a dynamic tiebout theory of voluntary vs involuntary provision of public goods this paper considers a dynamic model of tiebout like migration between communities that utilize distinct allocation procedures for public goods at issue is whether voluntary or compulsory procedures are more likely to prevail over time we model infinitely lived individuals who make repeated sequential location decisions over one of two communities each community uses a distinct mechanism for allocating public goods the first is one in which contributions are given voluntarily by the citizenry of the community the second is a compulsory scheme by which individuals are taxed proportionately to wealth with the tax determined by a majority vote opportunities to accumulate wealth exist via accumulation of public capital the markov perfect equilibria of the dynamic game are studied our main result shows that when accumulated wealth converges to a steady state individuals locational choices eventually select the involuntary provision mechanism this holds despite the fact that unanimous location in the voluntary provision community may in many cases remain as a nash equilibrium of the static game each period we also describe conditions under which voluntary provision survives these conditions require that accumulation of capital fails to decrease wealth dispersion over time the results are shown to be consistent with findings relating inequality to school choice

a tiebout theory of public vs private provision of collective goods abstract we study whether coercive public provision or voluntary private provision of public goods can survive when individuals who vote with their feet can choose between communities that differ in the way that public goods are provided we obtain the following findings i an equilibrium always exists in which all individuals migrate to the community which uses voluntary provision ii under very robust conditions on preferences and income distribution an equilibrium exists in which all individuals migrate to the community which uses coercive provision iii interior equilibria in which collections of individuals move to both communities exist when income distribution is sufficiently polarized such equilibria are shown to be stratified richer individuals migrate to the community with voluntary provision while poorer individuals reside in the public provision community in the case where there are two types of wealth endowments existence of stratified equilibria seems to require a negative trade off between the wealth ratio of the rich to the poor and the numerical ratio of rich to poor in society

sorting equilibrium in a multi jurisdiction model abstract this paper analyzes a general model of an economy with heterogeneous individuals choosing among two jurisdictions such as towns or political parties each jurisdiction is described by its constitution where a constitution is defined as a mapping from all possible population partitions into the possibly multidimensional policy space this study is the first to establish sufficient conditions for existence of sorting equilibria in a two jurisdiction model for a policy space of an arbitrary dimension

residential choice and the supply of local public goods abstract this paper deals with the supply of local public goods in an agglomeration consisting of a central city and a given number of suburban communities the properties of an equilibrium under free mobility are studied in particular a community s population size level of public good and public spending are analyzed as a function of distance to the central city an extension analyzes an equilibrium with two income classes and the corresponding income location pattern

note comment and letter to the editorsustainable oligopolies in this paper we show that an oligopoly market where both increasing returns to scale and competition are present can nevertheless satisfy stability conditions in a sustainable oligopoly 1 each consumer chooses the firm which proposes the price quality schedule he prefers 2 firms earn non negative profits 3 no new firm could attract consumers and make profits we prove that such a sustainable oligopoly exists under rather weak assumptions the results apply to most models of vertical or horizontal product differentiation or to models of quality differentiation due to congestion effects

efficient exchange with a variable number of consumers the notion of a club efficient allocation introduced in this paper is shown to allow for a unifying treatment of rather disparate matters the main result deals with the dual characterization of such allocations the fundamental theorems of welfare economics the limit theorem on the core and a general version of a henry george theorem on the relationship between aggregate land rent and local public expenditures all can be recovered as special cases of this paper s main result

second best taxation as a game second best theory usually lies in the realm of normative analysis it focuses attention on the best solutions which still can be obtained in problems where constraints of various natures forbid the attainment of first best pareto optimal situations its central concern is the characterization of such second best solutions and a large part of the literature concentrates on the optimal design of taxes or of policies of public firms taking a second best problem we try in this paper to shift the emphasis from normative to positive considerations the solution we are interested in is not optimal with respect to some a priori given social welfare function embodying justice objectives but it is supposed to reflect the power of the different agents in a negotiation process clearly the conceptual tools required for such an analysis are to be found in game theory and it is actually a game theoretical approach that we follow here the model we are looking at is presented in section ii it formalizes one of the simplest second best problems that can be imagined we have a twogood economy with one private good and one public good agents have different wealth in private good and the public good is financed through a wealth tax this latter fiscal system is clearly not flexible enough to adjust contributions with marginal willingnesses to pay so that we actually face a second best situation there is one decision variable in the society the tax rate which determines the public good production about which the agents have conflicting desires to this problem we associate a game which provides a precise framework for the analysis of the power of the agents the positive outcomes of the negotiation process are supposed to belong to the core of this game sections iii and iv concentrate on the analysis of the core the results strongly contrast with those obtained in the classical studies of the core of 67 0022 053 l 81 040067 25 02 00 o

a simple model of spatial banking competition abstract this paper applies the financial intermediation and optimal contract theories to the standard hotelling model in it we demonstrate that too little investment is undertaken and too much costly monitoring is involved in the unregulated banking industry thus our model suggests a rationale for the government to regulate bank locations

equilibrium in a finite local public goods economy abstract this paper examines the existence of a noncooperative equilibrium in a finite local public goods economy where consumers have quasi linear preferences jurisdictions consist of consumers who chose the same public project and finance the cost of production of public goods through either a proportional income tax or a poll tax we show that under a proportional income tax scheme a nash equilibria may fail to exist under a poll tax scheme an equilibrium always exists but in general nash equilibria violate a very weak efficiency condition we conclude by commenting on the stabilizing effect of zoning policies journal of economic literatureclassification number c71

the benefits and costs of strong patent protection a contribution to the current debate abstract today s conventional wisdom is that strong patent rights are conducive to economic progress yet not long ago students of the patent system took a more nuanced position arguing that often strong patents were not necessary to induce invention and entailed significant economic costs several empirical studies have supported this position however the current advocacy invokes theories of the positive benefits of patents that were repressed in the earlier more negative analyses this essay reviews these theories and the empirical evidence that might bear on them the authors conclude that there is reason for concern that the present movement towards stronger patent protection may hinder rather than stimulate technological and economic progress

bank commercial loan markets and the role of market structure evidence from surveys of commercial lending abstract this paper seeks to test two tenets that underlie the current practice of antitrust analysis in banking the first is the view that bank commercial loan markets are local in nature and the second is the view that banks in more concentrated markets are more likely to engage in some form of noncompetitive behavior tests of both of these tenets are conducted using an extensive set of loan specific survey information not previously employed to address these issues results consistent with the existence of local banking markets and the dominance of competitive differences as an explanation for observed differences in loan rates are found

political institutions and sorting in a tiebout model we construct a computational model of tiebout competition and show that political institutions differ in their ability to sort citizens effectively in particular we find that certain types of institutions those that become more politically unstable as citizen heterogeneity increases perform relatively poorly given a single jurisdiction yet these same institutions perform relatively well when there are multiple jurisdictions we provide an explanation for this phenomenon which draws upon simulated annealing a discrete nonlinear search algorithm jel

migration proof tiebout equilibrium existence and asymptotic efficiency abstract tiebout s basic claim was that when public goods are local competition between jurisdictions solves the free riding problem in the sense that equilibria exist and are always pareto efficient unfortunately the literature does not quite support this conjecture for finite economies one must choose between notions of tiebout equilibrium which are pareto optimal but which may be empty or which are nonempty but may be inefficient this paper introduces a new equilibrium notion called migration proof tiebout equilibrium which we argue is a natural refinement of nash equilibrium for a multijurisdictional environment we show for sufficiently large economies with homogeneous consumers such an equilibrium always exists is unique and is asymptotically pareto efficient

voting with ballots and feet existence of equilibrium in a local public good economy abstract this paper proves a general existence theorem for equilibrium in a local public good economy with free mobility by extending greenberg and shitovitz s j econ theory46 1988 223 236 approach each jurisdiction s collective choice rule is the d majority voting rule proposed by greenberg econometrica47 1979 627 636 spillover effects of local public goods externalities due to the population distribution and snob effects are all allowed we need transitivity and completeness of preferences these assumptions are not used by greenberg and shitovitz because they do not permit consumers to move free mobility of consumers causes disconnections in consumption sets a problem addressed here journal of economic literatureclassification numbers c62 d72 h72 r13

the consequences of overlapping tax bases for redistribution and public spending in a federation tax and expenditure policies are studied in a federation with imperfectly mobile households states implement a linear progressive tax and supply a public good a vertical fiscal externality reflecting the effect of state policies on federal revenues provides an incentive for state taxes to be too progressive a horizontal fiscal externality causes nonoptimal state taxes and expenditures because of the migration effect the federal government implements its own linear progressive tax and makes transfers to the states the federal government can nullify both externalities by appropriate fiscal policies and redistributive taxation can be decentralized to the states c 1998 elsevier science s a

the acquisition and commercialization of invention in american manufacturing incidence and impact abstract recent accounts suggest the development and commercialization of invention has become more open greater division of labor between inventors and innovators can enhance social welfare through gains from trade and economies of specialization moreover this extensive reliance upon outside sources for invention also suggests that understanding the factors that condition the extramural supply of inventions to innovators is crucial to understanding the determinants of the rate and direction of innovative activity this paper reports on a recent survey of over 5000 american manufacturing sector firms on the extent to which innovators rely upon external sources of invention our results indicate that between 2007 and 2009 16 of manufacturing firms had innovated meaning had introduced a product that was new to the industry of these 49 report that their most important new product had originated from an outside source notably customers suppliers and technology specialists i e universities independent inventors and r d contractors we also compare the contribution of each source to innovation in the us economy although customers are the most common outside source inventions acquired from technology specialists tend to be the more economically significant in term of their gross commercial value as a group external sources of invention make a significant contribution to the overall rate of innovation in the economy innovation policies both public and private should pay careful attention to the external supply of invention and the efficiency of the mechanisms affecting the relationships between inventors and innovators

local public goods with mobility existence and optimality of a general equilibrium abstract the existence and optimality of a general equilibrium in a model with a finite number of locations among which the continuum of individuals each individual belonging to one of a finite number of types have to choose is investigated each community finances its own production of public goods by taxes the way in which the tax burden in shared among the different types in the different regions is left arbitrary the model allows for restrictions on the mobility of either residents and or workers congestion and externalities in both production and consumption commuting costs preferences of an individual may also depend on his location as well as on the distribution of all individuals across locations

weakly democratic regular tax equilibria in a local public goods economy with perfect consumer mobility in this paper we study the existence of equilibria in a local public goods economy which has the following structure there are a finite number of geographical regions each region has a government which provides public goods locally by buying private goods inputs on competitive markets and transforming these inputs into outputs of public goods by using a convex technology the local public goods are pure in the sense that all the local residents consume the total produced with no spillovers to other regions each regional government raises revenue from the residents of its region to cover the costs of the public goods it provides the local governments are assumed to be weakly democratic in the sense that no public sector proposal that is a vector of public good provisions and a tax scheme to pay for it will be enacted for which there exists an alternative proposal which is unanimously preferred by the local residents note that it is not being assumed that unanimity is a necessary condition for a public sector proposal to be enacted private goods are produced by price taking profit maximizing producers using convex technologies and are traded across regions a continuum of price taking utility maximizing consumers who are perfectly mobile across regions treat parametrically the public sector proposals of the various local governments in deciding where to live there are a finite number of different types of consumers with type defined by a consumer s preferences initial endowments and share of private sector profits a feasible allocation is a specification of a partition of the consumers among the regions a vector of technically feasible public good provisions and an associated vector of private good inputs used in its production for

financial intermediation and delegated monitoring this paper develops a theory of financial intermediation based on minimizing the cost of monitoring information which is useful for resolving incentive problems between borrowers and lenders it presents a characterization of the costs of providing incentives for delegated monitoring by a financial intermediary diversification within an intermediary serves to reduce these costs even in a risk neutral economy the paper presents some more general analysis of the effect of diversification on resolving incentive problems in the environment assumed in the model debt contracts with costly bankruptcy are shown to be optimal the analysis has implications for the portfolio structure and capital structure of intermediaries

do local governments use their tax bases efficiently abstract this paper analyzes an economy with multiple governments and with mobility of individuals across jurisdictions where each government is constrained to raise revenue for public expenditures using distortionary taxes a government is said to be competitive if the total benefits and costs of its decisions including the excess burden are perceived to be internalized the competitive equilibrium allocations are not constrained efficient in general there exists another set of distortionary taxes and public expenditures such that when private sector behavior adjusts to maintain equilibrium all individuals in the economy are better off thus competitive decentralized decision making does not lead to an efficient use of the available tax instruments it is also shown that the source of the failure can be interpreted as a missing market and the form of the best decentralized remedy which involves pricing the tax base is derived

property taxes and property values evidence from proposition 212 abstract we examine the effect of proposition 2 1 2 on revenues and housing prices in massachusetts communities that were initially constrained by the law saw large increases in state aid and the use of fees we use these initial constraints as instruments for changes in other components of revenue while treating the change in the property tax as exogenously determined by proposition 2 1 2 our results strongly suggest that communities that were able to increase their property taxes more rapidly saw greater increases in their housing values in the period following passage of the law

political centralization and government accountability boffa acknowledges financial support from the free university of bolzano ww82 piolatto from the spanish ministry of science and innovation eco 2012 37131 and the government of catalonia 2014 sgr 420 ponzetto from the spanish ministry of science and innovation jci 2010 08414 and eco 2011 25624 the spanish ministry of economy and competitiveness ryc 2013 13838 the government of catalonia 2009 sgr 1157 and 2014 sgr 830 the barcelona gse and the bbva foundation through its first grant for researchers innovators and cultural creators

the case against patents evidence that they serve to increase innovation and productivity unless productivity is identifi ed with the number of patents awarded which as productivity is identifi ed with the number of patents awarded which as evidence shows has no correlation with measured productivity this disconnect is evidence shows has no correlation with measured productivity this disconnect is at the root of what is called the patent puzzle in spite of the enormous increase in at the root of what is called the patent puzzle in spite of the enormous increase in the number of patents and in the strength of their legal protection the us economy the number of patents and in the strength of their legal protection the us economy has seen neither a dramatic acceleration in the rate of technological progress nor a has seen neither a dramatic acceleration in the rate of technological progress nor a major increase in the levels of research and development expenditure major increase in the levels of research and development expenditure both theory and evidence suggest that while patents can have a partial equiboth theory and evidence suggest that while patents can have a partial equilibrium effect of improving incentives to invent the general equilibrium effect on librium effect of improving incentives to invent the general equilibrium effect on innovation can be negative the historical and international evidence suggests that innovation can be negative the historical and international evidence suggests that while weak patent systems may mildly increase innovation with limited side effects while weak patent systems may mildly increase innovation with limited side effects strong patent systems retard innovation with many negative side effects more generstrong patent systems retard innovation with many negative side effects more generally the initial eruption of innovations leading to the creation of a new industry from ally the initial eruption of innovations leading to the creation of a new industry from chemicals to cars from radio and television to personal computers and investment chemicals to cars from radio and television to personal computers and investment banking is seldom if ever born out of patent protection and is instead the fruit of a banking is seldom if ever born out of patent protection and is instead the fruit of a competitive environment it is only after the initial stage of rampant growth ends that competitive environment it is only after the initial stage of rampant growth ends that mature industries turn toward the legal protection of patents usually because their mature industries turn toward the legal protection of patents usually because their internal growth potential diminishes and they become more concentrated these internal growth potential diminishes and they become more concentrated these observations supported by a steadily increasing body of evidence are consistent with observations supported by a steadily increasing body of evidence are consistent with

strong tiebout equilibrium under restricted preferences domain abstract we investigate the existence and give a partial characterization of a strong tiebout equilibrium which consists of an endogenously formed partition of the individuals into disjoint jurisdictions with each jurisdiction producing and financing its own public goods and moreover there exists no group of individuals who can all benefit by establishing their own community in particular no single individual finds it desirable to migrate from his equilibrium jurisdiction the existence proof makes use of the notion of consecutive games which we introduce and show that for such games there always exists a partition with a nonempty core

pigou tiebout property taxation and the underprovision of local public goods abstract pigou s proposition that the use of distorting taxes rather than neutral head taxes reduces public service levels is examined in this paper a simple model with a national system of competing local governments is utilized to demonstrate that the use of a distorting property tax on mobile capital decreases the level of residential public services the case where public services are an intermediate producer good is also considered

competition among institutions abstract economic theory offers two different approaches to the analysis of group formation and the role of institutions general equilibrium approach explores the influence of the economic environment on formation of coalitions game theory explores the influence of institutional rules on equilibrium outcomes we introduce an integrative approach an institution s policy depends on its membership while its membership depends on the policies of all the institutions we present three distinct mathematical approaches to these models highlighting the algebraic nature of the question of existence of equilibrium our apparatus cover many economic and political environments including cases with multiple dimensions and multiple institutions journal of economic literature classification numbers c62 d50 d71 d72 h11 h40 r13 r53

does endogenous formation of jurisdictions lead to wealth stratification conditions under which endogenous processes of jurisdiction formation entail wealth stratification are examined in a model where unequally wealthy households with identical preferences form jurisdictions in order to produce a public good financed by proportional taxation we define a stable jurisdiction structure to be a partition of the households into jurisdictions that is immune to individual deviations we define a jurisdiction structure to be wealth stratified when each jurisdiction is composed of households who form an interval with respect to the ordering of their wealth we show that a necessary and sufficient condition for the stratification of any stable jurisdiction structure is for the individual preferences for the public and the private good to exhibit a relation of gross substitutability complementarity between the public good and the private good that is independent from prices and wealth

a critique of tiebout s theory of local public expenditures the last section of this paper presents a rigorous version of tiebout s theory of local public goods it is shown that equilibria exist and are pareto optimal this rigorous theory follows closely the more rigorous part of tiebout s work this rigorous theory makes a number of very special assumptions which make local public goods essentially private the body of this paper presents a series of examples which show that if one tries to generalize the rigorous version of tiebout s theory in a number of interesting directions then equilibria may no longer exist or may not be pareto optimal the conclusion is that tiebout s idea does not lead to a satisfactory general theory of local public goods the goal of this paper is to point out that tiebout s notion of equilibrium with local governments does not have the nice properties of general competitive equilibrium except under very restrictive assumptions tiebout 39 suggested that there are competitive forces which tend to make local governments allocate resources in a pareto optimal fashion consumers choose to live in those towns with the mix of taxes and public goods they prefer local governments choose this mix so as to attract inhabitants this idea may seem intriguing for it suggests that the invisible hand solves an important part of samuelson s perplexing public goods problem 32 tiebout in fact makes an argument which is nearly rigorous i give a rigorous version of his argument at the end of the paper however in this rigorous version so many restrictive assumptions are made that public goods become essentially private in the body of the paper i give a series of examples with which i try to convince the reader that one is forced to adopt tiebout s restrictive assumptions the idea is that if one changes any of his assumptions then either equilibria may not exist or may not be pareto optimal my examples are presented in the context of a general class of tiebout models i consider several subclasses one of which is the special case considered by tiebout in each of the subclasses except that considered by tiebout i give a counterexample either to the existence of equilibrium or to its pareto optimality the subclasses are so chosen that the difficulties they reveal would be shared by any reasonable tiebout model which differed from his special case i believe that my examples controvert tiebout s suggestion 39 last paragraph that his theory compares favorably with competitive equilibrium theory most of the examples in this paper have already appeared in the literature i cite related work as i go along what is new here is that i assemble the examples in a unified argument

on the dynamic selection of mechanisms for provision of public projects abstract how do individuals spatial decisions affect the institutions for public goods provision over time this paper describes a dynamic model in which the provision mechanism for a public project is itself the object of locational choice of individuals individuals in an ongoing society must choose between a location with a majority rule mechanism and one with a voluntary contribution mechanism each mechanism determines a funding decision for a local public project which is repeated over time generations of individuals asynchronously supercede their parents creating an entry exit process that allows individuals with possibly different beliefs to enter society a self confirming equilibrium sce belief process describes an evolution of beliefs in this society consistent with a self confirming equilibrium fudenberg and levine 1993 of the repeated location provision game it is shown that the process with belief mutation as new individuals enter society results in a globally absorbing state in which the majority rule mechanism is the unique survivor of the two

local government structure and urban residential location the large research literature on the tiebout model has developed with little attention paid to the urban economic structure in which local government functions this paper attempts to examine the theoretical consequences of local jurisdictions functioning within a conventional monocentric urban model it also discusses a mathematical formulation of a two jurisdiction linear city in which the local service level and local property tax rate might be used as strategic variables in a game theory sense it is concluded that for this to happen the local service level has to have more than one element which is intuitively appealing some references are developed to current british local government and possible changes

clubs and the market large finite economies abstract this paper builds a general equilibrium model of finite economies with exchange and club formation agents trade multiple private goods widely in the market can belong to several clubs and care about the characteristics of other club members because club memberships are indivisible and choices of club memberships must be coordinated across the population the core of such an economy may be empty and equilibrium may not exist however for large finite club economies an approximate core is not empty and states in this approximate core can be approximately decentralized by prices for private goods and for club memberships the arguments use convexification tools familiar from the literature on private goods economies and a new tool of some independent interest that addresses the special problems created by the nature of club memberships journal of economic literature classification numbers d2 d5 h4

the consequences of labour mobility for redistribution tax vs transfer competition abstract in a context where both the poor and the rich are imperfectly mobile this paper compares the nash equilibrium levels of income redistribution from the rich to the poor when jurisdictions compete either in taxes in transfers or both in taxes and transfers although taxes and transfers are linked through the budget balanced requirement the analysis reveals intriguing differences indeed it turns out that transfer competition results in much less redistribution than tax competition while tax transfer competition involves an intermediate level of redistribution in each approach the mobility of the rich is detrimental to redistribution and an increase in the dependency ratio reduces taxes concerning the effect of the mobility of the poor these approaches reach opposite conclusions that is the mobility of the poor is beneficial to redistribution under tax competition but reduces redistribution under transfer competition

household location and tiebout do families sort according to preferences for locational amenities abstract if households sort efficiently across locations then at a given location families receive the same marginal benefit from the locational amenities we test for such sorting by imposing cross equation restrictions on hedonic regressions that difference away location versus house specific effects estimates are obtained using a unique subset of the american housing survey in which adjacent housing units are grouped together and observed in both 1985 and 1989 rejection of the cross equation restrictions unambiguously implies an inefficient sorting of households in contrast the data support the cross equation restrictions which is a necessary but not sufficient condition for efficient sorting

tiebout sorting and neighborhood stratification tiebout s classic 1956 paper has strong implications regarding stratification across and within jurisdictions predicting in the simplest instance a hierarchy of internally homogeneous communities ordered by income typically urban areas are less than fully stratified and the question arises how much do departures from standard tiebout assumptions contribute to observed within neighborhood mixing this paper quantifies the separate effects of employment geography via costly commuting and preferences for housing attributes on neighborhood stratification it does so using an equilibrium sorting model estimated with rich census micro data simulations based on the model and credible preference estimates show that counterfactual reductions in commuting costs lead to marked increases in racial and education segregation and to a lesser degree increases in income segregation given that households now find it easier to locate in neighborhoods with like households while turning off preferences for housing characteristics increases racial segregation especially for blacks doing so reduces income segregation indicating that heterogeneity in the housing stock serves to stratify households based on ability to pay further we show that differences in housing help to accentuate differences in the consumption of local amenities

existence of a spatial equilibrium we prove the existence of a competitive equilibrium in a simple canonical model of spatial economics we emphasize the single difficulty introduced by the use of a continuum of agents to convexify the fundamental locational nonconvexity individual consumption bundles are not bounded above by the aggregate boundedness of initial resources

towards european monetary union without the ems towards emu without the ems paul de grauwe this paper examines the causes of the breakdown of the ems arguing that ems credibility has always been impaired by recessions this has relevance both for the future of monetary union in europe and for the path by which it might be attained i argue that in comparison with the erm the present more flexible exchange rate arrangements will ease not exacerbate some of the technical problems in making the transition to emu i then analyse the political economy of monetary union and identify the main stumbling blocks that remain finally i set out a specific proposal that takes advantage of the new opportunities to move forward towards emu

equivalence of the core and competitive equilibrium in a tiebout economy with crowding types abstract we propose a new model of a local public goods economy with differentiated crowding the new feature is that taste and crowding characteristics of agents are distinguished from one another we prove that if the economy satisfies strict small group effectiveness then the core is equivalent to the set of tiebout equilibrium outcomes equilibrium prices are defined to depend solely on crowding characteristics this implies that only publicly observable information and not private information such as preferences is needed to induce agents to sort themselves into efficient jurisdictions thus our model allows us to satisfy bewley s 6 anonymity requirement on taxes in his well known criticism of the tiebout hypothesis

the paradox of openness appropriability external search and collaboration a b s t r a c t to innovate firms often need to draw from and collaborate with a large number of actors from outside their organization at the same time firms need also to be focused on capturing the returns from their innovative ideas this gives rise to a paradox of openness the creation of innovations often requires openness but the commercialization of innovations requires protection based on econometric analysis of data from a uk innovation survey we find a concave relationship between firms breadth of external search and formal collaboration for innovation and the strength of the firms appropriability strategies we show that this concave relationship is stronger for breadth of formal collaboration than for external search there is also partial evidence suggesting that the relationship is less pronounced for both external search and formal collaboration if firms do not draw ideas from or collaborate with competitors we explore the implications of these findings for the literature on open innovation and innovation strategy 2013 the authors published by elsevier b v all rights reserved