopolies with the help of emerging modelling techniques.

ese issues in strategic interaction-developed with an intensive use of game theory-corresponded to a new and substantial methodological element in industrial organisation.

e theoretical and empirical orientation taken by the Journal of Industrial Economics after Brunner had left the Editorial Board was also indicative of the increasing interest in applied microeconomics and game theory. In particular, when Hay took over the Editorship, he made a speci c e ort to align the Journal's aims and objectives with research in game theory. He was convinced that such a reorientation was the only strategy that would help to keep the Journal successful within the academic community. 15 As a result, the issues published from the beginning of the 1980s became increasingly formalised and less and less empirical in Andrews' initial sense of industrial economics.

Conclusion

Until the beginning of the twentieth century, economists were mostly focused on the theory of value and of income distribution whereas studies of rms and industries were conducted within the framework of price theory. However, the evolution of management techniques led scholars to shift their attention towards the internal organisation of the rm and industrial dynamics. From a theoretical perspective, the separation of the theory of the rm from the theory of value resulted from the Cost Controversy in Cambridge accompanied by a new interpretation of the work of Alfred Marshall. is chapter has shown that Oxford's contribution to industrial economics is not attributable to any speci c school of thought that it produced, as could be argued was the case for Cambridge. e lack of emblematic gures at Oxford and/or the relative isolation of successive individuals elected to the Drummond Chair (in particular Edgeworth and Macgregor) did not produce a uni ed body of knowledge until, perhaps, the innovations made by the OERG which, despite its heterogeneous interests, still paved the way for a more homogenous methodology and theoretical orientation. Hence, although industrial economics today does not resemble the discipline as Philip Andrews knew it, his legacy was to institutionally establish it at Oxford.

Oxford took a unique approach to industrial economics due to the OERG and the empirical analysis of the rm, this a reaction to the theory of imperfect competition popularised at Cambridge in the 1930s. e methodology, in particular the use of questionnaires, was at the time speci c to Oxford. e development of industrial economics at Oxford was also strongly in uenced by George Richardson and Harald Malmgren who focused on information and knowledge between rms and contributed to a deeper understanding of the organisation of rms. In this way, they shed light on the emergence of more recent knowledge-based economies. e modern evolutionary theory of the rm is based on the concepts of capabilities and competences as proposed by Richardson and Malmgren which views the rm as a complex and organised set of competences and resources that is continuously faced with uncertainty. Later on, two key players in the development of industrial economics at Oxford were Donald Hay and Derek Morris, whose Industrial Economics: eory and Evidence served as a foundation for the teaching of the subject and which represented an important manifestation of the direction taken by the discipline at the University.

Finally, industrial economics was shaped by the institutions of Oxford itself. e BPhil seminar on industrial economics and the Journal of Industrial Economics, both introduced by Andrews in the 1950s, exemplify the applied orientation of the discipline based on an empirical methodology. Saying this, Andrews' in uence did later wane with the rise of industrial organisation based on game theory exported from the United States.

  Business was published in 1949 in a very speci c context. It constituted, on the one hand, a reaction to the well-known Cambridge Cost Controversies of the 1920s and 1930s and was, on the other hand, to a large extent a continuation of the famous Hall and Hitch empirical investigation which appeared in 1939. e Cost Controversies questioned the theoretical meaning of Marshall's work and especially Pigou's speci c interpretation of it.

  to the development of industrial economics at Oxford went one step further after the publication of Manufacturing Business with his creation of the Journal of Industrial Economics in 1952. In parallel, further developments in the discipline in terms of information-and knowledge-based approaches to the analysis of the behaviour of industrial rms helped to propel Oxford's importance in the eld.

  . e Group was created in 1936 and was initially led by Sir Hubert Henderson who was the sole Professor of Economics at Oxford. e earliest members were all economists and teaching fellows at Oxford at the time. ey are listed in Appendix 1 at the end of this chapter. Andrews, who came to Oxford in 1937 as a member of the research sta , became Secretary of the OERG. A couple of years after the establishment of the rst Sub-Faculty in Economics at Oxford in 1932, All Souls College o ered a Readership in Economic Statistics to promote systematic empirical work in social studies.

s Contributions to Industrial Economics from the 1920s…

	(continued) Name and affiliation Edward Radice 1936-? Years in the group L. Arena (continued) 3 Oxford't2.28	Main research interests Reasons for departure Monetary economics;	t1.1 t1.47
	t2.29				macroeconomics,	t1.2 t1.48
	t2.30				especially savings	t1.3 t1.49
	t2.31				issues		t1.4 t1.50
	t2.32	Richard Sayers	1936-1947		British monetary	Cassel Professor of	t1.5 t1.51
	t2.33	(Pembroke)			economics	Economics at LSE,	t1.6 t1.52
	t2.34						1947-1968	t1.7 t1.53
	t2.35	George Shackle	1936-1939		Macroeconomics,	t1.8 t1.54
	t2.36	(OIS)			especially the theory	t1.9 t1.55
	t2.37				of uncertainty and	t1.10 t1.56
	t2.38				business cycle theory	t1.11 t1.57
	t2.39						t1.12
	t2.40						t1.13
	t2.41						t1.14
	t2.42						t1.15
	t2.43						t1.16
	t2.44						t1.17
	t2.45						t1.18
	t2.46						t1.19
	t2.47						t1.20 t2.1
	t2.48						t1.21 t2.2
	t2.49						t1.22 t2.3
	t2.50						t1.23 t2.4
	t2.51						t1.24 t2.5
	t2.52						t1.25 t2.6
	t2.53						t1.26 t2.7
	t2.54						t1.27 t2.8
	t2.55						t1.28 t2.9
	t2.56						t1.29 t2.10
	t2.57						t1.30 t2.11
							t1.31 t2.12
							t1.32 t2.13
							t1.33 t2.14
							t1.34 t2.15
							t1.35 t2.16
							t1.36 t2.17
							t1.37 t2.18
							t1.38 t2.19
							t1.39 t2.20
							t1.40 t2.21
							t1.41 t2.22
						Development economics	t1.42 t2.23
							t1.43 t2.24
		Hubert Henderson (All	1935-1959	Statistics and applied economics	t1.44 t2.25
		Souls)					t1.45 t2.26
		John Hicks (All Souls)	1950-1965	Trade cycle theory	t1.46 t2.27
							(continued)

Oxford's Contributions to Industrial Economics from the 1920s…

For example, in 1937, the "Current Notes" section in the Journal of the Royal Statistical Society states that 'Middle-aged students of industrial combinations will remember the publication in 1906 of an important work on that subject by D.H. Macgregor … It has been for some time out of print, and we are indebted to the London School of Economics and Political Science for securing its re-issue as the rst of a series of reprints of scarce works on political economy … Even after thirty years it will repay perusal, for it di ers from the usual books con ned to description or denunciation and is a dispassionate study of the economic aspects of the movement'(Current Notes 1937: 144-145). 3 Oxford's Contributions to Industrial Economics from the 1920s…

To a large extent, therefore, Andrews' innovations were analytically rooted. In this context, some years after the publication of Manufacturing Business, he wrote: 'As I interpret Marshall, the root cause of his treatment of long run supply at the level of the individual rm is that he thinks of falling, rising or constant cost as being equally conceivable conditions in what he wishes to analyse as competitive industries and-as so many passages show-he thinks of manufacturing industry as typically showing falling average costs as expanded outputs are maintained in the long run' (Andrews' Lecture Notes IV, 2 December 1968, Andrews and Brunner Archive, LSE: 2).L. Arena

Or 'SMET', as Andrews referred to the marginalist approach in his Lecture Notes. 3 Oxford's Contributions to Industrial Economics from the 1920s…

L. Arena

Malmgren (private correspondence, 2008). 3 Oxford's Contributions to Industrial Economics from the 1920s…

'First, as in several areas of economics, there is often disagreement on both the theoretical and empirical issues involved … Second, and more serious, there is both confusion and con ict over the three main elements of this (or any) discipline-its scope or purpose, its concepts and its methodology' (ibid.: 3).L. Arena

Oral conversation between Brunner and Hay mentioned in an interview with Hay on 18 July 2006, Social Sciences Faculty, University of Oxford.3 Oxford's Contributions to Industrial Economics from the 1920s…

It can be deleted in the text. Thank you.