Valerio Cerretano

Keywords: Central bank, industrial policy, interwar, public shareholding JEL : E5, L5, N14, N44, N84

This article describes how the Trade Facilities Act (TFA) and the liquidation of certain governmentowned assets spurred the industrial intervention of the Bank of England in the 1920s. What emerges is a much greater role of the Treasury in the Bank of England's industrial intervention than has been hitherto suggested. This essay places the theme of the Bank of England's industrial intervention within the broader discussions about Treasury history and Britain's post-war reconstruction, and refines the argument that the original involvement of the Bank of England with industry merely represented an extension of its pre-war operations of branch banking and its duties as a central bank.

RESUME

Cet article décrit comment le Trade Facilities Act (TFA) et la liquidation d'actifs possédées par l'Etat conduisirent à une intervention de la Banque d'Angleterre dans l'industrie dans les années 1920. Y apparaît un rôle beaucoup plus grand du Trésor dans les interventions industrielles de la Banque d'Angleterre que ce que suggérait l'historiographie jusqu'à présent. Cet article montre que ces interventions représentent à la fois la prolongation des opérations de banque de réseau que la Banque menait avant-guerre et la prise en compte de ses obligations de banque centrale.

The Treasury, Britain's post-war reconstruction and the industrial intervention of the Bank of England, 1921-1929 Valerio Cerretano *

The involvement of the Bank of England with industry has been, in general, well documented. 1 There is a well-established argument that the Bank of England was originally drawn into industrial intervention in response to exceptional problems that impinged, however, upon its traditional responsibilities. The Bank of England's involvement with the giant armament group Armstrong and the metallurgical industry -thus the argument goes -can been regarded as an extension of its pre-war practice of combining commercial banking business with its duties as a central bank. 2 Bank of England intervention into the cotton trade, pursued to avoid a major banking collapse in Lancashire, had the double purpose to aid cotton spinning firms as well as their dangerously illiquid bankers. As Sayers seemed to point out, it was the scale of intervention that marked a radical departure from pre-war central banking practice. 3 Bowden and Collins have forcefully argued that the duties of the Bank of England as a central bank were never clear-cut, and changed as a result of the different 'pressure of circumstances' and of the different interplay of Yet, overall, previous scholarship tends not to lend much weight to the Treasury as a possible factor at work behind the increasing intervention of the Bank of England in industry. Howson, Burke, Booth, Peden, and -although from a different perspective -Daunton have demonstrated that the Treasury -whose overarching preoccupation from1919 until the mid-1920s was the restoration of the gold standard at pre-war parity, a goal which implied, among other things, a tight monetary policy and a dramatic reduction of public spending -extended considerably its functions from the end of the war throughout the inter-war period. Then, the question is: did the Treasury and its postwar strategy of financial restoration add to what Bowden and Collins term the 'pressure of circumstances' in changing the mandate and central banking practice of the Bank of England? This essay concludes that the Treasury and post-war financial restoration contributed significantly to shape the form and direction of the Bank of England's early industrial intervention, which did not stem from its ordinary functions alone. Reduction of public expenditure, dear money, the tax reform, mass-unemployment and the restoration of the pre-war financial system in the first half of the 1920s -it is argued here -all formed the background in which the Bank of England began to get involved with industry. These points will be made more concrete when charting the evolution of the TFA and of the 'Securities Trust'(SET), key aspects in the Bank of England's industrial intervention in the 1920s hitherto neglected by historians. The former represented the most significant reflationary measure that British governments implemented in the 1920s; the latter was a holding company that the Treasury and the Bank of England jointly set up in 1924 to dispose of certain government-owned assets. Although in very differing ways and with a time-lag of a few years, the TFA and SET, as will be seen here, spurred Treasury and Bank of England industrial intervention.

The debate about Treasury history will be here of particular significance in explaining the motives of the Bank of England's early involvement with industry. 13 Treasury and monetary historians agree that the Bank of England enjoyed undisputed independence from the Treasury until 13 Peden; The Treasury, 73-189; Kynaston 'The Bank'; Burk, 'The Treasury' 1914, and that the war, while prompting closer relations between the Treasury and the City, marked a shift in power from the Bank of England to the Treasury. 14 Kynaston concludes that the Bank of England only retained 'operational independence' from the Treasury. 15 He also suggests that the crossover, which would have been inconceivable until 1914, of certain officials (notably Otto E.

Niemeyer, Sir Basil Blackett and Sir Joshiah Stamp) from the Treasury to the Bank of England in the latter half of the 1920s testifies to this shift in power. 16 As will be seen here, the role that these officials, whose grip of Treasury machinery grew with government instability in the 1920s, 17 played in the involvement of the Bank of England with industry can hardly be exaggerated. This essay thus analyses the involvement of the Bank of England with industry within the context of its changing relationship with the Treasury and against the background of Britain's postwar reconstruction. Historians tend to be mainly preoccupied with the adequacy and consistency of the Bank of England's intervention in industry in the 1930s. Insofar as it focuses on the 1920s and adds new material to the broader subject matter of Britain's post-war reconstruction, this essay takes a different perspective from current debate. How the TFA stimulated the industrial intervention of the Bank of England and the circumstances leading to the launch of SET are described in the first two sections. The remainder examines the operations of SET. This article concludes by exploring the implications for the debates about Britain's post-war reconstruction and the Bank of England's industrial intervention.

I

Table 1 and 2 estimate the industrial investments of the Bank of England in the inter-war era. While providing some insights into the size and timing of the Bank of England's industrial intervention, these tables suggest that intervention was not triggered by branch banking and bank rescuing operations alone. Alongside a number of government-owned securities held by SET, the Bank of 14 Peden,The Treasury,75,79;Kynaston,'The Bank', Id, 29 16 Id, 25. On these officials, see Sayers, The Bank, II, 621; Vickers Archives, Cambridge University Library [Vickers A] 'Royal Commission Papers ',folder 43,vol57,443,9;Peden,The Treasury,Daunton,Just Taxes,The Treasury,133 6 6 England accumulated a host of debt issues guaranteed by the Treasury under the TFA -in particular, the debt issues of 'North British Aluminium Co.Ltd', the 'Stanton Iron Works' and the 'North Wales Power Co.Ltd' exhibited in Table 2. These deserve some attention here.

As will soon be seen, the TFA enabled certain firms to borrow under Treasury guarantee, and triggered Treasury and Bank of England intervention in industry when, by the late 1920s, those firms became unable to repay their guaranteed debt. The TFA has only received a passing mention in most histories of Britain's inter-war economic policy. Before dwelling on the question as to how it spurred the industrial intervention of the Bank of England and the Treasury, it is, therefore, necessary briefly to sketch its history.

The TFA followed from a proposal that Hilton Young, the financial secretary to the Treasury, put forward during the discussions which took place at Gairloch, Scotland, late in September 1921, when the coalition government led by Lloyd George devised a package of measures to relieve unemployment, which had grown dramatically since April 1920 as a result of both credit stringency and the post-war slump. 18 The Young proposal sought to reconcile the mounting request for government intervention with the orthodox view of the Treasury. 19 Two elements characterised it. The first was that the state should assist industry without increasing monetary circulation, held responsible, in Treasury's mind, for mass-unemployment through price-inflation and increasing monetary wages. 20 The second was that this assistance should only be temporary in order not to hinder the reduction of wages, a precondition to the decrease in unemployment. State assistance, the argument went, 'should enable works to be undertaken' and 'would give by its initiative an impulse towards industrial revival'. This impulse was to come in the form of Treasury guarantees of interest and capital to be raised by the borrower in order to complete major capital works. The rationale was to 18 Peden, 'The Road to and from Gairloch ',and id,The Treasury, On this view see Peden,The Treasury,Daunton,Just Taxes,Burk 'The Treasury',[START_REF] Daunton | [END_REF][START_REF]' 88 Eigner ' Interlocking directorships', 260-1 (Table[END_REF][86][87][88][89][90]Howson,'The Origins',90 20 National Archives (Public Record Office), Kew Gardens, London [P.R.0.], T172/1208 'Draft proposal of commander Hilton Young, 2 October 1921' and Peden, 'The Road to and from Gairloch', 239 speed up large-scale investments, when new hikes in interest rates, and expectation for their reduction, delayed the execution of these capital works. Young's original scheme -it should be stressed -also envisaged a 'National Development Loan' to be raised in order to counteract possible inflation arising from the increased expenditure of the Treasury. 21 The TFA was passed in November 1921 and renewed until 1927. The limits upon guarantees were progressively increased from 25 to 75 million pounds, and, by 1924, also foreign companies and firms operating in the Empire, but making their purchases in Britain, were allowed to borrow under its auspices. 22 Keynes noted in June 1924 that the TFA, although pointing 'the way to a new method of administering an important part of the savings of the public', was not innovative enough, for it did not reduce the risk of enterprise. 'It is -concluded This conclusion does not seem to hold valid when the total debt issues and the projects guaranteed by the Treasury under the TFA (see Table 3 and4) are taken under consideration.

Guaranteed debt issues were executed mostly in three sectors: shipbuilding, shipping and metallurgy (see Table 4). These tables seem to suggest that Treasury guarantees shifted significant financial resources from potentially profitable investments (public debt and new industries) to unprofitable and over-exanded industries (shipbuilding in particular). These also point to the conclusion that the TFA very probably constituted a sine qua non to the survival of certain staple industries in Britain in the 1920s. Given the financial and trade conditions of Britain in that decade, it is very unlikely that, without Treasury guarantees, those sectors would have attracted such a large amount of capital -more than £63 million within four years -via debt issues. As Thomas emphasised, the success of debt issues, unlike equity issues, depended, to a considerable extent, on the reputation of the borrowers, and the reputation of shipping, shipbuilding and metallurgical firms was increasingly prejudiced by spring 1920. 24 P.R.O., T172/1208 'Draft proposal of commander Hilton Young, 2 October 1921' Balfour Committee, Factors, 41-2, 389-90 Collected Writings, XIX, 231, 405 Thomas, The Finance, 16-7, 19 (Table 1.6) The fact that the TFA interfered with the traditional working of the money market, thus representing a major innovation in industrial finance, constituted the main reason why the Bank of England and the Treasury opposed its renewal after 1921. The Bank of England and the Treasury feared that the TFA would reduce the market for government debt, increasing its costs and delaying the return to the gold standard, and that, in addition, it would stimulate their involvement with industry, had the firms enjoying its benefits been unable to pay the interest on guaranteed loans.

Late in 1926, Norman strongly advised against TFA assistance to Beardmore on the grounds that 'the Exchequer can ill afford such guarantees' and that 'in the event of Goverment intervention, it will be difficult to limit the amount to any reasonable figure'. To Norman, receivership was the best solution to Beardmore's difficulties. 25 In a similar vein, Niemeyer argued that the TFA, while shifting resources towards already over-expanded sectors (shipbuilding), would exacerbate the issue of unemployment in the medium term. 26 It then was necessary to resist the pressure from the shipbuilding industry, 27 suggested Niemeyer late in 1924, and to circumscribe the TFA to the finance of more productive sectors, primarily electricity. [START_REF]Memo by Niemeyer to Hipwood and Sainsbury[END_REF] When, however, the Ministry for Transport and the Weir Committee submitted a scheme for the electrification of the country which contemplated a debt issue of £250 million, 125 million of which to be guaranteed by the Treasury, 29 Niemeyer criticised the use of Treasury guarantees on the ground that they would worsen the glut of gilt-edged securities, thus making conversion operations slower and more costly for the government. [START_REF]Electricity' by Niemeyer to Churchill[END_REF] When repealing the TFA in 1927, Churchill deployed the same argument. 31 This probably explains why a 'National Development Loan' was never processed and provides further evidence about the innovative character of the TFA. It should be mentioned at this juncture that during the discussions about the merger between the armament branches of the giant firms Vickers and Armstrong late in 1927, these concerns asked Churchill to reintroduce the TFA to back their move, 32 thus raising the opposition of Niemeyer, who forcefully argued that this request 'would lay us [the Treasury] open to similar demands from all other steel firms'. 33 During 1928 and[START_REF]' 88 Eigner ' Interlocking directorships', 260-1 (Table[END_REF], the reintroduction of the TFA as an instrument to further industrial concentration became matter of intense debate within the government. 34 Norman probably speeded up the launch, late in 1929, of the 'Securities Management Trust' (SMT) -the industrial arm of the Bank of England in the 1930s (see also Table 2) -to avert its reintroduction. 'There has lately been increasing pressure on the Board of Trade, the Prime Minister and the Treasury for a new Trade Facilities Act -read the minutes of the Treasury Court of the Bank of England -it is doubtful whether a new act can permanently be avoided unless industry is given a reasonable prospect of obtaining from the City such essential moneys as may be needed…the Bank of England will find the money to a moderate extent in support of any approved scheme of rationalisation'. 35 But how did the TFA stimulate the Treasury and the Bank of England's intervention in industry?

To begin with, the Bank of England subscribed to Treasury guaranteed loans. 36 In December 1921, the Treasury and the Bank of England struck an agreement -in the words of Blackett the 'arrangement governing all arrangements'-whereby the latter provided loans guaranteed by the Treasury to certain firms 37 and to 'any others which may seem advisable to treat in a similar In addition, as already mentioned, a number of firms which resorted to the TFA found themselves in financial need by the late 1920s and were unable to repay their guaranteed debt. As a consequence of this, the Bank of England, on behalf of the Treasury, took securities as collateral and became involved with their management. Of these, the shipping and shipbuilding firms of the Kylsant-Royal Mail Group deserve special mention.

The numerous firms of the Kylsant Group -notably those controlled by the Royal Mail Steam Packet Group and White Star Group -borrowed £9.75 million under the TFA between 1921 and1927. 42 This money financed an ambitious program of vertical and horizontal integration, which 38 B.O.E., C40/498 'Blackett to the Governor and Deputy Governor, 28 December 1921' 39 Arthur H. Brandt: £104,000; Pinto Leite& Nephews: £ 248,000; The London Merchant Bank £340,000; A. Ruffer &Son: £1,100,000; Fred Anth&Co.: £620,000; Total: £ 2,412,000. B.O.E., C40/498 'A.H. Trotter (Bank of England) to the Treasury, 4 September 1922' 40 B.O.E., AC 30/441. North British Aluminium Co. 4 ½ Guaranteed Debenture Stock, 1931-55 41 The Treasury and the Bank, while selling a large interest in the Newfoundland undertaking to a U.S. competitor in 1927-8, kept a stake and their representatives (Frater-Taylor for the Bank and Ritchie for the Treasury) in this concern until the late 1930s. P.R.0., T190/59; Vickers A, 'Memorandum by W.A.Whyte to J.D.Scott, 6 March 1958'; B.O.E., G14/64 'Memorandum by E.N. Travers of Branch Office, May 1930'; Sayers,The Bank, II, 315-6. 42 Green and Moss, A Business of National Importance, 93; Sayers, The Bank,I, 328 was formulated by Lord Kylsant when freight rates were still very high. 43 By October 1929, the Kylsant Group became unable to repay its outstanding debt with the Treasury, and, as a consequence, the Bank of England and the Treasury obtained, as collateral, large parcels of securities from the Kylsant Group, as well as becoming increasingly involved with its management, and with the negotiations leading to the reconstruction of the shipping trade in the 1930s. 44

II

The Bank of England intervened in industry in conjunction with the Treasury also to liquidate certain stakes that the government had acquired during the war (see Table 2, the entry SET). The Treasury transferred these assets to the Bank of England after that the Liquidation and Disposal Commission, a body established on the cessation of the Ministry of Munitions in 1921, failed swiftly to place them on the market. In order to dispose of them, the Bank of England set up SET, which, along the way, financed the reconstruction of these state-owned companies. Financial aid was, however, as temporary as instrumental to the ultimate objectives of the Treasury: to sever their financial ties with the government and to sell them without losses as quickly as possible.

Those assets were not as large as the interest that the Bank of England possessed in the metallurgical and cotton trades. Yet these state-owned assets implied an unforeseeable financial commitment both for the Treasury and the Bank of England, which could not easily be reconciled with the policy objectives of public expenditure reduction and a rapid return to the gold standard. It was, by contrast, very likely to grow, as the 1920-1 slump and credit stringency reduced their value and delayed their liquidation.

The issue of the liquidation of government-owned assets connected with the twin issue of the expansion of the public sector during the First World War. But how much the government spent in company promotion, in absolute terms and relative to the war budget, remains obscure. It is safe to 43 Green and Moss, A Business of National Importance, 41-90, 50 infer, however, that this component of war related expenditure grew remarkably after that early in 1915, under the pressure of vested interests and the impact of the ammunition crisis, Lloyd George removed from the Treasury the power of supervision on this expenditure. 45 The support from the Bank of England lay behind this decision. Discussions about the disposal of government-owned holdings were in full sway between the Bank of England and the Treasury in spring 1923, during which year the Bank of England liquidated a number of holdings (in particular the 'British American Nickel Co.') on behalf of the Treasury and with the assistance of the merchant bank Hambro. 53 After some delay due to the settlement of certain guaranteed debts (the £700 thousand debt of 'Ruffers&Son Co.Ltd' and the £205 thousand debt of the 'London Merchant Bank'), SET was finally incorporated in January 1924.

Table 5 exhibits the assets that SET took from the Disposal and Liquidation Commission, whereas Table 6 and7 1920s. 55 Thirdly, and more generally, these tables seem to support Barstow's view about the development of a 'state capitalism' in Britain during the war. The government-owned firms operated in shipping and shipbuilding, certain innovative industries (notably oil), and British foreign banking, all sectors which benefited from war and post-war developments. As will be seen later, the 'commercial gentlemen who have got a footing' in the Ministry of Munitions, in particular armament businessmen, played a role in their launch.

But why did not the Treasury set up an ad hoc state-owned agency for the disposal of those assets? Why did it involve the Bank of England with this task?

The disposal of the state-owned assets implied 'a continuous policy', 56 namely investments to be distributed over a relatively long period. An organisation was required to fulfil this task, and to guard off the Treasury from company promoters, a major preoccupation for the Treasury in the early 1920s. As will be seen later, these were largely responsible for the involvement of the government with industry during and immediately after the First World War. When presenting the case for SET, Norman inferred that the inducement of the Treasury in the setting up of a holding company was, besides 'the cash to be obtained...the fact that you [the Treasury] could no longer be worried by slippery dealers.' 57 However, in 1923, Norman proposed the creation of an agency for the liquidation of the government-owned assets. 58 This was to be controlled by the Treasury, through a small deferred capital, and financed by the Bank of England or the public via guaranteed debt issues. However, just as Norman secured the Treasury Court's approval to this scheme, Niemeyer rejected any formal connection with SET on political grounds. The Treasury feared to raise further criticism from the Parliament and the press, fuelled, as will be seen later, by the enquiries of the 'Select Committee on 54 B.O.E., G10/6 'SET: Balance Sheets and Revenue Accounts, 1928'. 55 SET's realisations resumed in 1934 (see Tables 6 and7) and followed the speculative waves in equity shares which took place in Britain in the inter-war period (in 1919-20; in 1927-9; and after 1934). Thomas, The Finance, 16-7 ( Fig. 1.5), 19 (Fig. 1 National Expenditures' in 1918-9. 59 Mounting demands for the reduction of expenditure and taxation formed the background to these developments: these made any formal link between the Treasury and SET politically unviable. As a result of this, the Treasury decided that the Bank of England would wholly control it. 60 One reason as to why the Treasury entrusted the Bank of England with the disposal of the government-owned industrial assets is clearly to be found in the relations of the latter with the City, crucial to their successful liquidation. Probably, the Treasury involved the Bank of England with this task also because of the latter's funds and reserves. As will be seen later, the disposal of those assets was an expensive business, whereas Treasury resources were increasingly limited. How large the funds of the Bank of England were is unclear, for it did not publish balance sheets and profitand-loss accounts in the time-period under consideration. However, as the 'Select Committee on National Expenditures' emphasised, the profits of the Bank of England -a joint-stock banking company until its nationalisation in 1946 -grew remarkably during the war, and very likely, as interest rates went up and public debt grew, also in the subsequent period. 61 When presenting the case for SMT to the directors of the Bank of England in November 1929, Norman spelled out that 'the Bank of England through no particular merit of their own has accumulated large reserves, and that in his opinion the Directors were not so much directors of a Banking concern as Trustees of a National Institution on behalf of the public'. 62 Large reserves and increasing public criticism, in other words, seemed to justify the Bank of England's assistance to industry.

III

Through SET, the Bank of England and the Treasury assisted the post-war reconstruction of the rayon-maker British Celanese. This reconstruction, whose positive outcome could not at all be taken for granted in the early 1920s, revolved around the attempt to market acetate, a cellulose compound, in the form of textile filaments, a goal which posed tremendous financial problems. In the 1920s, British Celanese became a world's leading producer of acetate yarn, a high-tech product.

Inasmuch as they financed the diversification of British Celanese, the Bank of England and the Treasury contributed to the rapid development of this innovative sector in Britain.

Before the First World War, acetate was employed as a varnish for aeroplanes, and was produced on a small scale in Germany, France and Switzerland. In Britain, its manufacture began in 1916, after that certain chemical and armament businessmen, seizing the opportunities offered by the loss of shipping space and the expansion of aviation, launched the 'British Cellulose and Chemical Manufacturing Co.' (British Celanese by 1923), in conjunction with the Swiss chemists Henry and Camille Dreyfus, the owners of the acetate patents on the basis of which British Celanese operated. 63 Coleman spelled out that British Celanese constituted not only a shining example of technological 'spin off', but also an instance of war time relations between business and government. 64 A sub-committee of the 'Select Committee on National Expenditure' threw much light on those relations in 1918-9. 65 The sub-committee revealed that the main promoters of British Celanese, 66 in particular Colonel Morden and Trevor Dawson, while speculating on the company's shares, deployed their friendly relations with the Chancellor of the Exchequer Reginald McKenna, the Canadian Minister of Militia Hughes and the technical staff of the various war departments to obtain tax breaks (in particular on the excess-duty profit), the monopoly over the manufacture of acetate, as well as certain chemical compounds (synthetic acetic acid), and starting capital to launch British Celanese.

The sub-committee also emphasised that other potential producers of acetate, primarily Courtaulds 63 and United Alkali Co, were not even asked to tender, whereas British Celanese had been unable to supply the agreed quantity of acetate, which the Ministry of Munitions continued to import it from France until the end of the war. In addition, the Dreyfus brothers and their British associatesalleged the sub-committee -employed public money to enter into the rayon industry and to set subsidiaries abroad. 67 The fact that the idea of spinning acetate was put forward before the First World War and that British Celanese set up subsidiaries in Canada and in the USA in 1918-9 seemed to substantiate these allegations. However, the moral argument was probably over-emphasised by the press and the Parliament. As the sub-committee pointed out, there was 'neither corruption nor favouritism' in the setting up of British Celanese. 68 Erroneous decisions and waste found their origins in the acceleration of the submarine war which called for hasty decisions, and, more broadly, in the lack of co-ordination between the various war departments. The government extended its economic powers unsystematically through the war departments and ad hoc committees (238 in 1918), where industrialists, who were recruited for their particular skills, could shape the goals and the direction of war planning 69 . Coleman maintained that Robson and Trevor Dawson launched British Celanese to provide their firms with acetate. It is more likely, however, that British Celanese fell within their strategy of post-war diversification. British Celanese doubtless represented an instance of 'state capitalism'. Its history, however, suggests that armament and chemical industrialists exploited their role within war planning and promoted British Celanese, more than to 're-equip the country on the most modern lines', to smooth post-war diversification, their main preoccupation since 1915.

Out of a total investment of £3.7 million, the Ministry of Munitions provided £1.45 million to British Celanese. 70 The Treasury transmuted this credit into a participation when, in 1920, British Celanese became a public company with a paid up capital of £6 million. 71 Treasury refused to grant another loan to British Celanese, and surrendered a nominal participation of £950 thousand at £500 thousand (it thus retained a stake of £500 thousand) to the Belgian financier and company promoter Alfred Lowenstein 72 and his Canadian associate James Dunn.

With three officials (William Alexander, Josiah Stamp and Philip Henriques) on the company's board, the Treasury remained in the voting pool of British Celanese until 1927. The Bank of England took up the bulk of the British Celanese £700 thousand debt bonds in 1923, and subscribed to a further debt issue of £300 thousand entirely in 1925. 73 Early in January 1924, Norman pressed the Bank of England to keep its stake in British Celanese arguing that 'the company has a futureprobably a great future'. 74 This seems to indicate that there was an industrial strategy behind this participation. However, it was the Treasury, and not the Bank of England, the main actor behind this strategy. Norman monitored the reconstruction of British Celanese in conjunction with Stamp and Henriques, who supported the strategy of Henry Dreyfus, managing director of the company. 75 'I do not wish or intend to be mixed up in Celanese affairs at all -wrote Norman to Henriques late in 1924 -as far as I am concerned nothing is being done or will be done unless you [the Treasury] wish it'. 76 Time and again, the Treasury emphasised the impact of British Celanese on employment. 77 As Niemeyer pointed out to Churchill in September 1926, the main preoccupation of the Treasury was, however, to sell its stake in British Celanese at a reasonable price. 78 The aid from the Treasury and the Bank of England to British Celanese came at a critical stage in the post-war diversification of the company, whose reconstruction was put in jeopardy by a major confrontation between Lowenstein and the Anglo-Swiss interests which revolved around the branching out of British Celanese into weaving and in the chemical business. In 1925, the Treasury and the Bank of England helped oust Lowenstein, thus allowing British Celanese to continue to 72 On Lowenstein see 'The Economist', 12 May 1928, 106, 969 Churchill, 30 August 1926' and 'Niemeyer to Churchill, 24 September 1926' invest in its weaving department, whose growth Stamp and Dreyfus considered a sine qua non to stimulate the use of acetate yarn among weavers. 79 Critical to these developments was the loan of £300 thousand that the Bank of England processed in October 1925, with which British Celanese completed its weaving department. [START_REF]Henriques to Norman[END_REF] The Bank of England finally sold its stake in British Celanese at £500 thousand to the Dreyfus brothers in 1927. [START_REF]Norman to Niemeyer, 5 May 1927' 82 Between 1927 and 1928, the amounted to £4 million[END_REF] British Celanese continued to execute enormous investments until the early 1930s. 82 Helped by the import duties on rayon and silk that the Chancellor of the Exchequer Winston Churchill imposed in 1925, British Celanese began to make profits (from 1927 and throughout the slump), although it paid dividends only by the late 1930s. This is not necessarily indicative, however, of an unsound investment policy. The success of British Celanese must rather be found in its innovative strategy of integration between rayon, textiles and chemicals, as well as in the impact that the company made on the British rayon industry.

These developments beg the question as to whether Churchill imposed the import duty on rayon to smooth the reconstruction of British Celanese.

Tolliday argued that this tariff, as with government intervention in the acetate business, was 'a matter of national strategic importance'. 83 Whether, however, there was a clear industrial vision behind this intervention, as already seen, is debatable. Churchill imposed the rayon tariff for revenue purposes: the tax reform and the introduction of a pension system, as well as the erroneous assumption that rayon as with silk was a luxury, formed its background. [START_REF] Daunton | [END_REF] The import duty, moreover, was accompanied by a duty on domestic consumption (the excise rayon duty), a fact which confirms that its primary purpose was not to shelter this trade. On its part, the Treasury granted, in the words of Barstow, no 'exceptional treatment' to British Celanese, partly to avert criticism from Parliament and Courtaulds, partly as a result of its laissez-faire approach when it came to industrial matters. [START_REF]' 88 Eigner ' Interlocking directorships', 260-1 (Table[END_REF] Little wonder that in 1929 the Treasury rejected a request from Courtaulds to eliminate the excise duty. 86 The implication of Courtaulds' proposal was to leave the import duty unaltered, and this -argued the Treasury -would have implied a measure of protection which was impossible to defend in Parliament and which was far in excess of anything hitherto granted to industries which were sheltered under the Safeguarding of Industries Act of 1921. 87

IV

While supporting the diversification of British Celanese, the Bank of England and the Treasury, through the medium of SET, reconstructed a number of banks operating in Central and Eastern Europe, notably the 'Anglo-Austrian Bank' (AAB) and the 'Banque des Pays de l'Europe Centrale' (BEC).

Established in the last quarter of the 19 th century by British and French interests, these universal banks expanded into the rapidly growing Austrian and Czechoslovakian industry from the 1890s. 88 During the First World War, their London offices borrowed from the Treasury and the Bank of England. According to Teichova, the Bank of England pursued their reconstruction not simply to recollect their loans, but also to facilitate the penetration of certain British interests into the banking, trade and industrial systems of the former Habsburg Empire. 89 These interests invested there for a number of reasons: to supplant the Germans, to share in the growth of local industry, to control newly-established competitors, and, above all, to secure large engineering contracts (railways). As will be seen later, this represented a potentially vast outlet for the armament business, now under reconstruction.

The history of SET confirms that the Bank of England and the Treasury facilitated this strategy of penetration. Teichova, however, does not explain why the Bank of England began to sell these banks and their properties to national interests by the mid-1920s. Evidence suggests that the Bank of England reconstructed these banks with the primary purpose of liquidating its participation.

The reconstruction of AAB began once it became clear that this bank would be unable to repay its debt. Soon after 1914, AAB, formally an Austrian bank, was impeded by the Enemy Trading Act to do business. It received, however, £2 million from the Bank of England under the Treasury Act of September 1914, by which foreign banks were allowed to borrow from the Treasury and the Bank of England to meet pre-moratorium acceptances. Early in 1921, AAB owed £1.5 million to the Bank of England. Its sterling assets were insufficient to meet this debt, whereas Austrian inflation and hyperinflation reduced the value of its continental assets, hindering their liquidation and transfer to London. 90 Reconstruction moved along two lines: the British-nationalisation of AAB, as well as the promotion of a Czechoslovak bank -the 'Anglo-Czechoslovak Bank' -in 1922-3, and, then, the sale of its subsidiaries and properties in the former Habsburg Empire by the mid-1920s. As Teichova and Natmeßnig point out, the British nationalisation of AAB and the creation of the 'Anglo-Czechoslovak Bank' came in response to the increasing economic nationalism of the successor states. Teichova and Natmeßnig also emphasise that the reconstruction of AAB followed very closely that of the 'Laenderbank', indebted with the Bank of England during the war and merged a stable influence over the former Habsburg Empire. 91 After that BEC became a French bank and its capital was increased from 64 to 100 million francs, the Bank of England transmuted its credit into debt certificates worth £1.75 million. Although it was controlled by 'Paribas', British interests in BEC were sizeable. 92 The Bank of England transmuted its credit with AAB into an interest of almost £1 million (£375 thousand of ordinary shares and £625 thousand of old ordinary shares). 93 In addition, it subscribed to a debt issue of £700 thousand and made a cash advance of £400 thousand in conjunction with the merchant bank Glynn Mills. In order to avert its acquisition by the Italian-Austrian speculator Castiglioni, the Bank of England made another loan to AAB in 1923, obtaining a further interest (100 thousand preference shares and 375 thousand ordinary shares) as collateral.

Hyperinflation in 1922-3 and the subsequent stabilization crisis in 1924-5 hit the numerous firms that AAB controlled, with effects on its liquidity. The Bank of England succeeded in selling its Austrian properties and branches to the Viennese universal bank 'Credit-Anstalt' and other interests operating in the former Austrian Empire in 1926-7. At the same time, it sought to merger the remainder of AAB with other British foreign banks, notably the 'British Trade Corporation' (BTC), with which AAB merged into AIB in 1927. 94 This merger proved fairly expensive for the Bank of England that took over, in exchange for £934 thousand arising from the liquidation of the Gold Austrian Bonds held by SET (see Table 6), 600 thousand ordinary shares of AIB. In 1928, SET liquidated this holding, but as early as 1929-30 it bought a small interest (80 thousand shares) and advanced £100 thousand to help AIB cover the expenses (£344 thousand) arising from the Norman to Blackett, 13 April 1921', Teichova 'Versailles', 339-41; Natmeßnig, Britische, 233-9 acquisition of BTC. This help came after that the Treasury had refused to lend £300 thousand to AIB. 95 After this operation, however, AIB never prospered (it was finally liquidated in 1951). AIB fell within a strategy which aimed at laying the foundations of industrial credit in Britain and at furthering a major trade offensive in foreign outlets, and which certain armament interests, (Vickers and Armstrong) began to formulate in connection with important interests of the City (Glynn Mills) since the war years. These objectives went hand in hand in the intention of those interests: the heavy industry, which exported the bulk of its output, and certain houses of the City, whose investments had stimulated those exports in the past. Probably, it was no coincidence that the leading figure of AIB was Sir Alexander Herbert Lawrence, representative of Glynn Mills, a director of BEC and chairman of 'Vickers-Armstrong Ltd', the company resulting from the merger of the armament branches of Vickers and Armstrong, which took place -it should be stressed -in concomitance with the launch of AIB.

Along with a number of deposit banks and metallurgical concerns, the same interests (Vickers, Armstrong and Glynn Mills) were behind the launch of BTC in April 1917. 96 BTC was the chosen instrument of these interests to reform industrial finance in Britain, an issue which the Bank of England allegedly sought to tackle by the end of the 1920s.

BTC stemmed from the recommendations of the Jackson Committee in 1915 and of the Farrington Committee in 1916, created by the President of the Board of Trade Walter Runciman 'to consider the best means of British firms after the war as regards financial facilities for trade, particularly with reference to the financing of large overseas contracts'. 97 For this purpose, the Farrington committee, composed, among others, by Blackett and Dudley Docker, suggested the creation of a giant bank with an authorised capital of £ 10 million, £ 1 million of which were issued in 1917. 98 To the mind of its main promoters, Dudley Docker in particular, BTC was to help British firms supplant German competitors in foreign markets and push British trade, by swiftly forming investment syndicates and by issuing large debenture loans. 99 There was in this scheme an overt criticism towards British industrial finance, an echo of which was still traceable in the Balfour and Macmillan reports published in 1927-8 and in 1931 respectively, and an equally overt attempt to reshape it on the German example with the assistance of the state. British joint stock banks, with their large liabilities and small capital -the argument went -did not allow large scale investments for long periods, whereas ordinary issuing houses lacked the technical and industrial expertise to avoid 'hasty issuing' of unproved concerns. German banks, by contrast, deployed this expertise and long-term financing to secure large engineering works and supplant British firms in foreign outlets. 100 The Farrington Committee requested government assistance for BTC in the form of lower interest rates, a subsidy of £25 thousand a year, help in the creation of an information bureau and Experiments of indirect intervention -concluded Bradbury -were more likely to fail and, in this sense, these were more likely to pave the way for the restoration the 'old British sanity' in industrial credit. In broad lines -it should be noted -this was the same argument that Norman deployed when presenting in 1929 the launch of SMT, designed partly to provide some help to industry, largely to deflect demands for the direct involvement of the state with industry. 102 Shortly after its launch, BTC acquired interests in Istanbul, Bulgaria, Roumania and Egypt, but, in effect, it never became the 'industrial bank' envisaged by Docker and Farringdon. BTC was deployed by the Ministry of Munitions to dispose of certain war materials (wooden buildings, timber, motor boats, patrol vessels, building material and so forth) in the Macedonian, Egyptian and Mesopotamian fronts by late 1918. Although not very profitable, their sale seemed to offer a unique opportunity for a trade offensive where Austrian and German interests had long been preponderant. 103 V Because of space limits, the role of the Treasury in the involvement of the Bank of England with the metallurgical and cotton trades, the sectors where the latter came to hold its largest industrial assets, has been omitted here. This involvement, at any rate, has already been well documented. 104 Evidence suggests that the Treasury also influenced the intervention of the Bank of England in these sectors. As already mentioned, the Bank of England got originally involved with the iron and steel industry through Armstrong, a customer of its Newcastle branch since the mid-19 th century.

The Bank of England had increasingly extended its financial provisions (overdraft facilities and short-termloans) to industrial customers before 1914: 105 this fact may suggest that it made loans to Armstrong during the war on a sound commercial basis. Yet the Bank of England gave unlimited financial provisions to Armstrong only after 1915, 106 the year of the ammunition crisis. How the government affected this development is unclear. However, two facts should be stressed here. The first is that, although it may be conceded that the war constituted a profitable business for Armstrong, the concession of unlimited financial provisions represented a major break to the rule of 102 Heim, 'Limits to intervention', 535 103 P.R.O., Mun 4/5739 ' War material in the Near East, by Graham Green, Secretary to the Ministry of Munitions, 24 September 1918', 'Agreement between the Ministry of Munitions and BTC, 13 February 1919' 104 Sayers,The Bank,I,Clay,Lord Norman,Bamberg,'Rationalisation';Tolliday,Business,Central Bank,109 joint stock banking -also followed by the Bank of England -by which resources should not be 'locked up' in one single investment for a long period. 107 Secondly, and more broadly, given the growing weight of both Armstrong and the government within Britain's wartime economy, it would not be entirely surprising that, during the war, the Bank of England invested in Armstrong under government pressure. To sum up, it seems that the factors at work behind the early involvement of the Bank of England with industry were more complex than has been hitherto suggested. The history of the TFA and SET conveys three conclusions in particular. The first is that the Bank of England was not independent from the Treasury when intervening in industry. 'The government, through the Treasury -wrote Norman in 1941 -seeks continuously the advice of the Bank of England, but retains undivided responsibility for major questions of policy…the Bank of England remains the administrative agent' of the government. 110 There was probably some exaggeration in this B.O.E., G14/21 ' Memorandum on Armstrong by the Branch Bank Office, 14 May 1921 ' Thomas, The Finance, 48-54 Ibid, 54 Bamberg, 'Rationalisation', 87 Quoted by Kynaston, 'The Bank', 29 statement. As the vicissitudes of the failed intervention in the film industry in the latter half of 1930s illustrate, the Bank of England was able to avert Treasury interference when intervening in industry. 111 Yet there was some truth in these words: as also the episode of the TFA and SET indicates, the weight that Norman and the rationalisation creed had in Bank of England industrial intervention has probably been overstated by historians. Another conclusion is that this intervention was designed to be temporary. The new evidence is fully consistent with the argument that the Treasury pursued a 'facilitative economy strategy'112 aimed at the re-establishment of a free-market economy in the 1920s. It also shows, however, that deflation, through mass-unemployment (a major motive behind the imposition of the TFA) and reduced public expenditure (a major motive behind the setting up of SET), seems to have prolonged Treasury and Bank of England industrial intervention, which found, however, its roots in the over-expansion of staple industries and of the public sector during the war.

The episode of the TFA and SET is also significant because of the insights it offers into the motives of the Bank of England's intervention in industry in the 1930s. Historians agree that the Bank of England intervened in industry to avoid government intervention and keep relations between the City and industry unaltered. The new evidence -especially the episode of BTC -seems to suggest that the Treasury contributed to shape this defensive strategy, which began to be formulated during the war.

Footnote references

James Bamberg 'The Rationalisation of the British Cotton Industry in the Interwar Period ' Textile History, 19,1 (1988), 83-102 Alan Booth 'Britain in the 1930s: a managed economy? ' Economic History Review, 4 (1987), 499-502 Sue Bowden and Michael Collins 'The Bank of England, industrial regeneration and hire purchase between the wars' Economic History Review, 45, 1(1992), 120-36 Table 1 The Bank of England: Investment in British Government (X) and Industrial (Y) Securities, and their Share of the Bank's Total Assets (Z), 1922-39 (£ ,000) Source: BOE, G10/1 'Memo, Securities T Ltd: Distributions Paid to Shareholders up tp March 1943, 10 June 1943' and G10/6 ' Securities Trust Ltd: Yearly Balance Sheets and Revenue Accounts, 1925-61'

Securities

  38 By this agreement, the Bank of England lent almost £2.5 million to a number of firms in 1922, becoming partially involved with their management.39 On behalf of the Treasury, the Bank of England subscribed to the starting capital (£4 million, 2.5 million of which guaranteed) of the 'North British Aluminium Co.Ltd', which the Treasury launched in conjunction with the 'Lochaber Power Co.' and the 'British Aluminium Co.' in June 1924 to maintain aluminium and hydroelectric works in the Invernesshire, Scotland.40 The Bank of England and the Treasury, in addition, got involved with the launch of the 'Newfounland Power and Paper Co.Ltd', a wood-pulp company that Armstrong, controlled by the Bank of England from the mid-1920s, set up as part of its post-war diversification strategy. Out of £2 million assets, the Newfoundland undertaking in 1925 owed £9 million to the Treasury (£2 million), the Bank of England (£3 million) and the Newfoundland government. These were, in the main, debts guaranteed by the Treasury under the TFA.41

  When, in February 1918, the Ministry of Munitions was about to provide starting capital to electricity generating plants in the Midlands, commented Barstow of the Treasury: This is another instance of what is becoming evidently the policy of the Ministry of Munitions...not to provide for war necessities but to equip the country ... for after-the-war trade. It is a form of 'State Capitalism'. The commercial gentlemen who have got a footing in the ministry...think that they will never get such another opportunity ... to re-equip the country on the most modern lines at the risk of the general taxpayer' (emphasis in original). 46 A few weeks later, the Treasury set up the Surplus Government Property Council and the Surplus Government Disposal Board in conjunction with the Ministry for Reconstruction in order to curtail this expenditure. Although their operations remained circumscribed, owing to the strains between the Treasury and the Minister for Reconstruction Addison, who advocated a greater role for his ministry in post-war reconstruction, 47 these bodies prepared the ground for the Disposal and Liquidation Commission, which the Treasury set up in April 1921 and whose backdrop must be found in the recommendations for a substantial reduction of public and war related expenditure by the Geddes Committee set up in 1919. The Disposal and Liquidation Commission was to dispose of all properties that the Ministry of Munitions acquired, and to recollect the loans that it made, during and immediately after the war within March 1924. Its chairman Sir Howard Frank valued these assets and loans at £59.6 million, 48 £23 million of which were handed by the Disposal and Liquidation Commission to the Treasury in 1923. 49 By late 1922, it became evident, however, that a large proportion of this property, including loans to firms worth about £5.2 million, owing to the poor conditions of certain trades, credit stringency and the limited resources of the Treasury, could not be liquidated within March 1924 without major losses. 50 In summer 1923, three courses were open to the Treasury: the renewal of the Commission after March 1924, the transfer of its work to other government departments or its continuance as a branch of the Treasury. 51 In July 1923, the Treasury decided to continue the work of the commission on its own. 52

  provide some information about their liquidation. These tables convey three conclusions. Firstly, the payment of £2 million which the Bank of England made to the Treasury for the acquisition of those shares, along with an investment of £1 million in the newly-established 'Anglo-International Bank'(AIB) in 1927 and £566 thousand for the acquisition of Beardmore's debt issues in 1929, represented the largest investment that SET conducted until its liquidation in 1961. These figures, of course, exclude the advances that the Bank of England made to the companies that SET controlled. Secondly, SET proved successful until it took over debt certificates of Beardmore from the Treasury in 1929: it liquidated most of its interests by 1928, gaining back the money (£2 million) originally transferred to the Treasury and a bonus of £423 thousand.54 This success is attributable partly to the type of securities held by SET, very different from -and more saleable than -those possessed by SMT, partly to the buoyant money market in the latter half of the50 Id. 51 P.R.O., T 161/114, F. S8933/02 'Disposal and Liquidation Commission: Prospective Position of Disposal as at 31 March 1924, by Sigmund Dannreuter to George Barstow, 23 July 1923' 52 P.R.O., T 161/114, File S8933/02, 'Barstow to S. Dannreuter, 27 July 1923' 53 B.O.E., C40/927 'Norman to Niemeyer, 30 November 1923'

  with the 'Banque Imperiale Royale Priviligée des Pays Austrichienes' into BEC in 1919. A memorandum sent by the French bank 'Paribas' to the Bank of France in June 1919 underlined that the French-nationalisation and the increase in capital of that bank would have helped both French diplomacy to protect its property in the ongoing peace settlements and French corporations to keep 89 Teichova ' Versailles' 339; Natmeßnig 'The Establishment', 96-115 90 P.R.O., T 160/91, 321/1 'Blackett to Norman, 4 April 1921'; ' Niemeyer to Blackett, 17 March 1921'; 'Memorandum on reorganisation of Anglo-Austrian Bank, March-April 1921' ; 'Memorandum on Czechoslovakian branches of the Anglo-AustrianBank, 23 March 1923'; Natmeßnig 'The Establishment', 96-7

91

  Banque de France Archives, Paris [B.D.F.], 001200602/90 ' Projet de Transformation de la Banque I.R.P. des Pays Austrichiens en Banque Française des Pays de l'Europe Centrale, 23 juine 1919' 92 Its directors were: Sir Alexander Lawrence, of Glynn Mills; Michael Spencer Smith and O.E.Niemeyer of the Bank of England ; Erwin Philip of 'Dynamite Nobel' ; Edmond Philippi of 'Coats Paisley' ; Henry Strakosch British representative at the League of Nations. These were also directors of AAB and, later, AIB. B.D.F. 001200602/90 ' Projet de Transformation de la Banque I.R.P. des Pays Austrichiens en Banque Française des Pays de l'Europe Centrale, 23 juine 1919' e 0012006027/84 'Banque des Pays de l'Europe Centrale, 23 mars 1954' ; Teichova 'Versailles', 337 ; Natmeßnig, Britische, 187 ; P.R.O., T 160/91, 321/1 'Memorandum on Czechoslovakian branches of the Anglo-Austrian Bank, 23 March 1923'; B.O.E., G10/6 'Securities Trust: Balance Sheets and Revenue Accounts, financial years 1934 and 1935' 93 B.O.E., G10/6 'Securities Trust: Balance Sheets and Revenue Accounts, financial years 1934 and 1935' 94 P.R.O., T 160/91, 321/1 ' Memorandum by

  privileges in foreign trade (a charter). This proposal attracted the criticism of Parliament and the Treasury, which however accepted to grant the charter in June 1916. The reasons for this change in posture were explained by Bradbury in a long letter to McKenna. 101 Intervention in industrial finance could not be avoided -argued Bradbury -for public opinion, was 'very much in love with German [banking] ideals' while the British economy was about to enter into 'an epoch of grandmotherly direction'. The Treasury -emphasised Bradbury -had thus to back experiments of the sort envisioned by Docker and Farrington to avoid the direct intervention of the state.

  More visible was the intervention of the Treasury in the cotton trade in the early 1920s. A number of Lancashire banks found themselves in financial need as a result of the poor performance of cotton spinning mills to which the former had made large loans by 1919-20. As shown by Bamberg, the Bank of England intervened in the mid-1920s to sever the links between these banks and their cotton customers and to avert bank collapses. Following the recommendations of the Colwyn Committee on post-war banking reconstruction, the Treasury opposed schemes of bank amalgamation which included the Big Five. 108 Bamberg argues that this stood in the way of the Bank of England's rescue of the Lancashire banks. 109 As a result of this agreement, arguably, the Bank of England supplanted the Big Five when promoting, in 1928, the 'Lancashire Cotton Corporation', which took over the cotton assets of the Lancashire banks and which became a major force within the British cotton industry in the 1930s.

  Minutes of the Treasury Court, 29 February 1929'; Clay, Lord Norman, 326 36 For example, 'North Wales Power Co', ' Stanton Iron Works' (see Table 2) 37 See footnote 39

	31 P.R.O., T 160/550, F. 6930/4 'Budget speech, April 1929'
	32 Vickers A, 868, 'Memorandum to the Governor by William Plender, 22 June 1927'; Vickers A, 775, 'Churchill to Norman, 29 June
	1927', 'Norman to Peacock, 30 June 1927'; Vickers A, 561, 'Extract from Vickers-Armstrong Board Minutes, 20 May 1936'
	33 P.R.0., T161/656, 'Notes by Niemeyer to the Churchill, 27 June 1927'
	34 Greaves, Industrial, 40-1, 53.
	35 B.O.E., G 14/55 '

  .6), 24, 27 (Tab.2.1), 28-35 56 B.O.E., C40/928 'Memorandum on SET, October 1926' 57 B.O.E., C40/927 'Norman to Niemeyer, 18 May 1923' 58 Ibid.

  59 B.O.E., C40/928 'Memorandum on SET, October 1926', 'Answers to various points…with the formation of the Securities Trust Ltd, 16 March 1927'; B.O.E., C40/927, Norman to Niemeyer, 26 November 1923' 60 B.O.E., C40/928 'Memorandum on SET, October 1926' 61 P.R.O., WO 32/11296 'Fifth Report of the Select Committee on National Expenditure, 23 July 1918'.

62 B.O.E., G14/55, 'Informal Court Records, 21 November 1929' 16 16

  British Cellulose Equiry Commitee, House of Lords, 27 November 1918' 66 P.R.O., T 1/12365, file 34969/1919 'British Cellulose Enquiry Committee, House of Lords, 27 November 1918'; Coleman 'War Demand', 211 (Table). Besides the Dreyfus brothers, the promoters of British Celanese were Colonel Walter Grant Morden (staff member of the Canadian Minister of Militia Hughes; a director of Prudential Trust, a major shareholder in British Celanese), Sir Arthur Trevor Dawson (Vickers Ltd), Edward Robson ('Pinchin, Johnson & Co.) In 1918, Harry McGowan, later chairman of British Celanse, ('Imperial Chemical Industries' and 'Nobels Explosives Ltd'), and 'The Chilworth Gunpowder Co. Ltd' took stakes in British Celanese.

	Coleman, Courtaulds, II, 180-4, and 'War demand'; Cayez, Rhône-Poulenc,95-6
	64 Coleman, 'War Demand', 205
	65 P.R.O., WO 32/11296 ' British Cellulose Enquiry Committee: Report Presented to Parliament on 31 July 1919'; P.R.O., T1/ 12365,
	34969/1919 '

  In summer 1921, the P.R.O., WO 32/11296 'British Cellulose Enquiry Committee: Report Presented to Parliament on 31 July 1919' Ibid, 14 Clyne 'Winding Down',157, 159-60; French ' The Rise and Fall', 15, 25; Tawney 'The abolition', 149. P.R.O., T 161/ 99 'Philip Henriques to Sir Robert Horne ( Treasury), 5 October 1921' Hague, Economics, 40-45; Thomas, The Finance, 26

  ; B.O.E., C40/942 'Exposé par Alfred Lowenstein, November 1925'; P.R.O., T 161/99 'James Dunn to Churchill, 30 August 1926' 73 B.O.E., C40/942 'Henriques to Norman, 12 October 1925' 74 B.O.E., C40/942 ' Norman to Roney, 15 April 1924' 75 B.O.E., G30/12 'Stamp to Henry Dreyfus, 21 November 1924' and 'Norman to William Leese, 8 December 1924'. 76 B.O.E., G30/12 ' Norman to Henriques, 3 December 1924' 77 P.R.O., T 161/99 'Henriques to Horne, 3 October 1921'; 'Barstow to Baldwin, 6 December 1922' 78 P.R.O., T 161/99 'Dunn to

  95 Vickers A, Royal Commission Papers, Vol 57, folder 57, folio 182 'The Anglo-International Bank, 6 July 1935'; B.O.E., G10/13, Minute Book of SET, 27 August 1930; B.O.E., G10/6, SET: Balance sheet and revenue accounts, financial year 1927. 96 For the full list of shareholders: P.R.O., BT 13/83 'British Trade Corporation, April 1917' 97 P.R.O., T1/12057/20783 'The British Trade Corporation, April 1917'. 98 P.R.O., BT 13/83 'Memorandum on the British Trade Corporation, April 1917'

  99 P.R.O., T1/12057/20783 'Report of the Committee appointed by the Board of Trade to investigate the Question of Financial Facilities for Trade, 31 August 1916'; P.R.O., BT 13/83 'H.Hirst to Sir Edward Holden (City&Midland Bank), 28 June 1916 100 P.R.O., BT 13/83 'General case for an institution such as the British Trade Corporation, April 1917' 101 P.R.O., T1/12057/20783 'Bradbury to the Chancellor of the Exchequer, 29 June 1916'

Table 3

 3 Guarantees under the Trade Facilities Act, Novermber 1921-December 1925 Source: PRO, T 160/184, 'Co-operation in financial assistance to Imperial Development', Memorandum by the Colonial Office to the Board ofTrade, 9 April 1926'

			(£ ,000)
		Domestic	Empire	Foreign		Total
	Public utility	17,782	5,690	4,510	27,982	44.4
	Industry	13,719	2,560	1,635	17,914	28.4
	Shipping	15,231		2,041	17,272	27.2
	Total	46,733	8,250	8,186	63,169	100.0

Table 7

 7 Securities Trust: Dividends and realizations, advances from the Bank of England, interest and dividend paid to theBank of England , 1925-1939

	(£)

The Band of England's Archives, London [B.O.E.]., G14/240 'Minutes of Treasury Court on William Beardmore &Co.Ltd, 3 December 1926'; Clay, Lord Norman, 323

P.R.O., T 160/122 'Niemeyer to W.J. Sainsbury, 22 May 1922'; T 160/ 550, F.6930/1, 'Niemeyer to W.J. Sainsbury, 22 October 1924'

Sayers, The Bank, I, 327-30; Green and Moss, A Business of National Importance, 94-164 Peden, The Treasury, 118-9. Id, 118 P.R.O., RECO 1/157, 'Notes by Burter, 15 May 1918' and ' Notes by Nash, 10 June 1918' P.R.O., T 161/114, File S8933/01 ' Howard Frank to George Barstow, 27 September 1922' P.R.O., T 172/ 1359, 'Final Report of the Disposal and Liquidation Commission, March 1924'

B.O.E, SMT2/35 'Memorandum by Norman to Horace Wilson, 7 June 1937' and SMT2/43 'Notes on a meeting between Skinner, Thompson (Bank of England), Rowe-Dutton, Proctor, Bewley and Rendell (Treasury), Somervell (Board of Trade), 14 February 1941'; Sayers, The Bank, II, 530 fn

Booth 'Britain in the 1930s' , 499 and Peden 'Britain in the 1930s', 538-43

* This work stemmed from an idea of Marcello de Cecco, and was financed by the 'Scuola Normale Superiore di Pisa' and by the RTN "Unifying the European experience" of the European Union, which allowed me to spend three months at the Paris School of Economics during the summer of 2006.

P.S. 69,208 69,208 160,000 160,000 305,919 160,000 320,000 191,250 2,000,000 2,997,169 299,224 160,000 320,000 160,000 1,991,908 2,921,132 299,224 160,000 228,772 160,000 2,016,000 2,863,996 1,099,909 1,554,653 189,234 291,100 191,250 80,000 3,406,146 2,350,000 189,234 291,104 191,250 90,508 3,112,096 189,234 291,104 171,724 90,508 4,616,153 725,000 6,083,723 189,234 164,700 98,334 291,104 144,835 90,508 5,740,049 725,000 7,443,764 189,234 150,060 95,630 291,104 144,835 90,008 3,584,166 616,900 5,270,037 189,234 143,078 65,500 287,206 136,335 89,108 3,000,000 599,811 4,510,264 183,434 44,000 65,500 278,304 126,435 82,908 3,018,615 3,799,196 176,334 65,500 116,035 88,500 3,018,615 3,464,984 68,800 2,030,559 2,099,359 300,000 3,019,122 3,319,122 300,000 3,574,339 3,874,000 300,000 5,621,770 5,921,770


P Delano Ë
email: philippe.delanoe@unice.fr

VARIATIONAL HEURISTICS FOR THE MONGE PROBLEM ON COMPACT MANIFOLDS *

Keywords: optimal transport, minimizing diffeomorphism, c-potential, c-Hessian positivity AMS subject classifications. 53A45, 58D05, 58E99

We consider the Monge optimal transport problem posed on compact manifolds (possibly with boundary) when all data are smooth and the given measures, positive. If a diffeomorphism is stationary for the total cost, it was established that it must admit a potential function. If it realizes a local minimum of the total cost, we show that the c-Hessian of its potential function must be non-negative, positive if we further assume that the cost function c is non degenerate.

1. Introduction and statement of results. The solution of Monge's problem [START_REF] Monge | Mémoire sur la théorie des déblais et remblais[END_REF]] in optimal transportation theory, with a general cost function, has been applied to many questions in various domains tentatively listed in the survey paper [Guillen-McCann 2010], including in cosmology [Brenier et al 2003]. The book [Villani 2009] offers a modern account on the theory (see also [START_REF] Gangbo | The geometry of optimal transportation[END_REF] and references therein). In case data are smooth, manifolds compact, measures positive, maps one-to-one and the solution of Monge's problem unique, the question of the smoothness of that solution was addressed in the landmark paper [START_REF] Ma-Trudinger-Wang | Regularity of potential functions of the optimal transportation problem[END_REF]. In that case, restricting Monge's problem to diffeomorphisms becomes natural. Doing so, the use of differential geometry and the calculus of variations enables one to bypass the general optimal transportation approach and figure out directly some basic features of the solution map. Such a variational heuristics goes back to [START_REF] Appell | Mémoire sur les déblais et remblais des systèmes continus ou discontinus[END_REF]] and was elaborated stepwise in [Evans 1998, Urbas 1998, Brenier et al 2003, Trudinger 2007, Delanoë 2009] (see also [Brenier et al 2003]). In the present note, we take a new step in that elaboration. Specifically, working henceforth in the C ∞ category, we are given a couple of compact connected diffeomorphic manifolds each equipped with a probability volume measure, (M, µ) and (P, ̟), and a cost function c : Ω ⊂ M × P → R defined in a domain Ω projecting onto M and P by the canonical projections. Each manifold, either has no boundary, or it is the closure of a domain contained in some larger manifold. We consider the subset Diff µ,̟ (Ω) of diffeomorphisms from M to P , pushing µ to ̟, with graph lying in Ω (an obvious item missing in [Delanoë 2009]). The pushing condition means for a Borel map ϕ : M → P that, for any continuous function h : P → R, the following equality holds:

P h d̟ = M (h • ϕ) dµ, (1.1)
a property commonly denoted by ϕ # µ = ̟. The existence of diffeomorphisms pushing µ to ̟ is well-known [Moser 1965, Banyaga 1974[START_REF] Dacorogna | On a partial differential equation involving the Jacobian determinant[END_REF]. Setting Ω = {(p, m) ∈ P × M, (m, p) ∈ Ω}, one defines similarly the set Diff ̟,µ ( Ω). We view Diff µ,̟ (Ω) and Diff ̟,µ ( Ω) as manifolds respectively modeled on the Fréchet manifolds Diff ̟ (P ) := Diff ̟,̟ (P × P ) and Diff µ (M ) (see details in [Delanoë 2009, Ebin-Marsden 1970]). Finally, we consider the total cost functional

ϕ ∈ Diff µ,̟ (Ω) → C(ϕ) = M c(m, ϕ(m)) dµ,
and its counterpart ψ ∈ Diff ̟,µ ( Ω) → C(ψ) = P c(ψ(p), p) d̟, which satisfy the identity: C(ϕ) ≡ C(ϕ -1 ). In this setting, the restricted Monge problem consists naturally in minimizing the functional C and the variational heuristics of [Delanoë 2009], in writing down the Euler equation of that functional. It yields the following result:

Proposition 1.1. If ϕ ∈ Diff µ,̟ (Ω) is stationary for C, so is ϕ -1 for C, and there exists two functions f : M → R, f : P → R, defined up to addition of constants, such that each point of the graph of ϕ is stationary for the real function:

(m, p) ∈ Ω → c(m, p) + f (m) + f (p).
Let us call the function f (resp. f ) so determined (up to constant addition), the c-potential of the diffeomorphism ϕ (resp. ϕ -1 ). In [Delanoë 2009], we further assumed on the cost function c the generating condition sometimes called (A1) [START_REF] Ma-Trudinger-Wang | Regularity of potential functions of the optimal transportation problem[END_REF] or bi-twist [START_REF] Kim-Mccann | [END_REF], under which c-potentials completely determine the diffeomorphisms which give rise to them. Let us recall it: setting Ω P m = {p ∈ P, (m, p) ∈ Ω}, Ω M p = {m ∈ M, (m, p) ∈ Ω} and d M (resp. d P ) for the exterior derivative with respect to the argument in the manifold M (resp. P ), we will say that c is generating if, for each (m 0 , p 0 ) ∈ Ω, the maps

p ∈ Ω P m0 → -d M c(m 0 , p) and m ∈ Ω M p0 → -d P c(m, p 0 ) are one-to-one. (1.2)
For the moment, we do not assume this condition and stress that it is not required for the proof of Proposition 1.1, indeed solely based on the Helmholtz lemma. For the reader's convenience, let us indicate the argument (see [Delanoë 2009] for details).

We write δC = 0 with δC = M d P c(m, ϕ(m))(δϕ(ϕ(m)) dµ, where δϕ stands for a variation of the transporting diffeomorphism ϕ which keeps it on the manifold Diff µ,̟ (Ω), that is, a vector field of a special kind on P , evaluated at the image point ϕ(m). Specifically, such a vector field V on P should be: first of all tangential to the boundary of P , if any, so that its flow send P to itself (without crossing ∂P ); moreover, its flow should preserve the volume measure ̟ or, equivalently, V should satisfy: div ̟ V = 0. In other words, the tangent space to Diff µ,̟ (Ω) at ϕ is spanned by the tangential vectors that write V • ϕ with V ∈ ker div ̟ . Here, the symbol div ̟ denotes the divergence operator defined by the identity: P h div ̟ V d̟ ≡ P d P h(V ) d̟ valid for each function h : P → R and each vector field V on P (tangential, as said 1 ). Recalling (1.1), we thus find:

∀V ∈ ker div ̟ , P d P c(ϕ -1 (p), p)(V (p)) d̟ = 0.
Arguing likewise on C, we further get:

∀U ∈ ker div µ , M d M c(m, ϕ(m))(U (m)) dµ = 0.
1 otherwise, a boundary integral should occur, of course

The conclusion of Proposition 1.1 now readily follows from Helmholtz lemma, which we recall:

Lemma 1.2 (Helmholtz). Let (N, ν) be a measured manifold as above. A 1-form α on N satisfies: N α(Z) dν = 0 for each vector field Z ∈ ker div ν (tangential to ∂N if ∂N = ∅) if and only if α is exact.

The variational heuristics presented so far is incomplete since no local minimum condition is expressed yet for the total cost C. It is our aim in the present note to write down that minimum condition and to derive from it further properties of minimizing diffeomorphisms. Before stating our results, we require a notion of c-Hessian.

Definition 1.3. Let F : M → P be a map whose graph lies in Ω and h : M → R a function related to F by the equation d M c(m, F (m)) + dh(m) = 0 on M . The (c, F )-Hessian of h is the covariant symmetric 2-tensor on M , denoted by Hess c,F (f ), intrinsically defined, in any couple of source and target charts (x, y), by:

Hess c,F (h)(x 0 ) := ∂ 2 ∂x i ∂x j [c(x, y 0 ) + h(x)] at x = x 0 , where, if x 0 = x(m 0 ), we have set y 0 = y(F (m 0 )).
If ϕ ∈ Diff µ,̟ (Ω) is stationary for the total cost C, Proposition 1.1 shows that the couple (ϕ, f ), with f the c-potential of ϕ, fulfills the assumption of Definition 1.3. In that case, for simplicity, we will simply speak of the c-Hessian of f and denote it by Hess c (f ). We would define likewise the c-Hessian of the c-potential f of ϕ -1 by the local expression (stiking to the notations used in the preceding definition):

Hess c ( f )(y 0 ) := ∂ 2 ∂y i ∂y j c(x 0 , y) + f (y) at y = y 0 ,
where, if y 0 = y(p 0 ), x 0 = x ϕ -1 (p 0 ) . We are in position to state our first result:

Theorem 1.4. Let ϕ ∈ Diff µ,̟ (Ω) be stationary for the total cost C. The following properties are equivalent:

(i) C admits a local minimum at ϕ;

(ii) the c-potential f of ϕ satisfies: ∀U ∈ ker div µ , M Hess c (f )(U, U ) dµ 0; (iii) the c-potential f of ϕ -1 satisfies: ∀V ∈ ker div ̟ , P Hess c ( f )(V, V ) d̟ 0. Assuming (i), we will infer the pointwise non negativity of the c-Hessians from the conclusions (ii)(iii) of Theorem 1.4, arguing by contradiction with suitable localized divergence free vector fields. The resulting statement goes as follows:

Corollary 1.5. If the total cost C admits a local minimum at ϕ ∈ Diff µ,̟ (Ω), the c-Hessian of the c-potential of ϕ is non negative, and so is that of ϕ -1 .

This corollary itself can be strengthened by making a non degeneracy assumption on the cost function c, called condition (A2) in [Ma- [START_REF] Ma-Trudinger-Wang | Regularity of potential functions of the optimal transportation problem[END_REF], namely:

det(d M d P c) = 0 on Ω. (1.3)
Under that condition, the implicit function theorem provides, for each (m 0 , p 0 ) ∈ Ω, setting α 0 = -d M c(m 0 , p 0 ), neighborhoods U 0 of p 0 in P and W 0 of (m 0 , α 0 ) in T * M , and a map E

(m0,p0) c : W 0 → U 0 such that: α ≡ -d M c m, E (m0,p0) c (m, α) .
Following [START_REF] Kim-Mccann | [END_REF], maps like E (m0,p0) c may be called local c-exponential maps. Observe that, for any (m 1 , p 1 ) close enough to (m 0 , p 0 ) in Ω such that, setting

α 1 = -d M c(m 1 , p 1 ), the point (m 1 , α 1 ) lies in W 0 , the maps E (m0,p0) c and E (m1,p1) c coincide on W 0 ∩ W 1 . If M is simply connected, one can thus extend uniquely the map E (m0,p0) c
to a neighborhood W (m0,α0) of a global section of T * M passing through α 0 at m 0 and call it the (m 0 , p 0 )-determination of the c-exponential map on M . With these notions at hand, we can state the announced strengthened corollary:

Corollary 1.6. If the non degeneracy condition (1.3) holds and C admits a local minimum at ϕ ∈ Diff µ,̟ (Ω), the c-Hessian of the c-potential f of ϕ must be positive definite, and so must be that of ϕ -1 ; in particular, the local minimum of C must be strict. Moreover, the Jacobian equation expressing that ϕ lies in Diff µ,̟ (Ω), written locally in terms of f via a local exponential map, reads as a Monge-Ampère equation of elliptic type.

To understand the second part of the statement, one should be aware that, if the pushing condition (1.1) is satisfied by a diffeomorphism ϕ : M → P , one may use the change of variable p = ϕ(m) in the left-hand integral of (1.1) and infer pointwise, in any couple (x, y) of source and target charts, keeping abusively the notation y = ϕ(x) for the local expression of ϕ, the so-called Jacobian equation alluded to, namely:

d̟ dy (ϕ(x)) det ∂ϕ ∂x (x) = dµ dx (x), (1.4)
where dµ dx stands for the Radon-Nikodym derivative of the push-forward measure x # µ with respect to the Lebesgue measure dx of the chart x, and similarly for d̟ dy . Finally, let us record a uniqueness result easily seen to hold in case the cost function c is generating non degenerate. If so, all local c-exponential maps coincide with the one (just denoted by E c ) globally defined by the generating condition. Summing up the main facts obtained in this note, we can state the following:

Proposition 1. Proof. Indeed, if ϕ ∈ Diff µ,̟ (Ω) is such a minimizer, by Proposition 1.1 it must admit a c-potential f : M → R solving the Monge-Ampère equation obtained from (1.4) by setting ϕ(m) ≡ E c (m, df (m)). Furthermore, from Corollary 1.6, the c-Hessian of f must be positive definite, the local minimum, strict and the Monge-Ampère equation, elliptic. Being so, the latter admits at most one solution f up to addition of a constant, as a standard maximum principle argument shows

The next three sections contain respectively the proofs of Theorem 1.4 and of its two corollaries.

2. Proof of Theorem 1.4. Let ϕ ∈ Diff µ,̟ (Ω) be stationary for C and, for t a small real parameter, let t → ϕ t ∈ Diff µ,̟ (Ω) be an arbitrary path such that ϕ 0 = ϕ. We can uniquely write ϕ t = ξ t • ϕ with t → ξ t ∈ Diff ̟ (P ) such that ξ 0 = the identity of P . In particular, ξ0 is a tangential vector field on P lying in ker div ̟ (setting as usual ξ0 (p) = ∂ ∂t ξ t (p)| t=0 ). We will prove the equivalence (i) ⇐⇒ (ii) by establishing the equality:

d 2 dt 2 C(ϕ t )| t=0 = P Hess c ( f )( ξ0 , ξ0 ) d̟. (2.1)
Using arbitrary source and target charts x, y, and the Einstein summation convention, one routinely finds:

d dt C(ϕ t ) = M ∂c ∂y i (x, ϕ t (x)) ∂ϕ i t ∂t (x) dµ(x) where dµ(x) = dµ dx (x)dx,
then the second variation expression:

d 2 dt 2 C(ϕ t ) = M ∂c ∂y i (x, ϕ t (x)) ∂ 2 ϕ i t ∂t 2 (x) + ∂ 2 c ∂y i ∂y j (x, ϕ t (x)) ∂ϕ i t ∂t (x) ∂ϕ i t ∂t (x) dµ(x).
Here, to spare the unfamiliar reader, we did not use a global linear connection (on P ) to compute the second derivatives which occur in the integrand. Doing so, we must be careful, as explained in the following remark. Remark 1. Taken separately, the local scalar terms ∂c ∂y i (x, ϕ t (x))

∂ 2 ϕ i t ∂t 2 (x) and

∂ 2 c
∂y i ∂y j (x, ϕ t (x)) x) are not invariant under a change of charts, unlike their sum, indeed equal to the global real function:

∂ϕ i t ∂t (x) ∂ϕ i t ∂t (
m ∈ M → ∂ 2 ∂t 2 c(m, ϕ t (m))
. Therefore these terms cannot be integrated separately (unless the deformation ξ t is supported in the domain of a single chart of P , of course). Still, in each couple of source and target charts, splitting the local expression ∂ 2 ∂t 2 c(x, ϕ t (x)) of the global function into the above non invariant terms can be done in a unique way, by using the canonical flat connection of the P chart. Anytime we will have to integrate on a manifold a global real function splitting uniquely into a sum of non invariant local terms, we will stress that the integral should not be splitted by putting the sum between braces, as done above. As long as they are written in the same charts, the addition of two such sums {a 1 + a 2 } + {b 1 + b 2 } may, of course, be written between a single pair of braces

{a 1 + a 2 + b 1 + b 2 }.
Back to our proof, using ϕ t = ξ t • ϕ, recalling (1.1) and setting t = 0, we infer:

d 2 dt 2 C(ϕ t )| t=0 = P ξi 0 ∂c ∂y i (ϕ -1 (y), y) + ξi 0 ξj 0 ∂ 2 c ∂y i ∂y j (ϕ -1 (y), y) d̟(y), (2.2)
where d̟(y) = d̟ dy (y)dy and ξi 0 = ∂ 2 ∂t 2 ξ i t (y)| t=0 . To proceed further, we note that the integral P f (ξ t (y)) d̟(y) is independent of t. Differentiating it twice with respect to t at t = 0, we get:

0 = P ξi 0 ∂ f ∂y i (y) + ξi 0 ξj 0 ∂ 2 f ∂y i ∂y j (y) d̟(y).
Adding this vanishing integral to the right-hand side of (2.2), applying the last part of Remark 1 and recalling the stationary point equation:

∂c ∂y i (ϕ -1 (y), y) + ∂ f ∂y i (y) ≡ 0,
derived at once from Proposition 1.1, we obtain (2.1) as desired.

A similar argument would yield:

d 2 dt 2 C(ϕ -1 t )| t=0 = M Hess c (f )( ζ0 , ζ0 ) dµ,
with the vector field ζ0 ∈ ker div µ obtained by writing ϕ -1

t = ζ t • ϕ -1 for a unique path t → ζ t ∈ Diff µ (M ).
It would imply the other equivalence (i) ⇐⇒ (iii), since C(ϕ -1 ) ≡ C(ϕ) is a local minimum of C as well. The proof of Theorem 1.4 is complete.

3. Proof of Corollary 1.5. Strategy. Let ϕ ∈ Diff µ,̟ (Ω) realize a local minimum of the total cost C and let f : M → R denote its c-potential, as provided by Proposition 1.1. Arguing by contradiction, we suppose the existence of a point m 0 ∈ M such that the quadratic form associated to the symmetric bilinear one Hess c (f )(m 0 ) : T m0 M ×T m0 M → R can take negative values. We will contradict property (ii) of Theorem 1.4 by constructing a vector field U ∈ ker div µ supported near m 0 such that M Hess c (f )(U, U ) dµ < 0. A similar argument would hold for ϕ -1 , of course. We will proceed stepwise, choosing a good chart at m 0 , constructing the vector field U in that chart and evaluating the above integral.

Choice of a chart. We pick any chart y of P at ϕ(m 0 ) but a special chart x of M centered at m 0 , namely a chart which pushes the measure dµ to the canonical Lebesgue measure dx. The existence of such µ-adapted charts, to call them so, is well-known [Banyaga 1974[START_REF] Dacorogna | On a partial differential equation involving the Jacobian determinant[END_REF]] and timely, here, to transform the div µ operator on M into the usual div operator of R n (up to sign) that is, the divergence operator associated to the measure dx (simply denoted by div below). Since the orthogonal group O(n) preserves the measure dx, we may further choose the chart x such that the matrix H ij (0) of Hess c (f )(m 0 ) is diagonal, with eigenvalues λ 1 λ 2 . . . λ n (each repeated with its multiplicity). Under our assumption: λ 1 < 0. Since the unimodular group SL(n, R) preserves the measure dx, we may rescale the chart x in order to have: λ 1 -3 and, ∀i ∈ {2, . . . , n}, λ i 1 2 . Let the chart x be fixed so and let x → H ij (f )(x) denote the local expression of the map m → Hess c (f )(m). The inequality: ∀v

∈ R n , H ij (f )(0)v i v j -3(v 1 ) 2 + 1 2 n i=2 (v i ) 2 , combined with the continuity of the map (x, v) → H ij (f )(x)v i v j as (x, v) varies near x = 0 with v length 1 (say), implies the existence of a real ε > 0 such that: ∀(x, v) ∈ R n × R n , max 1 i n |x i | ε ⇒ H ij (f )(x)v i v j -2(v 1 ) 2 + n i=2 (v i ) 2 . (3.1)
Construction of a divergence free vector field. The vector field on R n given by w(x) = x 1 ∂ ∂x 2x 2 ∂ ∂x 1 satisfies div(w) = 0. The flow of w preserves any function h : R n → R factoring through a function H

: [0, ∞) × R n-2 → R as: h(x) = H( (x 1 ) 2 + (x 2 ) 2 , x 3 , . . . , x n ). Any such function h thus satisfies div(hw) = 0. Let us fix a cut-off function α : [0, ∞) → [0, 1] equal to 1 on [0, ε/2], vanishing on [ε/ √ 2, ∞)
, decreasing in-between, and consider the function h : R n → R given by:

h(x) = α (x 1 ) 2 + (x 2 ) 2 n i=3 α |x i | .
We know that div(hw) = 0 and that the vector field hw is supported in the open box

B n ε = x ∈ R n , max 1 i n |x i | < ε .
Since the chart x is µ-adapted, we may view hw as the expression in that chart of a div µ free vector field U in M supported in the inverse image

x -1 (B n ε ) ⊂ M . Calculation of an integral. Let us consider the integral M Hess c (f )(U, U )dµ which is equal to: B n ε h 2 (x)H ij (f )(x)w i w j dx. From (3.1), it is bounded above by: 2 ∞ 0 α 2 (ρ)dρ n-2 B 2 ε α 2 (x 1 ) 2 + (x 2 ) 2 -2(x 2 ) 2 + (x 1 ) 2 dx 1 dx 2 .
Note that the function (x 1 , x 2 ) → α (x 1 ) 2 + (x 2 ) 2 vanishes outside the Euclidean ball of radius ε centered at 0; using polar coordinates (r, θ) in R 2 \ {0}, we thus find that the last integral is equal to: Differentiating the latter yields (sticking to the notation Hessc(f ) = Hij(f )dx i dx j ):

H ij (f )(x) = - ∂ 2 c ∂y k ∂x i (x, y) y=ϕ(x) ∂ϕ k ∂x i (x).
Taking determinants, recalling that the symmetric matrix H ij (f )(x) is non negative (by Corollary 1.5) and using (1.4), we obtain a local Monge-Ampère equation satisfied by f , namely: , where y = ϕ(x) is given by (4.1). From (1.3), the right-hand side of this equation nowhere vanishes; so the matrix H ij (f )(x) must be positive definite. So must be the c-Hessian of f throughout the manifold M , since the point m 0 is arbitrary. Finally, as well-known, the positive definiteness just obtained implies, indeed, the ellipticity of the Monge-Ampère equation. A similar argument would hold for ϕ -1 .

  7. If the cost function satisfies (1.2)(1.3), there exists at most one local minimizer ϕ ∈ Diff µ,̟ (Ω) of the total cost functional C. If it exists, it should write m → ϕ(m) = E c (m, df (m)) for some c-potential f such that Hess c (f ) is positive definite on M ; moreover, the local minimum C(ϕ) is strict.

  r)r 3 dr.We conclude that M Hess c (f )(U, U )dµ is bounded above by a negative real, (r)r 3 dr, contradicting property (ii) of Theorem 1.4, as desired. 4. Proof of Corollary 1.6. Let again ϕ ∈ Diff µ,̟ (Ω) realize a local minimum of the total cost C. Fix an arbitrary point m 0 ∈ M and take a µ-adapted chart x of M centered at m 0 and a ̟-adapted chart y of P centered at p 0 = ϕ(m 0 ). From (1.3) and the definition of E (m0,p0) c , the map x → y = ϕ(x) is defined near x = 0 by the equation: ∂f ∂x i (x) + ∂c ∂x i (x, y)

  det (H ij (f )(x)) = det ∂ 2 c ∂y k ∂x i (x, y) y=ϕ(x)

Acknowledgments. The author got the idea of this note soon after returning from a visit at the Fields Institute during the "Concentration period on Partial Differential Equations and Geometric Analysis" (October 25-29, 2010). He wishes to thank the Institute for partial support and Robert McCann for his extremely nice invitation and a stimulating discussion.