Pierre Salmon

Ordinary Elections and Constitutional Arrangements by

Keywords: constitutional economics, elections, constitutional change Mots-clefs: économie constitutionnelle, élections, changements constitutionnels

It is widely held that voting in the course of ordinary elections has no significant influence on the constitutional regime or order of a country. At least three powerful arguments are provided in support of that view. First, to claim that, at the same time as they play, players can change the rules is, to say the least, logically puzzling. A second argument refers to the motivations and possibilities of voters: voters, this argument says, are not really interested in constitutional issues and, even if they were, are particularly ill-equiped to understand their implications. The third argument rests on the observation of what obtains in practice: as a matter of fact, constitutional issues are generally absent from electoral campaigns. After a discussion of what should be included in the constitutional "order, "regime" or "arrangements" of a country, the paper endeavours to neutralize each of the three arguments and show that voters do exercise a very susbstantial influence on constitutional matters simply by the way of their vote in ordinary elections.

Introduction

It is widely held that voting in the course of ordinary elections has no significant influence on the constitutional regime or order of a country. If voters have at all any influence on the constitutional set-up, which not everybody sees as evident, 1 this is generally considered to occur only on the relatively rare occasions when constitutional questions are submitted to a referendum or to a specially elected convention or constitutional assembly. At least three arguments are provided to support that opinion. A logical consideration comes first. Ordinary elections are parts of the political game and thus logically take place within the rules of that game -that is, within the constitutional order or regime of the country. To assume that, at the same time as they play, players can change the rules is, to say the least, logically puzzling.

The second argument refers to the motivations and possibilities of voters. Voters, this argument says, are not really interested in constitutional issues and, even if they were, are particularly ill equipped to understand their implications. The third argument rests on the observation of what obtains in practice. As a matter of fact, constitutional issues are generally absent from electoral platforms and campaigns.

In spite of its apparent strength, this three-pronged denial is not compelling, I will try to show. To defend the opposite view -that voters do exercise a substantial influence on constitutional matters simply by the way of their vote in ordinary elections -1 will endeavour to neutralise each of the three arguments mentioned above. The organisation of the paper reflects this objective. Thus I will explain in Section 3 why I think that ordinary elections having constitutional effects implies no logical contradiction; discuss in Section 4 voters' capacities and motivations, and argue in Section 5 that voters' influence on constitutional or institutional matters is compatible with the observation that these matters seldom come to the fore in electoral debates. But before proceeding to the main discussion, I must address in 1 Although the assumption that they have is implicit in the way the constitutional economics school sees its prescriptive or normative role (see, e.g., [START_REF] Vanberg | Rules and Choice in Economics[END_REF].

Section 2 the question of what one may want to include in the "constitutional regime" or "order". 2

What is constitutional?

By definition, the question is largely semantic but (pace Karl Popper and Milton Friedman) this does not mean that it is meaningless. In some cases, notably that of the United States, it is at least feasible or conceivable to equate the constitutional regime or order and the formal (paper) constitution itself. If this is done, then, because formal constitutions cannot be changed by simple majorities of voters, 3 it is trivially true that the constitutional order cannot be changed in this way either. However, in many cases, it is not feasible or conceivable to equate the constitutional regime with a constitution either because there is no such thing or because the one that exists is largely irrelevant. Furthermore, even when it is conceivable, the assimilation is, I would say, generally inadvisable. It implies for example that countries that have the same constitution have the same constitutional regime, which is not exactly what one would want to say of all the countries whose constitution was modelled on that of the United States. It also leads to the neglect of rules of the game which, albeit absent from the formal constitution, constitute major constraints on the way the game can be played and thus deserve to be considered, in some sense, "constitutional". 4In a country such as France, there are at least four sets of rules or arrangements that we might want to include in the constitutional regime although they are either not addressed at all or only alluded to in the formal constitution. One is the electoral system. The other three 2 "Constitutional order" is a bit pompous; it should be understood as more or less synonymous with "constitutional set-up", "regime", "system", "set of rules", "arrangements", etc. concern the rules which govern the relations between the politicians in power in the central government in Paris, on the one side, and, on the other side, first the bureaucracy, second the subnational elected governments (i.e., municipal, departmental and regional governments), third, the European institutions in Brussels. Whatever their origin or status, the rules or arrangements currently in force in these four areas have a considerable incidence not only on political life in general but also on matters that are addressed at length by the formal constitution.

I will refer to decentralisation and to the relationship between politicians and bureaucrats in subsequent sections. At this stage let me give some illustrations of the constitutional relevance of Europe and of the electoral system. With regard to Europe, the European Court of Justice itself has repeatedly referred to the EEC Treaty as, "albeit concluded in the form of an international agreement", being "the basic constitutional charter" (see Weatherill 1995, p. 184). This is not a purely rhetorical claim on the part of an institution whose objectivity on this point could be suspected. The constitutional relevance of the European treaties can be illustrated in many ways. For instance, many scholars, especially among economists, consider the protection of individual rights of a more economic kind (property, income from capital, etc.) to be an essential task of constitutions. The French constitution does fulfil in part this function, as the Socialist government discovered in 1981 when it was compelled by the Conseil Constitutionnel to raise the compensation paid to the owners of the firms transferred to the public sector. But this constitution is not in France the only protector of property rights. It is more than supplemented in this task by the rules adopted in the context of European integration for promoting the free movement of goods, factors and persons. One might even argue that, at the present stage of European integration (this could change at a later stage), the main protection of economic rights lies in the existence of these rules rather than in the constitutions of the member states. For instance, the former, not the latter, prevent in fact recourse to a confiscatorily high level of taxation of income or capital. The European rules concerned here legally constrain governments and thus should not be confused with the market forces referred to under the name of globalisation.

Because of this legally compelling character some at least of these European rules should be considered as essential components of the constitutional order currently prevailing in France, or for that matter in other member countries. 5 Another example concerning Europe is budgetary discipline. There is a provision in the French constitution (Article 40) that says: "The proposals and amendments initiated by members of parliament cannot be taken into consideration when their adoption would either reduce the fiscal revenue or impose a financial burden on the budget". 6 In the past, this may have contributed to budgetary discipline by making more transparently the executive branch of government responsible for any lack of it. But today the disposition has lost much of its relevance. It is overshadowed by the budgetary requirements imposed at the European level in the context of monetary unification. 7Let us turn to the electoral sytem. Its importance in the characterisation of the political system of a country needs not be stressed. Among many possible sources, a particularly illuminating one is Giovanni Sartori's excellent little book (1994) on "constitutional engineering". This term, Sartori indicates (p. 140), should be understood as "a shorthand that includes the electoral system, even though electoral systems are generally determined by ordinary legislation". Many examples of the close relationship between various aspects of the formal constitution and the electoral system can be found in Sartori's book: for instance, in the 5 This point is particularly important in the case of a country such as Britain, where, according to Walter [START_REF] Murphy | Constitutions, Constitutionalism, and Democracy[END_REF], "Parliament is supposedly the authoritative creator, emendator, and interpreter of the constitution, restrained only by the ballot box and its collective conscience", but only inasmuch as the European Economic Community or the European Convention on Human Rights are not involved (p. 15). In other words, in Britain the only formal constitutional constraints on parliamentary sovereignty are the European institutions.

"English system of government", the crucial importance of plurality voting (p. 104); or, in the "Washington model", of the way representatives are induced by the electoral system to concentrate on local interests, a characteristic that contributes to avoid deadlocks when the two branches of government are held by different parties (pp. 86-91).

A question that Sartori does not raise, at least in this book, is why electoral systems, despite their importance in constitutional matters, are seldom included in formal constitutions.

One reason might be that if they were, they could well turn out to be unfortunate given other features or circumstances of the countries concerned. The Weimar constitution and the constitution adopted in France under the Fifth Republic are similar in many respects.

However, the former (in its Article 22) imposed proportional representation whereas the latter imposed nothing. It seems agreed among specialists of Weimar that the pure system of proportional representation (applied to a single national constituency) that it used at least "exaggerated the multiplicity and divisiveness of German politics in the Reichstag" (Finn, 1991, p. 145). 8 By contrast, a major effect of an electoral system like the double ballot majority system used in France is to reduce the representation in parliament of "anti-system" parties (Sartori, 1994, pp. 67-69). 9 There are other means available for that purpose. 10 Among these, a particularly illustrative one was the apparentement system contrived in France in 1951 by the parties of the centre-left and centre-right to safeguard a majority of seats endangered by the converging electoral forces of the Gaullists and the Communists. 11 Without this device, allowed by the fact that electoral rules were not too difficult to change, it Possibly even (when access to the second round is limited to the first two runners) when one such anti-system party is the relative winner in the first round (Sartori, 1994, note 17, p. 78). 10 Including making anti-system parties anti-constitutional and dissolving them, as was done in West Germany.

11

The scheme gave the electoral alliance which obtained a relative majority a premium sufficient for it to have the majority in parliament although it (the scheme) maintained proportional representation within the alliance (see Sartori, 1994, pp. 6-7). A combination of proportional representation with a majoritarian premium is currently the rule in France for municipal elections. It works very well. is quite possible that the Fourth Republic would have come to an end earlier than it did.

Among others, the opposite cases of Weimar and of the apparentements show that the fact that an electoral system is not part of the formal constitution, and thus can be changed more easily, may actually contribute to the survival of the constitutional regime -a consideration that constitutional framers may well have had in mind in the first place.

Electoral systems can thus be seen to be a priori less permanent or structural than the dispositions included in the formal constitutions. In practice, however, it is often the case that electoral systems prove to be more stable or enduring than many of these dispositions. In any case, I think, together with many authors, that electoral systems are an essential characteristic of political systems at the constitutional level. From the perspective of this paper, the most important feature of an electoral system is whether it allows a swift replacement of office holders or of policies considered as unsatisfactory by a majority of voters. Indeed, as will become clear, if an electoral system has this property, it may well turn out to be a more essential component of the constitutional order than most other components.

Elections and the constitutional logic

A large part of the literature on constitutions and almost all of that small part of it which is produced by economists reflects what has been called "constitutionalism", that is, an exclusive concern with constraining, circumscribing, or binding majorities of voters.

A degree of mistrust of the majority of voters was expressed by James Madison among others (e.g., Benjamin Constant in France). For instance, Madison wrote:

In our Governments the real power lies in the majority of the Community, and the invasion of private rights is chiefly to be apprehended, not from acts of Government contrary to the sense of its constituents, but from acts in which Government is the mere instrument of the major number of constituents. 12The reasons for constraining the freedom of decision of majorities of voters are well known.

First, there is the protection of individual rights. In the long run and under a "veil of ignorance" all citizens may favour such protection, but in the short run there may be powerful incentives for a majority to transgress them. Hence the usefulness of binding (see, e.g., [START_REF] Buchanan | The Domain of Constitutional Economics[END_REF]. Second, in some cases, there may be the protection of perfectly identified and permanent minorities -ethnic, religious or linguistic minorities in particular. This protection may be accepted by a majority at 'a constitutional stage 1 because of ethical principles, or as a consequence of some constitutional logrolling, or just for the purpose of safeguarding internal peace. Third, the protection of property rights of an economic kind can be understood as an aspect of the protection of rights in general or as a means to foster investment and growth (which in turn may be deemed necessary for democratic stability, as argued among others by Peter [START_REF] Bernholz | Necessary and Sufficient Conditions for a Viable Democracy[END_REF]. Fourth, independently of the other reasons, constraining the majority of voters may be necessary to render more credible some commitments, either promises or threats. For instance, making central banks independent may be away to solve the time-inconsistency problem that plagues government policy-making in matters of money and inflation; or the constitutionally protected independence of judges and non-retroactivity of the law may be, as a side-effect, a means for a country to avoid being blackmailed by terrorists.

Inasmuch as constitutional rules and arrangements are seen as exclusively concerned with the task of binding majorities of voters, there is something akin to a logical contradiction in the possibility that these majorities could change the constitutional rules and arrangements.

Leaving them this freedom would be akin to leaving Ulysses the freedom to unbind himself. I wonder whether, even more than a normative concern, it is not this logical issue which underlies Dennis Mueller's reaction to the view, defended in particular by Bruce [START_REF] Ackerman | We the People: 1. Foundations[END_REF], that simple electoral majorities do in fact change the constitutional order. 13 That in the United States the constitutional order has changed a lot without formal constitutional amendments has been a major theme in the public choice and constitutional economics literature for some time (see, e.g., [START_REF] Buchanan | The Limits of Liberty[END_REF]McKenzie, 1984;[START_REF] Wagner | Parchments, Guns, and the Maintenance of Constitutional Contract[END_REF]Gwartney and Wagner, 1988;[START_REF] Niskanen | Conditions Affecting the Survival of Constitutional Rules[END_REF]. But inasmuch as the responsibility for this phenomenon is ascribed to the Supreme Court or to politicians, it raises a possibly difficult question about constitutional enforcement but no logical problem. The specificity of Ackerman's book is the claim that the ultimate legitimate source of the change in the constitutional order is to be found in the opinion or will of a majority of voters. Pushed too far this kind of argument is destructive of the notion of constitutional binding in general. It is clear that Ackerman himself is conscious of this danger. He insists on a number of requirements to be satisfied before it becomes possible for a majority to change the constitutional rules and on the paucity of situations in which these requirements have been met. The logical problem raised by f self-unbinding f (if I may use that term) is mitigated or solved when there are obstacles and costs to unbinding. Thus it is natural to impose conditions for constitutional change brought about by elections as demanding as those included in formal amendment procedures.

Constitutions, however, have a second function that does not raise this kind of problem when considered in isolation. This second function consists in organising the principal-agent relation between voters (the principals) and their representatives (agents). The problem then is to design institutions and rules in such a way that the preferences or interests of a majority of voters get satisfied. Under that second perspective, there is nothing strange or self-destructing 13 Mueller (1996, p. 337, note 20) raises the question "To what extent does a minority remain party to the constitutional contract, if the contract can be amended whenever a substantial majority so chooses?" In reality this question is far-reaching. It points to a puzzle that affects the whole construction of constitution-as-contract (see [START_REF] Hardin | Contractarianism: Wistful Thinking[END_REF][START_REF] Ordeshook | Constitutional Stability[END_REF].

in simple majorities of voters changing some rules or institutions in view of getting a better alignment between government decision-making and their preferences or interests.

It is understandable that, for the majority of authors concerned with constitutional economics -that is, with individual rights -this second perspective is of little importance.

Whether the government or the legislature violates the constitutional rules protecting minorities and rights because, as an agent, it does not itself respect the mandate or trust received from a majority of voters or because the majority of voters itself has an interest in these rules being violated is relatively secondary. In the vocabulary employed in some of this literature, the important issue is whether what gets favoured is "prédation" or "exchange" [START_REF] Wagner | Parchments, Guns, and the Maintenance of Constitutional Contract[END_REF]. If, with the complicity of the courts, what gets favoured is prédation, it does not really matter whether the predator is a majority of voters, a set of office-holders, or, more likely, a combination of the two.

Without adopting this position, one must admit that disentangling the two functions of constitutional or quasi-constitutional rules or arrangements is not an easy task. What constitutions do, materially, is to restrict politicians, not directly voters. In so doing they at the same time, in generally unknown or undecidable proportions, fulfil the two tasks of fostering the interests of a majority of voters (the principal-agent perspective) and of restraining the same voters (the constitutionalist perspective). For instance, constitutional provisions concerned with budgetary discipline, such as the already mentioned Article 40 of the French constitution, or like the much more ambitious constitutional constraints defended for the United States by Buchanan and others, reflect a distrust indistinctly of legislators and of majorities of voters.

For the purpose of justifying my proposition, what creates a problem is when the representatives of a majority of voters change components of the constitutional order in the direction of increased power or freedom for themselves. Let me assume that this is done with the acquiescence of voters. If one could be sure that the change has no bearing on the first function of the constitution (concerning the relations between voters), but only on the second function (concerning the agency relationship between voters and their representatives), it could be considered as non-destructive of constitutional principles. But I am not sure that ascertaining independent effects in such a way is even only sometimes possible. Thus, as already noted, taking into account principal-agent considerations changes nothing in practice to our logical problem. Since this is the situation which Buchanan and his followers focus on, they are not inconsistent. 14 When, on the contrary, with the approval of voters as expressed in ordinary elections, representatives change components of the constitutional order in the direction of decreased power or freedom for themselves, the logical problem is more or less absent. Extra self-binding is much les puzzling than self-unbinding, so to say. Of course, such behaviour may be puzzling for other reasons. One problem may be solved but others arise. I turn to some of the other problems now.

Voters' concerns and capabilities

Consumers are not generally concerned with how production is organised. Similarly, it is often claimed that voters are and/or should be concerned only with the outputs of governmental activity and the cost or tax prices associated with these outputs and not with the internal organisation of the state. One possible reason for their unconcern could be that they can trust their representatives, the elected politicians, to organise the state in their (the voters 1 ) interests. Another possibility is that voters can rely on their assessment of policy outputs and tax prices, combined with voting, as sufficient to ensure that they are provided with the policies they want. The reason which is probably the one most people think of in priority is that voters are completely ignorant of constitutional matters and know that they are. Although apparently convincing this last argument is possibly the weakest. It is probably true that most voters are rather ignorant of the way government is organised.

However, the main features of this organisation or the main problems that it raises are not more difficult for them to understand than many other issues, economic and social issues in particular, which they are not supposed to be completely unable to understand in most accounts of electoral behaviour. Compare for instance the informational problems involved in deciding whether the president should be elected for five years with a possibility of being reelected once, for seven years with also this possibility, or for seven years without it, and the information required to answer the question of whether a lot of influence on employment is lost when monetary policy becomes unavailable as a consequence of fixed exchange rates or monetary unification. Both questions are or have been recently part of the political debate in France. The first is typically constitutional but it calls for considerations that many citizens are perfectly able to grasp, it seems to me. The second calls for an understanding and comparative assessment of full-blown models (involving expectation-augmented Philips curves, time inconsistency, sunspot equilibria and what have you) that should tax the analytical capacity of the most competent economists. I do not say that voters are deprived of any means of making their mind on these matters as on others (see Wittman, 1995, chapter 1), but I refuse to adopt the widely-shared presumption that issues similar to the second question, typical of the most relevant questions in the economic domain, are more easily decidable by voters than questions alike the first, typical of the constitutional agenda.

Let me turn now to the question of whether, assuming that they are sufficiently competent, voters should be concerned with constitutional or quasi-constitutional issues, pertaining for instance to the organisation of the relationship between politicians and bureaucrats. 15 15 In Section 2,1 mentioned three relationships whose organization should be considered, in the case of France at least, to be part of constitutional arrangements. In work published previously [START_REF] Salmon | Decentralisation as an Incentive Scheme[END_REF][START_REF] Salmon | Checks and Balances and International Openness[END_REF][START_REF] Salmon | Nations Conspiring Against Themselves: An Interpretation of European Integration[END_REF], I the mid-1980s to adopt the principal-agent framework. They model bureaucrats as the agents of elected politicians. At the same time, they assume elected politicians to be the agents of voters and they treat these two agency relationships as if they were independent. This implicit assumption has unfortunate consequences. It implies that the stronger the agency relationship between politicians and bureaucrats, the better from the standpoint of voters, whatever the state of their relationship with politicians. But, when the relationship between voters and politicians is defective (as is necessarily the case in our actual, generally imperfect, world), it is far from clear that voters should wish the relation between politicians and bureaucrats to be as good or tight as possible (supposing that they should is a mistake akin to the mistake whose elimination motivated the theory of the second best). For instance, if we do not trust our president or Prime Minister, do we wish him to enjoy a perfectly symbiotic relationship with the head of the police? If the assumptions that could justify a positive answer to that question were stated explicitly, it would be clear that they are unacceptable, but they are usually made implicitly in the context of the study of one of the two relationships at the time. This allows many authors to suppose, as if it were obvious, that a perfect control of politicians over the bureaucracy would be a good thing for democracy, that a major problem of our democratic societies is that this control is highly imperfect.

For our purpose, what the foregoing discussion suggests is that voters could remain completely unconcerned with the organisation of relations between politicians and bureaucrats only if they could fully trust their representatives, the politicians, to shape these relations in their (the voters 1 ) best interests. I have some sympathy for the minority view, defended notably by Albert Breton (1996, e.g.) and Donald Wittman (1995, e.g.), that have devoted some attention to how voters may have some influence on the relationship between central and subcentral governments and between central (member-state) governments and European institutions. For a while, in this section, I draw on an analysis of the relationship between voters, bureaucrats, and politicians adumbrated in [START_REF] Salmon | Politicians and Bureaucrats: A Relationship Shaped by Voters[END_REF].

powerful mechanisms are at work which make politicians exert themselves and respond fairly well to the preferences of voters (not worse than business firms with regard to the preferences of consumers, to use a comparison both authors make). However, even if we accept this general perspective, I think that at least two sets of considerations prevent us from considering the relationship between voters and politicians as unproblematic. One set is related to what is known as the "fear of the state": voters may be afraid or distrustful of the power of the rulers or they may be afraid or distrustful of their fellow voters or of themselves.

Even accepting Breton's view that the government or the state is not a monolith, that "governemental systems" are very competitive, the question remains of whether voters can rely in all circumstances on this competition. It is not inconceivable, for instance, that a single disciplined party could conquer many centres of power, at all levels of jurisdiction, and then that its leaders could misuse the considerable power that such concentration or monopolisation would provide them with. Since the damage caused by a chain of events of that kind could be serious, a small probability of its occurrence would be sufficient to justify the fear of the state on the part of risk-averse citizens. The existence of relatively independent or protected non-elected decision-makers, such as civil servants and judges, might be valuable to voters under that perspective. Even closer to counterfactual reasoning, another question arises: is the fragmentation of the state into smaller mutually competitive units independent of the fear of the state? The checks and balances and other institutional arrangements which allow competition to develop may themselves have something to do with that fear.

A second set of qualifications is related to the fact that, while retrospective assessments necessarily play a major role in the vote, they cannot bear with the same reliability or strength on all policies or aspects of policies. To refer to my own work (1987, e.g.), I have called performance competition a mechanism based on the assumption that office-holders in one jurisdiction know, albeit with some degree of uncertainty, that many voters in their electorate compare policy outcomes in the jurisdiction to policy outcomes elsewhere. This gives office-holders an incentive to exert themselves, that is, in some sense, to move the policy-mix toward the production frontier. If this mechanism worked perfectly well, voters could concern themselves exclusively with policy outputs and disregard completely the way governments are organised (provided of course that their power to dismiss is safeguarded by the electoral rules). However, a major problem that this mechanism encounters, or more generally that any mechanism based on retrospective voting encounters, stems from the fact that policy outputs are not equally measurable by voters. As a consequence, politicians may be induced to concentrate their efforts on policies whose outcomes are more easily measurable and sacrifice other policies which would also be useful to voters (see [START_REF] Salmon | Checks and Balances and International Openness[END_REF][START_REF] Tirole | The Internal Organization of Government[END_REF]and, in a more general context, [START_REF] Holmstrom | Multi-Task Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design[END_REF].

Policies yielding benefits only in the long run may be particularly vulnerable to distortions of that kind. Admittedly, some aspects of these policies may well be relatively easily assessable by voters before they bear fruit: voters may understand that investment in tangible or human capital may be favourable to future growth, they may welcome land reclamation or reforestation programmes, they may perceive or accept the claimed causality between new laws or new agencies and some relatively distant objectives. There are however many aspects of long-term oriented policies which they will find more difficult to observe or assess. The literature on the interaction between the polity and the bureaucracy focuses on making and implementing rules, changing policies, creating agencies. But the major part of what the state or the government does, and should be doing, is more basic and less related to change. As a matter of course, the state (including subcentral governments) provides citizens with a regular and continuous flow of . Maintaining the future capacity to deliver these services, at a constant and sufficient level of quality, is typically a long-term policy which cannot easily be assessed by voters. If political competition is very severe, which may be a good thing in itself, this might well have the unfortunate side-effect of literally compelling incumbents to sacrifice all policies which do not 'pay' in terms of probability of re-election, this kind of policy in particular. The organisation of the state, including for instance an institution such as the civil service, may mitigate that problem. But it is unlikely to follow such an objective if voters leave politicians free to shape it according to their (the politicians') preferences.

The foregoing discussion shows, I hope, that voters should not trust completely the politicians, or the perfection of the agency or delegation relationship which they have with politicians, and should not be unconcerned by the organisation of government. The question now is whether they can and do have an influence on this organisation. This needs dealing with the observation that this type of issues seems to be more or less absent from electoral campaigns.

Institutional or constitutional issues in elections

Many of these issues are dealt with on the occasion of formal constitution making or amending. Others, such as the ones we focus on in this paper cannot. For instance, the relationship between the polity and the bureaucracy is not addressed in formal constitutions.

The relations between the central government and subcentral governments is not based on a distribution of constitutional rights in unitary states -or even, for that matter, in all federal states (see Ordeshook, 1992, p. 167). This means that the form of institutional design which is of interest to us is not of a constitutional kind in the formal sense of that term. Received wisdom is that institutional design or change which is not of a constitutional kind in the formal sense is the business of politicians, or perhaps the result of spontaneous evolution, but cannot be in any case influenced by voters in the course of ordinary elections. In addition to the idea, discussed in the preceding section, that voters have neither the motivations nor the capacities to be concerned with these issues, what could make the influence of voters on institutions (by the means of ordinary elections) somewhat doubtful is that institutional issues seldom become salient issues in electoral contests. Seldom is not "never" and in a sense it might not be abnormal that constitutional issues come to the fore only intermittently or discontinuously. On some occasions, it is the case that voters clearly want institutional change. Then, we can often count on political entrepreneurship to bring that change about. In the United States as in France, presidents or candidates in presidential elections are the most likely constitutional entrepreneurs. But this may be relatively recent phenomenon (see [START_REF] Ackerman | We the People: 1. Foundations[END_REF]). An American illustration of a process starting from below is the way the Progressive movement imposed reforms at the turn of the century, in particular at the level of municipal government (see, e.g., Maser 1985, Knott and[START_REF] Knott | Reforming Bureaucracy: The Politics of Institutional Choice[END_REF]. Municipal governments were typically dominated by party machines under a generalised system of patronage. Although this often worked well or speedily in terms of policy outputs, many voters, especially in the middle classes, were revolted by at least some aspects of the system. The National Municipal League pushed for a reform including the introduction of a relatively neutral or independent civil service for government employees.

The issue became a salient one in elections at the local and state levels. As a result, many municipal charters were changed. Although the story is complicated, with some moot points (see the discussion following Maser's paper and the references in Knott and Miller), it seems generally agreed that the discontent of a large part of the electorate with the existing institutions was a major cause of their reform. Other examples that come to mind are in the United States the anti-slavery movements before the Civil War and the civil rights movement in the 1960s, in various countries the women's suffrage movement.

Even if we accept that open "constitutional politics" at the electoral level is infrequent, this fact may not reflect a disinterest of voters for institutional issues but the existence of an attachment of voters to the institutional status quo and the knowledge of this preference by politicians (it is natural enough that attachment to the status quo plays an important role in constitutional and institutional matters).

In the article already cited (1987), I discussed the case of the surprisingly radical decentralisation law passed in France in 1982-83. Decentralisation had not come out as an important issue in the 1981 presidential and legislative elections, both won by the left, and it was not clear, when the law was passed, whether it would be an asset for the incumbents at the following election. Thus, I do not deny that the influence of voters was unimportant in the decision to make the law. 16 In fact, I do not know whether the reform was an asset during the 1986 legislative election, which was dominated by economic and social issues, and which the left in any case lost (see Penniman, 1988). What is clear, however, is that the politicians who were hostile to the law (there were many of them on both sides, but they were the majority on the right) did not raise the issue during that election, nor in the following ones. Presumably, they knew that public opinion had become rapidly attached to the new subcentral institutions and to the new division of powers. Given this support, questioning the reform would have been electorally dangerous. The same kind of stories could be told about the creation of a number of independent authorities, or the granting of more independence to existing ones.

Again in France, a case in point is the striking disappearance of opposition to the independence of the central bank granted in the wake of the Maastricht. In earlier work [START_REF] Salmon | Nations Conspiring Against Themselves: An Interpretation of European Integration[END_REF], I have proposed a small model along similar lines to account for the roundabout nature of the transfer of powers to European institutions. An alternative explanation of many of the phenomena mentioned here could be based on the theoretical framework proposed by Breton in his recent book (1996). Adopting his framework, one should say that what ensures the survival of subcentral governments, supranational institutions or independent authorities is the consent that people give these power centres in exchange for the goods and services that they provide (see especially his though. In particular, in Breton's account, consent is related to the goods and services that an institution has produced in the past or at the limit is currently producing, whereas I can accept that consent can also be given to institutions that have as yet produced nothing or perhaps do not even exist, except on paper. To account for this possibility, I suggest, one must see voters as being, at least sometime or to some extent, principals within a hierarchical relation rather than buyers on a market. The same need applies, I think, to an issue such as the politicisation of the administration. In France, this issue has several times become a salient one in presidential elections, mostly in the form of a denunciation of, or a warning against, either the 'Etat-RPR' (i.e., 'RPR State') or the 'Etat-PS' (i.e., 'PS State'). 17 The attention that some voters give to that issue constrains (perhaps increasingly) the proclivity of the party in power to politicise appointments to the top jobs. To generalise, under the perspective that I defend, only voters can be the ultimate guardians of the structural characteristics of the system, including its democratic and competitive characters. 18

Concluding remarks

The foregoing discussion has comforted the claim, I hope, that an institution or a set of institutional rules can be entrenched in voters' preferences rather than in a constitution. This is how and why voters have a profound influence on institutional design, as I claimed in the last section. The discussion also suggests that it might be easier to explain why an institution or arrangement endures than to explain how or why it was established or came about in the first place. 17 RPR is for Rassemblement du Peuple Français, the name of the neo-gaullist party; PS is for Parti Socialiste.

18

In the United States, as Robert Inman and Daniel Rubinfeld write (1997, p. 104), "when a political institution did rise to the defense of the federalist constitution -whether it was the executive, the judiciary, or a legislative political party -a single truth prevailed: the vast majority of the citizens in that society believed the federalist constitution to be worth protecting".

To conclude, let me stress an important point. Although I recognised the possibility of constitutional change being initiated from below, all along the paper I rather assumed voters' influence to be typically of a reactive or monitoring kind, the main initiators or producers of change being the politicians. But, for voter's reactions or potential reactions to have an effect, the politicians must take them into account. This means two things. First, the electoral system must favour the influence of voter preferences on politics. In this sense, the electoral system, as noted in Section 2, is a very basic component of the system. If it is of the right, highly competitive type all the rest follows. If not, for instance if it gives too much security to political parties, things become uncertain. Second, the substitution in the literature on elections of probabilistic voting to deterministic voting is a great help toward making the foregoing reasoning plausible. Probabilistic voting means that politicians, insecure about any individual voter's choice, take into account the preferences of all the voters, not only those of the pivotal voter as is the case in non-probabilistic voting. As a consequence, even institutional concerns shared by a minority of voters or, if shared by a majority, considered as secondary by all, are taken into account by politicians or parties submitted to sufficiently tight electoral competition. In other words, institutional or constitutional concerns among voters may be not only negative or latent, as argued earlier, but also relatively weak, and nonetheless constitute an essential underlying cause of the shape taken by institutions.

3

  Disregarding the case of countries, such as Britain, which have no formal constitution, only in Iceland is a 51 per cent majority sufficient to change the constitution.

  writes: "Pace Lijphart, more than by any other factor Weimar was undermined by PR [proportional representation] (a defect remedied by the French with the double ballot majority system)." 9

14

  Whether their factual beliefs or interpretations are true is another matter, discussed for instance by Wittman, 1995, pp. 137-48, with regard to "takings" clauses.

  chapter 5). Most of the time, I think, the two interpretations come to the same. Not always, 16 Gaston Deferre, at the time simultaneously Minister of the Interior and mayor of Marseilles, was the politician most involved in the design of the law.

James[START_REF] Buchanan | Constitutional Economics[END_REF] refers to the "set of legal-institutional-constitutional rules that constrain the choices and activities of economic and political agents" or, somewhat more economically, to the "legal-institutionalconstitutional structure of the polity."

SeeSartori, 1994, p. 201.

For an interesting analysis of the close relationship that may exist between constitutions and treaties, see[START_REF] Ackerman | The Rise of World Constitutionalism[END_REF]. For Bruce Ackerman (p. 9), "the (uncertain) transformation of a treaty into a constitution is at the center of the European Union today; it was also at the center of the American experience between the Revolution and the Civil War". See alsoWeatherill (1995, chapter 6).

Letter of October 17, 1988 to Thomas Jefferson (quoted byMurphy, 1993, p. 6).


Économiques Umr5118

Kristian Behrens

François Thisse

Christian Michelot

Jean- Marie Huriot

LABORATOIRE D'ANALYSE ET DE TECHNIQUES

Keywords: agglomeration, trade, imperfect competition, comer solutions JE L Classification : Dll, F12, L13, R12

We develop a spatial general equilibrium model in which the absence of trade is an endogenous outcome and we show that trade is not a necessary condition for agglomeration to arise. More precisely, extending the model developed by Ottaviano et al. [13], we show that equilibria without trade differ significantly from those obtained in the presence of trade. Somewhat surprisingly, equilibrium structures without trade are richer than those with trade, since partial agglomeration becomes a feasible outcome. Equilibria now depend on the ratio of mobile to immobile factors and an increase in that ratio triggers a process of spatial agglomeration. Résumé Nous développons un modèle d'équilibre général spatial dans lequel l'absence de commerce est un résultat endogène et nous montrons que le commerce n'est pas une condition nécessaire à l'agglomération. Plus précisément, nous étendons le modèle de Ottaviano et al. [13] et nous montrons que les équilibres sans commerce diffèrent significativement de ceux obtenus avec commerce. Il est surprenant que les structures d'équilibre sans commerce sont plus riches que celles avec, puisque l'agglomération partielle peut se produire.

Les équilibres dépendent du ratio de facteurs mobiles et immobiles; un ac croissement de ce ratio mène à un processus d'agglomération spatial.

Introduction

Since the Industrial Revolution, the transport costs of goods have decreased enor mously. The 19th century witnessed a first 'revolution' in transportation technologies, with the advent of railroads and steamships, while the 20th century witnessed a second 'revolution' with the rapid development of air freight and mass communication tech nologies. Those transport revolutions were accompanied by a rapid increase in both the volume of trade and the size of urban structures (see Bairoch [START_REF] Bairoch | De Jericho à Mexico -Villes et économie dans l'histoire[END_REF]). Since about a decade, and the seminal paper by Krugman [START_REF] Krugman | Increasing returns and economic geography[END_REF], economists have started to investigate more closely the various links between transport costs, trade and agglomeration in a spatial general equilibrium context. One of the fundamental results of the so-called 'new' economic geography states that agglomeration usually arises when transport costs are sufficiently low, while dispersion is the equilibrium outcome when transport costs are high (see Fujita et al. [START_REF] Fajita | The Spatial Economy -Cities, regions and international trade[END_REF], Krugman [START_REF] Krugman | Increasing returns and economic geography[END_REF], Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF] and Puga [START_REF] Puga | The rise and fall of regional inequalities[END_REF]). This result is well summarized by Henderson et al. [START_REF] Henderson | Geography and development[END_REF] who state that, "if transport and communication costs are very high then activity must be dispersed". Therefore, even if trade is not a sufficient condition, it seems that trade is at least a necessary condition for agglomeration to occur. In the present paper, we investigate if there can be agglomeration without trade or if the absence of trade always implies the dispersion of economic activity. To put it differently, we would like to know if trade is really a necessary condition for agglomeration or if agglomerated no-trade equilibria exist. We think it is worth mentioning right from the start that, as shown in this paper, trade is not a necessary condition for agglomeration to occur and that the equilibrium structures are, somewhat surprisingly, even richer when there is no trade than in the presence of trade.

It is a bit surprising that the question concerning the possibility of agglomeration without trade has, to the best of our knowledge, not been addressed in economic geog raphy. Indeed, one of the striking features of the space-economy is the empirical fact that only a small fraction of all goods produced in an industry is available in any one particular location. This fact, which we believe is about as characteristic o f a spatial economy as the uneven distribution o f production, has not received the attention it deserves (see Tabuchi and Thisse [START_REF] Tabuchi | Regional specialization and transport costs[END_REF] for an exception). A closer look at the main canonical models of the 'new' economic geography (Krugman [11] or Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF]) reveals that those models are all build, either explicitly or implicitly, on the assumption that each economic agent consumes a strictly positive quantity of all goods produced in the economy, no matter how firms and consumers are distributed in space.

This clearly highlights the fact that those models are not suited to deal with the spatial location of nontradeables, since they assume that all goods are tradeable. Hence while, as Wong [START_REF] Wong | International trade in goods and factor mobility[END_REF] argues, "the theory o f international trade has paid too much attention to trade in goods and far too little to factor mobility", it seems that the 'new' economic geography suffers from the opposite deficiency by systematically assuming that goods are mobile. Yet, in many countries, despite the secular decline in transportation costs, several goods and most services are only available in major metropolitan regions (think of most buisness-to-consumer services). Krugman [START_REF] Krugman | Pop internationalism[END_REF] neatly explains that we, some what paradoxically, observe that "while we ship manufactured goods back and forth with unprecedented abandon, such "tradeables" constitute a steadily shrinking share o f our economy". How does the spatial immobility of some outputs and the resulting absence of interregional trade in them affect the spatial equilibrium configurations?

In order to tackle this question and to shed some light on the possible necessity of trade in the agglomeration process, we move away from the constant elasticity of substitution (CES) framework usually used in the literature. Indeed, this framework implies that there is always at least some bilateral interregional trade (see Fujita et al. [START_REF] Fajita | The Spatial Economy -Cities, regions and international trade[END_REF], Krugman [START_REF] Krugman | Increasing returns and economic geography[END_REF] and Puga [START_REF] Puga | The rise and fall of regional inequalities[END_REF]).1 An alternative modeling strategy is proposed by Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF], who have shown that the core-periphery model can be analyzed 1 Since the CES approach is analytically unable to deal with the case in which certain goods are not bought in certain locations, in choosing this framework we implicitly accept the fact that all goods are consumed everywhere, which clearly contradicts our main point of interest. In order to apply the CES to cases with corner solutions we have to use a translated

CES function (the traditional CES never allows for that type of solution) (see Deaton and

Muellbauer [START_REF] Deaton | Economics and consumer behavior[END_REF]). This translated function, which has been used in applied demand theory and econometrics, does unfortunately not allow for analytical resolution of firm's optimization problem and seems to be of limited interest in theoretical modeling.

in a much clearer and analytically tractable fashion with the help of the quadratic utility.

While the qualitative results are similar to those obtained in the CES core-periphery model, those authors have shown that several drawbacks of the CES are overcome by the quadratic utility: solutions are in closed-form and there is no need for numerical simulation, the economic meaning of the various parameters is disentangled and the artifical flavor of the particular consequences of the iso-elastic approach disappear.

Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF] especially show that the demand functions and equilibrium prices now depend on all the fundamentals of the model (including the distribution of firms in space), a result which is more in line with what is known in spatial pricing and demand theory. More important, as shown in Section 2, the quadratic utility is compatible with a simple analytical approach to demand systems with corner solutions. Thus this modeling framework allows us to conveniently addressed the questions concerning the regional availablity of goods and possible equilibria when there is no trade.

The remainder of this paper is organized as follows. In Section 2, we develop an analytical framework that helps us tackle the question of which firms are active in which markets. In Section 3, we apply this framework to the general equilibrium model initially developed by Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF]. We show that agglomeration can arise even in the absence of trade, which highlights the fact that trade is not a necessary condition fo r agglomeration to occur. Section 4 offers some conclusions and points towards future research directions.

Q uadratic utility, corner solutions and firms

One approach to consumer problems that allows for both interior and comer solutions with clear-cut analytical results is that of the quadratic utility. Recent works in economic geography, though focusing exclusively on the case of interior solutions, have shown that this kind of modelization may actually be analytically superior to the traditional CES approach (refer to Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF] and Ottaviano and Thisse [START_REF] Ottaviano | On economic geography in economic theory: in creasing returns and pecuniary externalities[END_REF]).

The basic quadratic utility problem, with a mass of N differentiated varieties, can be stated as follows,

V>q)< maxX0)I a f N s.t. / p(i)x(i)di + xq = w + 0 o ^0
where the price of the homogenous good xq is taken as the numéraire, 0 o is the initial endowment in good x 0 and a > 0 and fi > 7 > 0 are parameters. One should note that the positivity constraints on demands x(i) are (as almost always in economics) implicit in this kind of formalization, since one assumes that all varieties will be consumed at the optimum. Since we want to examine the incidence on the spatial equilibrium configurations of certain firms not operating in certain markets, we have to take the comer solutions of (Vq ) explicitly into consideration. In order to solve (Vq ) easily, we substitute the constraint into the objective function. This yields an unconstrained optimization problem which, since the objective is quadratic in x , has first order conditions given by a linear system of equations for all i e [0, N]. In what follows, we set e := /? -7 for notational convenience.

The parameter e can be interpreted as a substitutability parameter between varieties.

Varieties become perfect substitutes in the case in which ¡3 -► 7 (i.e. when e -> 0) and they become independent in the case in which 7 0 (i.e. when t ¡3). The demands

(2) can be rewritten in a more compact way as Straightforward resolution of conditions (1) yields the demand functions a)

'N p (j)d j (2) x*(i) = a -(b -f cN)p(i) + cP (i), ( 3
)
where a, b and c are positive coefficients, given by and where ------, b = -------andc = ------ [START_REF] Fujita | Economics of Agglomeration[END_REF] x

a 1 7 a = -
*(i) = [a -(b + cN)p(i) + cP(i)] + (7) b -f cN if p(i) < p(i) 0 if p(i) > p(i) (8)
and

f -b -cN if p(i) < p(i) X*r(i) = \ (9) 1 0 if p(i)>P(i)
where the subscripts I and r refer to the left-and right-hand derivatives respectively.

In order to keep things simple, we do not explicitly incorporate strategic decisions concerning the choice of active markets into our model but we rather treat both the choice of prices and the 'choice' of active markets via firm's optimization problem.

This yields a rudimentary and myopic model of firm "behavior" that assumes that each firm is active in each market where it can make at least a short-term zero profit; that most of firm's real-world decisions concerning markets are essentially based on long-term considerations will be neglected for the sake of tractability. Each firm in our model has two types of markets: active markets in which it can make at least a zero profit and inactive markets in which it cannot profitably operate. We assume that even if a firm is not active in a market, it quotes a fictional price on that market, which can loosely be interpreted as the price consumers would have to pay in order to get the good at that particular location. As Ottaviano and Thisse [START_REF] Ottaviano | On economic geography in economic theory: in creasing returns and pecuniary externalities[END_REF] argue, "it is precisely because in such locations potential prices are either too high for buyers or too low for sellers that the corresponding good is not traded there".

We assume, as usual in a monopolistic competition context, that each firm pro duces a single variety of the differentiated good under increasing returns to scale using

7T(i) = L[p(i) -r]x*(i) -w(f>, ( 11
)
where w is the wage rate of labor. The fundamental problem the firm faces when trying to be active in the market is highlighted by ( 6) and ( 11). On the one hand, the firm must set a delivered price that is low enough and satisfies (6) in order to have a positive market share; on the other hand, this delivered price must be high enough to allow the firm to cover (part of) the loss in trade costs, as can be seen from [START_REF] Krugman | Increasing returns and economic geography[END_REF]. It is therefore possible that a firm cannot satisfy simultaneously those two opposing constraints for a given set of parameters, so that it always makes a negative profit in the market. In that case, the profit maximizing solution is to set a price such that the demand it faces is equal to zero. This scenario can, for theoretical convenience, be considered as the firm 'choosing' not to be active in the market. When the firm can simultaneously set a price below the shock-off price (6), that is compatible with the level of trade costs (11), it will be able to sell her output and be active in the market.

The maximization of profit (11) with respect to p(i) yields the following left-and right-hand derivatives:

*■«(*) = £[**(*') + (p(i) ~ T)x*j(i)] (12)
< (*) = L[x*(i) + (p(i) -t )x*'t{i )}. ( 13
)
The optimality conditions in the two possible cases (that of the firm being active or not) can be analyzed as follows. First, we know that the condition 0 G [ttJ (z), 7rJ.

(i)] is

Unfortunately, our approach in terms of extended demand functions does not allow for analytical resolution of firm's profit maximization problem under either uniform delivered or mill pricing. always necessary for p(i) to be a profit maximizing price. Using (8), ( 9) and ( 10) in ( 12) and ( 13), one can check that this condition trivially holds for all pricesp(i) > p(i), since for those prices consumer demand is equal to zero. In order for the cut-off price (6) (corresponding to the comer solution x*(i) = 0) to be optimal, we have to examine under which conditions

lira M i) -a + cP(i) -(b + c N ) t < 0. (14)
p(*)<p(»)

In case condition (14) holds, firm's profit increases monotonically as its price ap proaches the cut-off price, which maximizes its profit (stricto sensu this price mini mizes firm's losses on the market). As one can check, (14) holds if and only if r > p(i).

Using the definitions of a, b and c, given by (4), we can rewrite this condition as r > " + (X5) € 4-N 7 Condition (15) highlights the fundamental trade-off which determines whether the firm will be active in the market or not. This trade-off depends on the level of trade costs r, the degree of competition in the market (given by P(i) and N ) and the degree of product differentiation (given by e and 7). Condition [START_REF] Puga | The rise and fall of regional inequalities[END_REF] shows that stronger competition (given by a relatively lower P(i) and higher N ) works against firm i being active in the market. As expected, the competition effect vanishes as varieties become independent (i.e. when 7 -» 0). Stronger product differentiation (e not too close to 0) and higher preference for the differentiated good make conditions ( 14) and (15) more unlikely to hold, so that firm i will be active in the market. Note that if varieties become perfect substitutes (i.e. when e -► 0), transport costs must be less than the average price of the industry in order for firm i to be active in the market.

Finally, as expected, [START_REF] Puga | The rise and fall of regional inequalities[END_REF] shows that for a given set of parameters, a higher level of trade costs r will make the presence of firm i in the market less likely. All those results agree with what is known in spatial demand theory.

If we turn to the second case r < p(i), so that condition (15) does not hold, the firm can make a positive profit in the market and we hence get interior solutions. If p(i) < p(i), the profit function ( 11) is differentiable so that the optimality conditions reduce to

7T'(¿) = a -2(6 + cN )p(i) + cP(i) + (b -f c N ) t = 0, which implies that _ * f:\ _ a + (b + c N )T + c P (*) " ^ v ( ,) " ----wTiwj---- (16)
is the profit maximizing price firm i sets on the market. As expected, this price is decreasing with the degree of competition and increasing with both the level of trade costs and the degree of product differentiation.

We have shown in this section that the quadratic utility approach allows us to model in a simple way patterns of demand involving both interior and comer solutions.

Depending on both the level o f trade costs and the degree o f competition, certain firms will be active in certain markets and will not be active in others. This leads to richer configurations than in the traditional models of the 'new' economic geography, in which every variety is consumed everywhere. Since the set of active firms in any particular location is determined by both the mass of firms and the aggregate price index in that location, which depends itself on the spatial distribution of firms, we see that the pattern of demand is endogenously determined by the locational decisions of individual economic agents. This approach hence lends itself well to the analysis of how demand patterns are influenced by, and in return influence, the distribution of economic activities in a spatial general equilibrium context. Firms choose prices that maximize profits and, in doing so, indirectly 'choose' in which markets to be active.

Therefore, firms' locational behavior determines which varieties are available in which locations, which in turn determines where other firms locate. This circular aspect is of fundamental importance and drives most of the subsequent results.

A gglom eration w ithout trade

In market s e {H, F}, s ^ r can be either interior or comer, depending on whether the firm can profitably be active in this market while being located in region r or not. This is in line with the fact that in order to be a potential export product, the product must be consumed in the home market. As seen in Section 2, being profitably active in s depends on the level of trade costs r and the degree of competition. The larger r and the fiercer the competition in s, the less likely a firm located in r can profitably enter this market. Indeed, since competition is fierce, prices of substitute varieties that consumers can locally buy from firms in s are relatively low. This implies that if a firm located in r wants to enter market s, it must charge a sufficiently low price in order to capture a strictly positive share of local demand. If trade costs are too high with respect to that price, the firm will always make a negative profit in market $, which simply means that it is not rational for it to be active in that market. Using optimality conditions (19), the first order conditions on the foreign market s yield where the expressions for the bilateral trade case, when r is sufficiently low, are of course the same as in Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF]. Note that the profit-maximizing prices depend on the price aggregates Ph and Pp, which depend themselves on individual prices set by rival firms. In order to determine the equilibrium prices, we use the same approach as Ottaviano et al. [START_REF] Ottaviano | Agglomeration and trade revisited[END_REF]. Each firm sets its optimal price taking aggregate market conditions as given, but taken together these aggregate market conditions must be consistent with optimal individual prices. The two regional price-indices of the M-industry are given by Solving (23) for r € {H ,F } for its fixed-point, using (20) and ( 22

AV*(0) = -( ---± J I l ± 1 ± A £ \ . ( 40
) W 2cf> \4 e [2e + jLij)-1]2 ) K '
The sign of expression (40) depends on the sign of

r l i 2 L2 2 e + -7
0 .

-4e 3 Le + 7 "7-1 " Ae < P (41)

Full agglomeration will be a stable spatial equilibrium if and only if (41) is non positive. This is the case if and only if

The critical size A s of the immobile factor will be called, in accordance with the literature, the sustain point of the autarkic economy; it is the immobile population size below which an agglomerated equilibrium can be sustained once somehow established. A -+4e4>---------------------- ( As one can see, when A < A 8y only full agglomeration is a stable equilibrium (the grayed circles in Figure 1) while the symmetric equilibrium is unstable (the empty circle). As A increases to 3.8 (hence A 8 < A < Af,), two partially agglomerated stable interior equilibria appear (grayed circles in Figure 2) while the symmetric equilibrium remains unstable (empty circle). Finally, when A = 5 > A\, gets large, the only stable equilibrium is given by the symmetric dispersed one (the grayed circle in Figure 3).

The conditions under which the symmetric equilibrium

I + 7 ( ' " ^

C onclusions

As we have shown in this paper, the question of which goods are available where matters in shaping the space-economy. When particular goods are only available in particular locations, the equilibrium configurations can be significantly different from those obtained when everything is available everywhere. In this paper, we have focused

  labor only. Each firm has a fixed production cost of < f > units of labor, zero marginal production cost and uses spatial discriminatory pricing. 2 In order to highlight the main forces at work in the model, we start with a simplified setting in this section. Assume there is a single market with a mass of L consumers. Each firm can access this market at a strictly positive unit trade cost r (expressed in terms of the numéraire), which includes all impedements to trade. Firm i 's profit is given by

  the following developments, we use the same framework and the same notation as Ottaviano et al.[START_REF] Ottaviano | Agglomeration and trade revisited[END_REF]. Consider a setting with two regions H and F. Variables associated with each region will be subscripted appropriately. We suppose that there are two production factors in the economy: mobile manufacturing workers (M-workers) which are employed in the manufacturing (resp. the modem) sector and produce a differentiated good under monopolistic competition and increasing returns to scale; and immobile agricultural workers (A-workers) which are employed in the agricultural (resp. the traditional) sector and produce a homogenous good (the numéraire) under perfect competition and constant returns to scale. Let L be the mass of M-workers and A the mass of A-workers. We denote by À G [0,1] the share of M-workers located in region H ; the A-workers are assumed to be evenly split between the two regions, each of which accommodates a mass A /2 o i them. Finally, let N be the mass of varieties of the differentiated good produced in the economy. Since we assume that there are no economies of scope, each firm produces one and only one variety, so that N is also equal to the mass of firms in the economy. Assume, for simplicity, that the homogenous good can be traded costlessly. The differentiated good can be traded at no cost in the interior of each region, while there is a strictly positive unit trade cost of r units of the numéraire in order to ship one unit from region H to F and vice versa. Since there are no intra-regional trade costs for M-goods, each M-firm is at least active in the market it has chosen to locate in. A firm located in H (resp. in F) therefore always sells in its home market H (resp. F) and can, under certain conditions that we explicit later, also sell in its foreign market F (resp. H). Using the demand functions (7), the demand a firm located in r € {H , F} faces in region s € {H , F} is given by =[a-(b + cN )p" + CP8} \ (17) where prs is the mill-price charged by a firm located in region r when selling in market s. 3 Hence, the profit of a firm located in region r E {H, F} is given by 7T r = P r r x * r ( P r r ) + (prs ~ T)x*a(prs) + (¡m ^J -<jwr -7rrr -f 7Trs -(fywr , s y£r (18) where x*r and x*s are the individual demands in the home and foreign market, given by (17), wr is the wage rate in region r and 0 is the fixed labor requirement in terms of mobile production factor L. Let n n = AL/0 and rip -[I -A)L/(f> be the mass of firms (respectively varieties) located in each of the two regions when labor markets clear. In accord with empirical evidence (see Greenhut [8] and Head and Mayer [9]), we assume that firms use a spatial discriminatory pricing policy and set a particular price for each market separately. Hence, firm's objective function is separable with respect to prices, so that maximization of total profit amounts to maximization of profits on each market separately. The conditions for profit maximization on each market, which are analogous to those discussed in the previous section, 7rrs are the gross revenues on each separate market. Since a firm located in region r € {H, F} is always active in market r, the solution on its home market is an interior one. Therefore, -off price in market r 6 {H ,F }. The price (20) depends of course on aggregate market conditions given by the price-index Pr. The solution on firm's foreign Q Since all firms are symmetric, we drop the firm index i in the following developments. Firms therefore only differ by the region they are located in and by the particular variety they produce.

= { 2 +

 2 nr p*r(Pr) +n"p*r(Pr), r,s € {H ,F }, r ■£ s. see from (25), both in the high and in the low trade cost case, the price p*r is a decreasing function of the mass of firms that operate in market r € {H , F} (recall that n 8 = Nnr). This is due to price competition between firms. The main difference is that in the low trade cost case this decrease is linear while it is strictly convex in the high trade cost case. 4 Hence, competition is weaker in the case of autarky since firms in region r are only subject to local competition while there is no competition from outside. Firms are thus able to maintain higher average prices in the case o f autarky as n r increases, which suggests that consumers will have less incentive to migrate to region r once the mass n r o f industry in that region gets large (there is a sort of decreasing effect of price competition with the mass of firms in the local market). As we explain later, this could be one possible reason for the existence of partially agglomerated equilibria in this configuration of the model.In the remainder of this paper, we focus on the case in which trade costs are 'high' in order to show that trade is not a necessary condition for agglomeration to emerge. We believe that the theoretical case of 'high' trade costs is as important as the case of 'low' trade costs because nobody neither knows for sure what 'high' or 'low' precisely means is in that type of models nor how it relates to actual trade costs in the real world. Ottaviano et al. [13] have shown that demand is non-negative for all spatial distributions of firms if and only if 4 In the bilateral trade case of Ottaviano et al. [13] the share of local firms A appears only in the numerator; in the case without trade, this share appears only in the denominator.This suggests that the results in both cases can be significantly different.In that case, trade costs are sufficiently low so that firms always sell in the foreign market, which corresponds to the traditional scenario in which all firms are active everywhere. We restrict our paper to the case in which condition (27) does not hold.More precisely, we start with the simplest case in which trade costs are so high that no inter-regional trade occurs at all no matter how firms are distributed between regions H and F. This scenario corresponds to what we call inconditional autarky and is the polar case of the one studied in Ottaviano et al. [13]. 5 In order for a firm located in F not to be active in H y C L -}■ cP% Since the right-hand side of (29) is decreasing with respect to A, we set A = 0 in order for it to hold for all distributions of firms. Hence T > Taut :=^=a (30) is the desired level of trade costs for which we have inconditional autarky. 6 Substituting the equilibrium prices (25) and (26) into (17), we obtain the equilibrium demands 5 As might be expected, there is a whole range of intermediate values of trade costs for which patterns of trade are more complex than in the simple autarky or bilateral case. Those conditional unilateral trade patterns, which are harder to analyze but which yield some very interesting results, will be more thoroughly examined in a forthcoming paper. 6 It is interesting to note that for trade between the two regions to occur for at least some spatial distributions of firms, the level of trade costs must be lower than consumer preferences a for the differentiated good. Therefore, if consumer preferences for the differentiated good are strong, trade can take place even if the absolute level of trade costs is high. the model's primitives. 7 It is of interest to note that equilibrium prices and quantities are functionally related. Those relations, which are similar to the ones obtained by Belleflamme et al. [2], are given by p*rr = (b + cN)~1x*r r =ex*rr, re{H,F} (33) and help us to simplify the expressions of the indirect utilities. The equilibrium wages are determined as in Ottaviano et al. [13] by a bargaining process in the monopolistically competitive industry, in which firms compete for workers by offering higher wages until no additional firm can profitably enter the market. Hence, all profits are absorbed by the wage bill, which is synonymous with zero profits for firms in the M-industry. Therefore, the wage rate in region r 6 {H, F} satisfies on firms' activities in market r since there is no export to the foreign region. Using (25) and (31) in (34), the equilibrium wage in region r 6 {H ,F } '**) m + ' c ir = ( j + H »[2. + m,? ' (35) Let us now derive the expression of the indirect utility in region r E {H, F}. Using the quadratic utility defined in ( V q ) , the symmetry between firms and relation (33), we have Note that the expressions of the import prices j > * fh and Vhf are of no interest since they will cancel out when multiplying the zero import quantities in the indirect utility. Hence we do not bother to establish their expressions. to be a polynomial of degree 4 in A. In reality, it turns out to be simply cubic (compare this result with the one obtained by Belleflamme et al. [2] in a partial equilibrium con text). Expression (39) shows that we can expect different results than in the traditional bilateral trade case of Ottaviano et al. [13], where the indirect utility differential is shown to be linear in A. Let us start with the conditions under which we have full agglomeration with A = 0 (due to the fact that A V ^l) = -AF*(0), the conditions for full agglomeration with A = 1 are the same). Consider Ay*(0) which, using (39), is given by

A = 1 / 2

 12 is stable are more difficult to examine (that this symmetric equilibrium exists is a direct consequence of the symmetry of AV* with respect to 1/ 2). In order to check for the stability of the dispersed equilibrium, we have to evaluate the sign of the derivative of the indirect utility differential at the symmetric equilibrium. Using (39), this derivative at A stability of the symmetric equilibrium depends on the sign of 6 e + ^(L-4A).

P ro p o sitio n 3 . 1 (x 2 y 4 - 3 (

 3143 that (44) be non-positive, the symmetric equilibrium is stable if and only if A>A = IM+j L 47 According to the literature, will be called the break point of the autarkic economy; it is the immobile population size below which symmetry must be broken because the symmetric equilibrium becomes unstable. It is easily verified that A a < Af, for all values of the model's parameters if 7 > 0 and L > 0. Hence, up to a symmetry there are never multiple equilibria in the inconditional autarky case. It is of interest to note that, since the sustain point lies strictly below the break point, there is a range of values of A for which we have interior equilibria which are characterized by partial agglomeration o f economic activities (the existence of a spatial equilibrium is a direct consequence of the continuity of the indirect utility differential; refer to Ginsburgh et al. [7] for more details). The stability of the partially agglomerated equilibria follows from the unicity and existence of equilibria in our model. Both uniqueness of equilibria and existence of stable partial agglomeration in our model are different from the traditional results as e.g. in the models of Krugman [11] or Ottaviano et al. [13]. In those models, partial agglomeration is never a (stable) equilibrium. 8 The catastrophic transitions from dispersion to agglomeration, characteristic of most models of the 'new' economic geography, are absent in our inconditional autarky case, in which the transition from dispersion to agglomeration is smooth. This allows for a wider range of different types 8 Belleflamme et al. [2] show in a quadratic utility model, that partial agglomeration of firms in industrial clusters is possible when there are exogenous spillovers on the production side. Their results are similar to ours but are obtained in a partial equilibrium context with very different underlying forces and scale of analysis. While we focus on agglomeration due to pecuniary externalities on a large regional scale, Belleflamme et al. [2] focus on agglomeration involving technological externalities on a much smaller spatial scale. of equilibria while not being subject to indeterminacy and catastrophic bifurcations. Our main results are summarized in the following proposition. INCONDITIONAL AUTARKY EQUILIBRIA) Suppose that r > r0. Then we have, depending on the mass of immobile factor A and mobile factor L in the economy; the following equilibria: • a completely agglomerated equilibrium with X = 0 or X = 1 if A lies below the sustain point A s. • a partially agglomerated equilibrium with 0 < A < 1, A / 1/2 if A lies between the sustain point Aa and the breakpoint Af,. In that case, w*-------r • a dispersed equilibrium with A = 1/2 if A lies above the break point A^. PROOF. The first part of the proposition is established by (42) and (45). In order to derive the analytical expressions for the interior equilibria, we have to solve for the roots other than A = 1/2 of (39). Putting (39) onto the same denominator and factorizing the obvious root, we need to solve > L

□Figures 1 , 2

 12 Figures 1, 2 and 3 illustrate the three fundamental types of spatial equilibria when A = 3, A = 3.8 and ^4 = 5 respectively (compare with Figure 5 in Puga [15]).

Figure 4

 4 Figure 4 illustrates a typical bifurcation diagram in our inconditional autarky scenario.As usual, bold solid lines correspond to stable equilibria while bold broken lines correspond to unstable ones. As one can see, there are no catastrophic transitions and the evolution of the spatial equilibria is smooth.

Figure 4 :

 4 Figure 4: Smooth transitions of equilibria under autarky on the extreme case of regional autarky in which all goods are only available locally. Although this assumption is not likely to hold for most of todays manufacturing industries, it remains suited either to historical applications, or to the analysis of the spatial distribution of non-tradeables or to the analysis of regional imbalances in developing countries with poor transport infrastructures. Our setting allows for a large range of possible equilibrium configurations, including stable partial agglomeration of activities in the two regions, despite the absence of interregional trade. 9 This clearly shows that trade is neither a necessary nor a sufficient condition fo r agglomeration to emerge. Taken together, both our paper and those of Puga [15] and Tabuchi and Thisse [16] illustrate that the catastrophic bang-bang behavior of many spatial models disappears when alternative hypotheses concerning the mobility of goods and factors are made. Whereas those models generate partial agglomeration by restricting the mobility of production factors, we have shown here that restricted mobility of outputs can play an analogous role. Therefore both the mobility o f factors and the mobility o f goods are fundamental in shaping the space-economy and should hence be treated as 9 To the best of our knowledge, the existence of stable partial agglomeration, which is mainly due to the fact that not both goods and factors are simultaneously perfectly mobile, has only been recently shown in a different general equilibrium context by Puga [15] and Tabuchi and Thisse [16].

is an aggregate price index of the differentiated industry. As one can see from (3), demand for variety i is decreasing at a constant rate -(b + cN) with respect to own price p(i). This implies that there is a cut-off price beyond which demand is no longer positive. Using (3), we see that demand for variety i is positive if and only if i.e. if the price p(i) charged by firm i is lower than the cut-off price p(i)y whose analytical expression is quite easily established. As one can see from (6), firm i is more likely to have a positive demand if competition is mild (hence if N is small), if goods are bad substitutes (hence if c is small) and if market-size is large (as noticed by Belleflamme et al. [2] and Ottaviano and Thisse [14], the parameter a, and hence a, can be interpreted in terms of market-size). Since we are interested in both corner and interior solutions, we integrate the positivity constraints indirectly into the demand functions in order to ensure that demands are non-negative for all prices (refer to the appendix for a mathematical justification of this approach). The demands (3) can be redefined in extended form as where [/]+ denotes the positive part of / . Expression (7) shows that the extended demand functions are piecewise affine, convex and not differentiable. Being convex, the functions (7) allow for directional derivatives everywhere. Those are given by

	e + N 7	e H-N 7	-e(e + N'y)	(4)
				(5)

Using the well-known equalities max {x

	^x } } = §(#i + x 2) +	-x 2\ and
	[/]

+ = max {0, / } , an alternative expression for x*(i) is finally given by ar*(z) = | [

	a -(b + cN)p(i) + cP(i)]

4-\ \a -(b -1 -cN)p{i) + cP (i)|. (10) Let us turn next to firm's profit maximization problem. Traditionally, one only focuses on firm's price selection problem and eliminates one important strategic aspect: firm's choices concerning the markets in which it wants to be active. As far as we know, this question has not been addressed in a spatial general equilibrium context until now.