On Krugman's model of economic geography

Geojorum. Vol. 27. No. 4. pp. 439-452. 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0016-7lW96 $151X)+0.00

Pergamon

SOO16-7185(96)00029-2

On Krugman’ s Model of Economic Geography

GARY

A. DYMSKI,*

California,

U.S.A.

Abstract: This essay evaluates the evolution of Paul Krugman’s ideas about economic geography between 1989 and 1996, focusing on the scope and intention of his work. While Krugman’s geographical writings have acknowledged diverse research traditions, he has increasingly focused his efforts on formal spatial models that embody the methods of mainstream economic modeling. This emphasis reflects Krugman’s view that formal modeling holds the most promise for understanding spatial aspects of urbanization. Krugman’s interventions into economic geography have in turn allowed him to develop and articulate his own view of the future of social science: that is, the explanation of self-organizing behaviour should be the focal point of research, and formal modelling is the key means of advancing this agenda. Copyright 0 1996 Elsevier Science Ltd

1. Introduction

rium models,

Paul

in the opposite direction. Macmillan perhaps no longer describe Krugman

Krugman

has since

1989 published

papers and three books on economic essay evaluates and themes spatial

Krugman

through about

Examining

this lens leads

interventions.

and geographers As Martin

(1996)

demonstrates,

economic

questions”

careful

of his

(Macmillan,

initial

specialized

formal

traces to abstract

theorists

man has insisted

ever more

choice/equilibrium

models

models)

should

regain

models, of spatial

pride

spatial

whose relations.

forcefully (here of place

work

to articulate time he has roots he Krug-

that rationaltermed

RCE

in economic

geography;

spatial

omic methodology has limitations, the alternatives are worse. In sum, Krugman’s work has become less

to the analysis 1994), Krugman

he argues

that while

mainstream

econ-

an invitation to geographers to enjoy mutual gains from trade than an incursion into underdeveloped theoretical terrain.

have long appreci“the limitations of of has

Sections

joined many geographers in arguing that models of general competitive equilibrium do not and cannot describe real spatial dynamics. Yet while many geographers have turned away from formalized equilib-

*Department of Economics, University Riverside, CA 92521-0427, U.S.A.

Krugman’s

have moved could today as a foe of

survey

and industrial agglomerarguments by Marshall

approaches

orthodoxy.

adopted

novel

economists

Krugman’s

and Chamberlin that geographers ated. Further, in acknowledging spatial

economic

spatial writings

drew on non-mainstream contributions tentative broad assertions; but over

Krugman’s

to some

have applauded

and Sunley’s

models of increasing returns ation extend (‘microfound’)

traditional

This

of topics

their scope and intentions.

is among the most celebrated

his generation, article

geography.

development

in these writings,

ideas

conclusions

the sequential

numerous

Krugman’s

2 and 3 divide Krugman’s

spatial models into

two thematic strands. Section 2 chronicles the development of his spatial increasing-returns model, which he uses to advance two interrelated arguments: increasing-returns models yield more satisfactory insights into questions in location theory than other formal models; and problems in economic geography are best attacked with the tools of mainstream econ-

of California 439

440

Critical Reviews

omit theory. Section 3 pursues the second strand, Krugman’s more recent argument that selforganization provides a general thematic basis for modeling path-dependence and complexity. Section 4 critically evaluates Krugman’s increasing-returns models, especially as an explanation of urban development. Section 5 puts Krugman’s spatial writing into the context of mainstream economic theory. Section 6 contrasts Krugman’s approach with political economic approaches to economic geography. Section 7 concludes.

2.

The

Evolution

Increasing-Returns

of

Krugman’s

Spatial

Model

The May 1989 paper, ‘History vs. expectations’ (published as 1991a) marks the starting point in Krugman’s intellectual engagement with spatial questions. This paper begins by recognizing the recurrence within economic theory of models with “positive external economies in production”, all of which “have been seen as a way to formulate rigorously a number of heterodox challenges to standard economic doctrine.” Among these challenges Krugman lists his own work on uneven development between rich and poor nations. In models of this sort, history (past outcomes), expectations about future outcomes, or both may govern dynamic paths.’ The paper proposes a method of determining whether history or expectations predominates in a given case. Krugman’s first paper on economic geography per se, ‘Increasing Returns and Economic Geography,’ was completed several months later (March 1990; published as 1991b). Krugman first remarks that economics has largely ignored the “long if somewhat thin” tradition of research on location, and the work on external economies by authors such as Myrdal and Hirschman. Krugman attributes this oversight to these early authors’ failure to follow the trend in economic theory toward rigorous micro-founded theorizing.’ Krugman suggests that bringing to bear “techniques derived from theoretical industrial organization,” especially advances in forma1 models of imperfect competition, will rescue economic geography from this obscurity. Increasing returns create situations of imperfect competition. And until recently, formal models have been much more adept at characterizing behaviour under perfect than under imperfect com-

petition. For whereas agents in perfect competition take prices as given and choose production quantities in isolation, agents’ decisions under imperfect competition are affected by, and hence depend on, what other agents do. However, recent theoretical advances, which Krugman has also exploited in his work on trade theory, have improved the fit between formal models and imperfect competition. In this paper, Krugman proposes a framework that reflects these theoretical advances; he has retained the principal features of this model in all of his subsequent spatial theorizing about increasing returns. Households are spread evenly across the spatial landscape; they engage in agriculture, which provides their subsistence and also income they use to buy products manufactured by the industrial sector. Meanwhile, every producer makes and sets the price of a unique good. Industrial monopolies arise naturally because every firm’s average costs fall as its output expands.’ But firms do not earn excessive profits; for if they did, new firms would enter, produce close substitutes for existing goods, and drive profits to zero. This construct, due to Chamberlin and rigorously exposited by Dixit and Stiglitz (1977), suggests how firms that each have an absolute productivity advantage set prices that allow no one firm to earn excess profits..’ Krugman’s question here is why industrial clusters emerge. Marshall and subsequent analysts have realized that the answer must involve an externality. Marsha11 suggested two such factors: first, the benetits from pooling the labour supply and demand for specialized nontradable inputs: second, the benefits from technology and training spillovers, such as research and development and workforce education. Krugman sets aside technology and training spillovers, remarking that these factors frustrate ‘concrete’ analysis because they “arise in some invisible form.“” Krugman instead reinterprets Marshall’s first factor: he shows that if the industrial sector itself constitutes a principal source of demand for industrial products, and if transportation costs increase with distance, then firms will cluster because they produce under increasing returns. Then transportation costs ensure that multiple clusters will exist instead of one monocentric city: the ‘pull’ of Krugman’s pecuniary externalities balances the ‘push’ of transportation costs. Krugman pulls his evolving ideas together in three

Critical

441

Reviews

October 1990 lectures published in Geography and Trade (1991~). Krugman begins this volume by sum-

Krugman

marizing

work

his own contribution

theory.

Standard

goods

to international

trade theory

can be costlessly

assumes

are immobile;

to inherent

comparative

but factors

so it attributes advantages

blind eye to the fact that countries exist in space.” factors

In Krugman’s

of production

transportation parative

trade flows

both occupy

goods

of

and “turn[s]

model,

a and

by contrast,

presents

some

empirical

closely together, economic

geography.’

theory,

trade

evidence

accident.h

firms locate Krugman

that firms locate agglomer-

fact” in the field of

This stylized

fact is fortuitous.

this same author

He argues that spatial

agglomeration

has explored.” must be associ-

ated with increasing returns of some kind, and expresses the hope that new analytical tools for handling increasing raphy

returns

as a major

can “resurrect

field within

the causes of “agglomeration-the

of cities.”

Central-place

scale economies

economic

economics”

geog-

(1991~. p.

7)”

to this theory: behaviour

book’s

how

central

increasing

market-spillover

geographic

returns

section

of the

(pecuniary)

hexagons,

then

shows

technological

type.

together

and with

these

Krugman

with his own model: on where

behaviour

limitations there

explains

firms

Krugman

instruments

in Elkhart,

Indiana).

as musical

Krugman

presents

his two-region Dixit-Stiglitz model, but his discussion ranges widely over many more examples of increasing returns

than are captured

by his model.

Indeed,

the

a primary

and rational

firm

acknowledges

the

in his framework:

“it does not quite hang . . [although]

as a piece of microeconomics

is a compensating

payoff

us if we insisted

in simplicity on complete

and rigor”

(pp. 4-5). He views his own model “as a complement to other approaches as a substitute” Krugman’s returns

most

strand

to the issue of urbanization,

not

(p. 2). recent

writing

in this increasingDevelopment,

is his 1995 volume,

Ge-

ography, and Economic Theory, which divides neatly into the three chapters indicated in its title.” Chapter on why ‘high’ development

1950s work of Albert

Hirschman,

others--has that while

these

possibilities

that are neglected

become

models,”

not formulating root, involved

theory-the

Arthur

Lewis and

peripheral today. His answer is theorists unearthed “important

rium

(such

city formation

then firms’ demand

locate;

clearly what they were talking

activities

Leaving

cities.

work,

insight . . . denied

agents’

outcomes.“’

demand,

then creates

As in his earlier together

his RCE critique

since firms constitute

source of one another’s depends

applies

ation

economic

that when costs exist,

it does not show how rational

transportation costs, lead both to core-periphery patterns within a country and to the surprising localizof some

suggests

and linear transportation

will generate

1 reflects The

theory

formation

Krugman

and

for patterns of industrial agglomeration are consistent with increasing returns. whose implications for international

for

chical hexagons.

country.

“stylized

frame-

allows

so com-

and argues that industrial

ation is the outstanding

which

is costly;

of why trading any given

one

areas will take the shape of hierar-

of historical accident in explaining countries leads to Krugman’s entry

they do within

general

continuously varying costs and returns among all spatial points. This technical refinement brings Krugman into contact with a central question in location

aside

where

a more

cities and market

may be socially constructed,

point here: the problems

with

January

his two-region

but the

trade flows may be the result of historical

The importance trade between

in a subsequent

mobile

are costlessly

of tradable

advantage

that tradable

transported,

production

trade

refines his model

1991 paper (1991d): he replaces

they RCE

“failed

in competitive even about”

models.

equilib-

to communicate (1995, p. 28) by

Since their

ideas,

at

increasing returns and pathdependence. these themes have only recently been properly modelled and thus reemerged in economic

theme of the volume is that the presence of numerous industrial clusters due to historical accident demon-

discourse. Krugman develops no substantive insights of his own here, though he sketches out an increasing-

strates “what Nicholas Kaldor called ‘the irrelevance of equilibrium economics’,” as against “Kaldor’s vision of a dynamic world driven by cumulative processes” (pp. 9-10). Krugman contrasts his vision of a world driven by historical contingency with an equilibrium economics vision in which history is the hand-

returns

maiden

of necessity.

model of industrialization.

Chapter 2, ‘Geography Lost and Found,’ pulls together the 1991 and 1992 refinements to Krugman’s original spatial model. The author remarks that spatial theory has been a blind spot for economic theory because its core “problem of market structure

442

Critical Reviews

in the face of increasing returns,” has made it “inherently unfriendly terrain for the kind of modeling mainstream economists know how to do” (p. 35). Krugman argues that five traditions in spatial location theory rest on common “core ideas that make considerable sense . . . but that [have been] unacceptable to mainstream economics” because they resisted formulation in RCE models: Christaller/Losch centralplace theory; statistical regularities such as Zipf’s law and gravity theory; cumulative causation; local external economies; and Von Thunen’s model of land rent. All these traditions lack ‘economic foundations’explicit descriptions of market structure. In consequence, economic geography has “languished along the periphery of economics proper” (p. 55). I2 Krugman offers his monopolistic-competition model as a way “into the mainstream” (p. 59). He acknowledges that his model leaves even basic features of market behaviour unexplored; for example, “the monopolistic competition assumption neatly, if implausibly, disposes of problems like strategic behaviour” (p. 61). Nonetheless it offers a good starting point because it captures the central features of his five spatial-theory traditions. Here he presents only the main results of this model, and presents a skeletal version of it in an appendix.

rests on its recognition of this methodological imperative. Well-specified models incorporate maximization and equilibrium-“obvious opportunities for gain are rarely left unexploited, and things add up” (p. 75). So describing market structure means formulating models that explicitly include these two elements. Other aspects of economic interactions are extraneous; dynamics often attributed to “power and class struggle,” such as the rent paid on land, can instead be understood using the mainstream’s “basic principles of economics . . independent of the[se] details” (p. 75). ” Anticipating criticism from post-modern quarters, Krugman argues that “there is no alternative to models” (p. 79): all thinking takes place in metaphors; but only for the metaphors suggested in formal models can the truth content of causal connections be rigorously evaluated. Krugman concludes that “for those, like me, who basically try to understand the world through the metaphors provided by models, . . [tlhere may be some very interesting things out there [in social theories outside of such models]. Strangely, though, I can’t think of any” (p. 88).

3. Evolving Ideas About Complexity The author’s principal theme here is that his own approach to spatial problems fits better with the mainstream RCE standard than do earlier approaches to these problems. This constitutes a shift in orientation. In his early geographic writings Krugman acknowledged some kinship with nonmainstream theorists; in this volume, his appreciation is tempered. The last chapter, ‘Models and Metaphors,’ dwells entirely on how social theory should be done. This chapter argues that complex systems of relations in both the physical and social realms are best described by simple models, which are best able to elucidate basic principles. Whether an explanation is useful depends on whether it is tractable and whether it is logically consistent; and the only way to determine the latter is to evaluate its mathematical consistency when it is formalized. And while a successful model then “creates blind spots, at least at first” (p. 72), refinements over time will narrow these blind spots. For Krugman,

the scientific prestige of economics

Theory and

Space

Apart from increasing returns, a second strand has emerged in Krugman’s spatial writings: a deepening engagement with complexity theory.‘” This strand can be traced to a November 1992 paper on dynamic aspects of his increasing-returns model. The author begins by recalling the twin arguments of Brian Arthur (1994) that economists should use transdisciplinary concepts of complexity and selforganization to describe increasing returns and external economies, and that “real economies are characterized by strongly nonlinear dynamics.” Krugman adds a new element to his basic framework-an equation of motion describing how firms move. The idea is that initially firms’ returns vary in different areas. Firms will move from areas with belowaverage to above-average returns until returns equalize everywhere. Households, as before, are immobile.” Krugman then conducts some dynamic simulations to examine the conditions under which one or more manufacturing centres arise. It turns out that whether spatial equilibria are stable or unstable, and have one or multiple centres, depends on para-

Critical Reviews meter values. Agglomeration will occur if transportation costs are low enough.nj Krugman suggests the importance of selforganization and complexity in economic dynamics, and demonstrates these results with a simple linear equation of motion. The requisite non-linearity is already built into the point-in-time model he had worked out prior to 1991, nonlinearity was unnecessary in his equation of motion. He thus rejects Arthur’s suggestion that increasing-returns phenomena should be conceptualized using nonlinear dynamic models. Krugman has subsequently explored complexity theory more fully; the fruits of this exploration are presented in the 1996 volume The Self-Organizing Economy.‘7 This work marks a benchmark in that Krugman links his spatial theorizing to complexity theory, thus accepting this approach as a general framework for urban processes. The book begins with an overview of the multidisciplinary investigations of complexity, and suggests that all share one defining characteristic: “they are all seff-organizing systems: systems that, even when they start from an almost homogeneous or almost random state, spontaneously form large-scale patterns” (p. 3). Krugman then presents a number of “stories-1 do not want to dignify them by calling them models-about ways in which the economy organizes itself in space” (p. 7). He then presents two variants of spatial location theory, the Von Thunen-Mills model and centralplace theory. Both are criticized as “deeply unsatisfying if you want to explain cities as opposed to describing them” (p. 12), where explanation means accounting for the self-organization of urban space. He next presents Thomas Schelling’s (1978) model of residential segregation, wherein city-wide segregation emerges when urban residents’ decisions to move or stay put are based solely on how many of their immediate neighbours are of a different race. Krugman celebrates this model as a forerunner of complexity theory which demonstrates how “local, short-range interactions can create large-scale structure” (p. 17). He turns next to some of his own ideas about urban business clusters. He shows how many clusters emerge in a metropolis depends on its balance between centrifugal and centripetal forces. These forces, which are left unspecified, can give rise to either monocentric cities or multicentred ‘edge cities.’ Finally, Krugman turns to the rank-size rule for urban population. He argues that a 1955 idea by

443

Herbert Simon about power laws suggests a behavioural basis for this stylized fact: whether population growth leads to new cities or to larger cities depends on the relative size of the cities and growth cohorts in question. The remainder of this slim volume illustrates how edge cities and the rank-size rule might emerge from small-scale interactions. Krugman deploys his increasing-returns model as an account of edge-city growth-the centrifugal force required to make a metropolis multicentric arises because of the transportation costs needed to access the given distribution of worker households across space. At the same time, the author presents a very general (nonRCE) dynamic model of the ‘edge city’ which does not refer to any specific source of increasing returns. Clearly, this 1996 volume asserts the importance of formal equilibrium theorizing. However, the author leaves unresolved how this book relates to the views on methodology expressed in the third section of the 1995 volume (which goes unreferenced here). Of the four ‘stories’ Krugman introduces to show that selforganization activities lie behind numerous urban phenomena, none constitute fully-specified behaviour models as per his own (1995) definition. For each of these stories of dynamic urban processes, adding time to space creates barriers to theoretical consistency, because ‘rational’ agents in multiperiod settings should take action only after considering how these actions will affect their welfare in every period, present and future. But the requirement that agents engage in forward-looking behaviour (that they have ‘rational expectations’) binds a theorist’s hands: a rational solution in any one period requires an apriori solution for every future period: and this requires that agents possess perfect foresight. A theorist who accepts the requirement of inter-temporal rationality can only construct a model from which the effects of time on behaviour have been (calculated and hence) removed in advance. While a Chicago-influenced economist would gladly pay this price to preserve the postulate of rationality, it seems too dear to the avowedly Keynesian Krugman. Nonetheless, his section on the dynamic aspects of industrial clusters begins with several methodological apologies; for example, he acknowledges his omission of rational expectations and admits “[t]o many economists . . [this] disqualifies a model” (p. 23).

444 4. Critical Reflections

Critical Reviews on Krugman’s

Increasing

Returns Model

Krugman’s spatial increasing-returns model is a considerable achievement as an explanation of agglomeration based in agent optimization and market equilibrium. It will undoubtedly be tested empirically and extended by many other theorists.lx However, Krugman’s model is incomplete taken on its own terms as an explanation of firm location; and it constitutes just one of numerous possible approaches to uneven urban growth and agglomeration. As a model of industrial location, his framework is incomplete or misleading in several respects. First, McCann’s (1995) review of the microfoundational location literature points out that firm decisions in spatial settings have two irreducible dimensionshow much to produce, and where to produce it. Any disturbance to an equilibrium, such as the relocation of a given firm, affects both the production and location decisions of all other firms. This in turn implies that all firms’ cost and demand conditions may change; and even the character of firms’ output-and hence the demand for their outputmay change if changes in relative input costs induce shifts in production technologies. Krugman’s model focuses solely on the industrial-demand implications of firm relocations, with no attention to the other elements highlighted by McCann. A second element missing in Krugman’s model is any attention to the role of financing aspects of firm location and production decisions. Krugman’s firms can transport their ‘capital’ at will from one location to another. This approach assumes perfect capital markets which channel savings infallibly to firms whose decisions are grounded in economic ‘fundamentals’ (in this case, the market characteristics of different locations). To have capital markets this efficient in an increasing-returns economy assumes, at the least, privileged access to remarkably extensive information. If capital markets are not so blessed, then some firms’ production and location decisions will be credit-constrained. Thirdly, Krugman’s use of his increasing-returns model as a model of urban growth assumes the existence of an aggregate production function capable of shifting homogeneous (putty) capital costlessly from one use to another. The Cambridge capital controversy (summarized in Sheppard and Barnes

(1990)) demonstrated that if capital is not all putty, then aggregation from a given structure of production relations to a concave economy-wide production function is not logically possible, and pricing cannot be based on the marginal productivity of this aggregated capital. Generalizing Krugman’s model, in effect, from the industry to the urban economy requires very special assumptions about what capital is. . I’) More broadly, very different RCE explanations of uneven urban growth and agglomeration can beand have been-constructed than the industriallocation model suggested by Krugman.‘” We cite two alternative explanations here. First, Porteous (1995) develops a spatial model of financial intermediation under asymmetric information in which agglomeration occurs because the costs of finance rise as the distance between banks and firm borrowers increases; in effect, apart from any product-market effects like those identified by Krugman, financialmarket effects may encourage agglomeration.*’ Second, some economists have proposed models in which uneven spatial development occurs because spillover effects in the inter-generational transmission of economic status interact with the stratification of neighbourhoods by income.z2 For example, Benabou (1993, 1994) develops a model in which spatially separated agents must decide whether to become low-skill workers, obtain education and become high-skill workers, or not work. There are local increasing returns to education-the more workers in a given neighbourhood attend school, the easier it is to acquire skills. Under these assumptions, a separating equilibrium can be attained wherein some neighbourhoods have little educational investment and low-skill workers, while others have high educational attainment and high-skill workers. This second thread emphasizes residential decisions and the importance of residential neighbourhood effects, without explicit attention to firms’ locational decisions; by contrast, in Krugman’s model, firms move while households stay put. It is true that models in this thread emphasize sources of increasing returns that Krugman has criticized as vague and unmeasurable. Nonetheless, the importance of household decisions in regional growth is suggested by empirical evidence concerning the transfer of wealth through the housing market (Badcock, 1994). And Glaeser et al. (1992, 1995) provide some

Critical Reviews empirical evidence that human-capital spillovers, especially those due to education, are positively related to U.S. urban growth over the past 30 years (as Benabou suggests).

5. Mainstream

I and Mainstream

II Economics

How can Krugman have broken from economic orthodoxy even while advocating mainstream methods? And given the many approaches to agglomeration, why does Krugman (1995) insist that his own formal approach serve as a general framework for location theory (an insistence partially retracted in his 1996 book)? And what of Krugman’s recurrent assertions that formal models encompassing rationality and equilibrium should be the preferred method of inquiry in economic geography? This section considers the first two questions; section 6 takes up the third. Answering the first two questions requires understanding a realignment in economic theory which has altered economists’ terms of reference and effectively created two ‘mainstreams.’ The conceptual core of mainstream economic theory is the Walrasian general equilibrium (WGE) model. This model consists of a mathematical demonstration of how under idealized conditions, decentralized markets can create a unique allocation of available resources which maximizes social welfare measured in terms of individual utility.23 Among the assumptions required for this result are perfect competition, concave production functions (diminishing marginal returns), and the absence of externalities. For many economists, the WGE affirms what they already believe-economic efficiency is greatest when markets are freest and government activity least. Numerous micro- and macroeconomic analyses have been based on this premise, if not on the WGE per se. These analyses define what might be termed Mainstream I .24 After the WGE was established in the 1950s and 196Os, subsequent research has explored whether it is robust. These mathematical explorations have determined that the WGE result is fragile: any number of deviations from WGE assumptions are sufficient to overturn the central result that a unique equilibrium exists and is a social optimum. Of particular importance here is that if at least one market is missing, equilibrium is no longer unique.‘” Missing markets arise whenever agents cannot contract for goods

445

which exist and to which they attach positive value. Since such situations are common, WGE is the special case, and missing markets the general one. For a time, this distinction between WGE and missing-market situations created a methodological gap in economics. Real-world situations clearly violated the assumptions required for WGE, and hence fell outside of the mainstream’s central analytical apparatus. But work on idealized models had no clear applicability. An outpouring of analytical work on incomplete-market scenarios over the past 15 years has been aimed at closing this gap. Advances in information theory and in game theory-what Krugman calls “theoretical industrial organization”-have allowed economists to reformulate incompletemarket situations as scenarios of asymmetric information, efficiency wages, and so on, which have ready behavioural interpretations. It turns out that market equilibria under these circumstances differ significantly from WGE-for example, asymmetric information in credit and labour markets can lead to equilibrium credit rationing and unemployment.26 It also turns out that these results occur in models whose assumption sets differ only slightly from those required for WGE. Consequently, many economists have been engaged in constructing a Mainstream II: models of incomplete-market situations, which necessarily lack the Mainstream I feature that market allocations lead to unique social optima, but accept the methodological prerogative that well-specified models must account for rational choice and identify market equilibria (that is, agree to build RCE models).27 Since Mainstream II models can be formulated using numerous non-WGE assumption sets, they are very flexible. Indeed, the strength of Mainstream II lies in its plasticity. The renewed interest of economists in spatial issues is both an example of this plasticity and a manifestation of Mainstream II economics. Topics that are inherently intriguing in formal terms-such as central-place theory and the Von Thunen-Mills location model--can now be attacked with a much better (RCE) toolkit. The models of spatial agglomeration discussed above are Mainstream II models: they violate WGE assumptions-convexity for Krugman and Benabou, perfect information for Porteous-and develop RCE models given these violations. It might seem that the inescapability

of multiple

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Critical Reviews

equilibria in Mainstream II should encourage methodological tolerance. After all, models in which any one thing can happen can be reconfigured into models in which any other thing can happen. Krugman’s conclusions about industrial location depend as much on his implicit exclusion of, say, household mobility as on his explicit assumptions about firm technologies. A reassessment of the implicit power of formalization would seem to be in order; and more than one geographer has expressed the hope that Krugman’s critique of Mainstream I models implies his openness to alternative theoretical approaches.*’ But Krugman’s 1995 volume squelches this hope with its aggressive defence of formalism; and while his 1996 volume suggests a relaxed criterion for admissible formal models, it avoids any discussion of inherent limits to formalization. The rise of Mainstream II explains Krugman’s viewpoint. Mainstream II economists like Krugman and Stiglitz have more in common with Mainstream I than with social scientists who use non-Mainstream tools. This continued orientation leads Krugman and other Mainstream II economists into two methodological dilemmas. To see these, note first that retaining the WGE as a point of analytical reference means that relaxing just one assumption of WGE is better than relaxing two. For just one violation (increasing returns in production or asymmetric information, but not both) is sufficient to generate multiple equilibria and to show (in some cases) that laissez-faire outcomes are inefficient. The force of the deviant assumption is understood by the difference it makes in the benchmark WGE. This is what an economist has in mind when she asserts that a given assumption is ‘sufficient’ to generate a given result. Two or more simultaneous deviations from WGE make it unclear which creates the non-Walrasian result. Retaining the WGE as a reference point creates two dilemmas for Mainstream II economists. First, more than one deviation from WGE assumptions can generate any given result. For example, as Krugman (1992) acknowledges, nonlinear dynamics with constant-returns technology can generate path dependence, just as can the increasing-returns technology and stable dynamics he prefers. The choice of how to introduce path dependence is open, as Arthur (1994) shows. Second, choosing any one equilibrium from among the infinite possibilities in incompletemarkets contexts requires an additional restrictionone not determined by the model. For example,

Krugman supposes that firms move to eliminate excess profits, while households stay put; Benabou imagines households moving. The specifications of both models are open, a matter of their modelers’ choices, So the mathematics does not dictate the model; rather, different models give back the same mathematics. Therefore theorists will choose the same modeling approach only if it offers a larger payoff than competing approaches. This payoff depends on how many other economists, especially influential ones, are deploying this approach, and how successfully-that is, the payoff is subject to increasing returns. Modelling approaches are thus endogenous, as is theoretical development within Mainstream II. This explains Krugman’s use of the term ‘mainstream’: it is a rhetorical trump card aimed at influencing theoretical trajectories.

6. The Economics of Space and the Political Economy of Space/Time

What is to be made of Krugman’s argument that formal RCE modelling is the only means to progress in economic geography? For Krugman’s argument to hold, one of two propositions must be granted: either formal RCE models have implications so as to displace other approaches; or the research questions pursued in formal RCE models are more important, and the answers these models more convincing, than the questions and answers generated in other approaches to space/time. We consider and reject both propositions. The best measure of whether RCE models lead to preemptively important hypotheses is Krugman’s own increasing-returns model. This model suggests these hypotheses about why firms move and why urban centres form: large mobile firms with interrelated products should locate in industrial clusters; firms in young industrial clusters should have aboveaverage profits, while those in older clusters should have normal profits; and urban growth should be driven by self-organizing industrial clustering. The evidence suggests that Krugman’s hypotheses are empirically relevant; but they capture only a portion of the experience of recent urban growth. Glaeser et al. (1995), cited above, find that manufacturing employment share is negatively related to

Critical Reviews urban growth, instead of positively related as it should be under agglomeration theories like Krugman’s.2y Martin and Sunley (1995) puzzle over how Krugman’s hypotheses about firms relate to the literature on Post-Fordism, especially that on flexible specialization. For one thing, Krugman’s ‘firms’ are sketchily defined-it is not clear whether they are autonomous entities or affiliates of multinationals. And while Silicon Valley is a case example of increasing-returns clustering, Krugman’s model doesn’t address deindustrialization and out-sourcing. Further, some aspects of Krugman’s model may be historically inaccurate. In the modern era, the primitive assumption of immobile farmer residents with ready buying power is outmoded; workers are now as mobile as firms. Also, the idea of zero-profits equilibrium for cutting-edge firms deserves, at least, some empirical verification. Finally, the micro/macro linkage may not go one way (bottom up), as Krugman implicitly suggests, even in the case of industrial agglomeration. Scott (1993a) shows that agglomeration of the sort Krugman envisions depends on factors he ignores-state action and exogenous (state-determined) demand.‘” This suggests that ‘self-organization’ is at best half the story; macrostructural factors are the other half, and a spatial macro-structural framework cannot be built up consistently from microfoundations.” What of the idea that RCE models frame questions and generate answers more important than other approaches? Significantly, Krugman’s most recent spatial writings emphasize longstanding questions about city rank-size and central place, posed in the formal frameworks he reworks. Even his innovative model of edge cities is presented the context of central-place theory. The implicit assertion is that mathematical theorists have already posed the central questions-the “stylized questions”-to which all subsequent theory should be viewed as a response. Krugman then views earlier theorists responses to these questions through his own rational-choice lens. He dislikes the (classic) Weber-Christaller model because it does not answer questions that his methodology privileges: “Who is doing the minimizing? . . a private firm? How does it price? Does it face competitors . . ?” ( 1995, pp. 39-40). Of course these are important questions; but there are other equally compelling questions that neither classical theorists nor Krugman have posed: are there constraints on which firms can move? does the character of the local

447

labour market affect firm decisions? does the structure of household relations affect labour market dynamics? does racial inequality or discrimination affect households’ spatial locations? It is asking too much for rational-choice model to both explain how prices are set in micro-markets and how households are structured; for it to encompass not simply the formation of Silicon Valley but also the deindustrialization of Pittsburgh or Liverpool. To stretch Krugman’s formal framework or any other one to this extent is to break it. Of course, a relatively simple model can address any one of these questions. That is Krugman’s methodological point. But this does not make RCE modelling the only valid method. For while relatively simple frameworks can generate complexity in the sense of nonlinear trajectories or agglomeration reversals, such frameworks are illequipped to handling complexity in the sense of overlapping (mutually determined and determining) social relations and constraints. Yet the signature of contemporary economic geography is precisely its authors’ willingness to take on complexity in this second sense-and this has meant lowered expectations about what formal models can deliver. As Sheppard (1995) has observed, geography has in the past two decades undergone an insurgency against formal spatial analysis precisely because of its failure to incorporate concrete social dynamics. Many geographers have instead been examining the spatial aspects of numerous logics of social explanation. Several points about contemporary research in economic geography are relevant here. First, this openness to insights from different academic perspectives has made geographic research an epitome of trans-disciplinary thinking and synthesis. This laudatory feature of geographic theory has an important implication: theorists interested in influencing the trajectory of geographic theory must engage in a kind of continuous multi-layered translation, equivalent to identifying a given location in different maps. Second, much of contemporary geography involves precisely the challenge of negotiating the line between history, social relations, and meaning. This negotiation cannot be conducted under axiomatic rules of theory construction; it needs a political economy framework which encompasses “economic and social relations rather than hypothetical actors (e.g. ‘homo economicus’), with the spheres of production

448

Critical Reviews

and consumption as well as the area of exchange, with tensions, conflict and crisis rather than equilibrium, and with an historical dimension rather than without one” (Knox and Agnew, 1994, p. 4). The political economies that result from this negotiation will necessarily be diverse. Geographers build different histories of the same places, as (say) Soja (1989) and Scott (1993b) have for Los Angeles. Both excite geographic imagination(s), and the point of neither is to disprove the other. Contributions acquire identity in large part because they are co-respective and encompassing. No one layer of meaning wipes another off the theoretical map. Theorists pursue ‘truths’ in part by setting aside the quest for Truth. In effect, an analytical recognition of the density of social and economic relations in contemporary urban and suburban settlement forces theorists to appreciate the archaeologist’s respect for the significance of layers. Third, the ex ante complexity of space/time relations places a premium on the conduct of specific studies of specific contexts. Such studies identify and order the specific and only cautiously suggest the general. As Ed Soja commented concerning the relationship of financial and industrial capital in Harvey’s (1982) framework: The issue is thus a conjunctural one, referring to the ensemble of class relations arising at particular places during particular periods of time. To reduce Marxist analysis to the assertion of ultimate structural determinations is to eliminate all historical and geographical specificity-and hence to eliminate the city itself as a subject of analysis. (Soja, 1989, p. 99).

This insight is of fundamental importance, as can be seen by substituting ‘geographical’ or even ‘social’ for ‘Marxist’ in Soja’s second sentence. And investigating conjunctures means making use of history and context. This does not mean that axiomatic models based on individual rationality and equilibrium are of no value. Papageorgiou, Benabou, Krugman and other theorists have stretched the understanding of real spatial relations by their imaginative renderings of hyperspace. It does mean, however, that theorists exploring one set of methods cannot prejudge the merits of methods used by other theorists on a priori grounds. Something like peaceful coexistence seems the best strategy-and it may not be too much to hope for gains from trade.‘* Here Krugman’s resistance to this sort of coexistence in his own field (see Note 13 and many quotations

above) presents a sharp contrast. Perhaps some of Krugman’s intolerance of anything besides RCE models can be traced to stresses on economic theorists in the Mainstream II era. But certainly some of it reflects an asymmetry of power between theorists and political economists in economics very different from the balance found in geography.‘3 Economics itself contains a remarkable range of scholars and scholarship-Post Keynesian economics, feminist economics, radical political economy, methodologists, and economic historians, to name a fewcollectively dubbed the ‘heterodoxy.’ These theorists either construct models on problems not deemed important by mainstream economists, construct models that reject the RCE approach or modify it too severely, use a point of reference other than WGE, or all of the above. Scholars using similar (or the same) methods exploring related (or the same) questions are of course common in geography; but they are not in the same sort of peripheral position. One hopes that economics in this respect will over time become more like geography.

7. Conclusion That so accomplished and energetic an economist as Paul Krugman should intervene in the terrain of geography is a propitious event for those already ploughing spatial fields. That his increasing-returns model unearths new aspects of questions in economic cannot be doubted. Krugman’s geography increasing-returns model will take its place among choice-theoretic models of spatial processes, though it is unlikely to supplant competing RCE frameworks. Krugman observes in the forward to his 1991 volume that his appropriation of the term ‘geography’ may not please “geographers proper . [who] may deny that the kind of stylized models that economists find appealing are part of their field” (p. xi). This hasn’t stopped him from repeatedly asserting the advantages of RCE models for attacking spatial problems. But geographers inclined to agree with Krugman already use such models (if not his model); and those inclined to disagree with him are unlikely to accept his characterization of theorizing as an extended conversation with mainstream economics. So the longer Krugman’s work in this field continues, the more the question of his ultimate intentions in pursuing geographic questions comes to the fore.

Critical Krugman’s

two recent

at an equilibrium dimensions.

books on geography

point

which

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entered

into the discourse

priated

some

time’

do not make of

rather,

he suggests

in favour

of models

‘time’ separately

social

that can encompass

to greater

analytical

sits. One direction with spatial

‘space’ or

advantage.

This

Krugman’s

spatial

2.

from here is a deepening theories

and spatial

ists; one of this essay’s anonymous

referees

as revivifying

theor-

suggested

may come to “see himself

Isard,

geog-

setting aside ‘space/time’

writing

day Walter

with the ‘space/

contemporary

us to the cusp on which

that Krugman

as appro-

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contact

brings

engagement

has not so much

questions.

problematic

raphers;

in two

of geographers

geographic

interventions

leave him

is unstable

Krugman

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c3

as a latter-

regional

science.” 4.

Krugman

is not yet clearly willing to make this leap.

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toward

another

cusp-back

toward the familiar

economics.

His 1996 book

direction terrain

from this

of mainstream

aims at connecting

large

portions of economic theory disciplinary edifice of complexity

with the multitheory; and his

writing

primarily

to an audience

of

Krugman’s

very embrace

of

remains

economists. complexity cusp.

To

directed

However, theory

brings him to a second

sign on to the endeavour

theoretical

might itself eject him from the ranks of main-

stream

theorists;

for mainstream

complexity

some of the criteria of theoretical

economic

theory

6.

of complexity

theory

can embrace

5.

only

theorists

if they

relax

7.

by which they judge the adequacy

models. 8.

Krugman’s direction

1996 book

ends

from this unstable

without theoretical

indicating

his

equilibrium:

whether his spatial interventions represent another chapter in his ongoing conversation with mainstream economists,

or whether

these

an involvement

with spatial

that surpasses

the self-imposed

economic

theory.

interventions theory

In any event,

foretell

9.

and complexity

limits of mainstream the next chapter

IO.

will

not long remain unwritten or unread, as Paul Krugman’s model of economic geography unfolds. Acknowledgements-The author thanks J. Barkley Rosser Jr., Gil Skillman and anonymous referees of this journal for insightful comments and suggestions. All errors of attribution and interpretation remain the author’s responsibility.

Notes 11. 1. An externality arises when market rise to benefits or costs to agents

transactions other than

give those

I? li.

449

directly engaged in these transactions. Increasing returns occur when increasing the level of output reduces the per-unit cost of producing it. Increasing returns occur frequently in formal models. For example, suppose there is a fixed cost X associated with starting up a given firm; then as output Y expands, the fixed cost per unit of Y, X/Y, falls. So even if marginal production costs, dx, remain constant, the per-unit return increase5 as output rises. When production processes characterized by constant returns to scale (such that increasing output volume involves a pro-rata increase in inputs) give rise to externalities, increasing returns will also be present. Krugman observes that the same failure had inhibited the spread of many interesting but unorthodox insights within trade theory until they were “given rigour, and hence respectability.” With increasing returns, one firm can meet market demand more efficiently than multiple firms. Prices cannot be set competitively because one firm supplies the whole market. Many economic theorists, Krugman (lYY5, pp. 74-75) among them, view an economic model as poorly formulated if its equilibrium includes excess profits; the presumption is that this equilibrium will not persist because agents will make behavioural adjustments to capture those excess profits. The second set of factors have been emphasized in models of “endogenous growth,” which have become important in contemporary growth theory, as discussed in Romer (lYY4). This indeterminacy in trade outcomes arises because of increasing returns in Krugman’s model. Orthodox trade theory is equivalent to the perfect-competition model of efficient markets. with one extra constraint: the market for foreign exchange must balance in equilibrium. A stylized fact in economics is an empirical regularity which theorists accept as a defining feature of a given phenomenon, and then complete to explain using formal models. This parallelism may have helped spur Krugman‘s interest in complexity theory; in the theory of fractals, one of the formal approaches consonant with complexity, the presence of a given pattern at a lower level of analysis constitutes evidence for the same pattern at a higher level of analysis. However, G. Papageorgiou (lY79) develops a model of urbanization showing that increasing returns, while sufficient for agglomeration, are not necessary. Krugman applies his critique to the foundational classics. However, he is evidently unaware of more recent contributions in economic geography that do suggest microfoundations for central-place theory. The paper cited in Note Y proposes a RCE model of urbanization based on the notion of city as “service centre.” The numerous papers by Y. Papageorgiou and co-authors (for example, Papageorgiou and Smith, 1983; Berliant et 01.. 1YYO;Lconardi and Papageorgiou, lYY2) establish a microfoundational basis for urbanization and agglomeration beginning not with firms but with conwhose utility depends on their location. sumers. Greenhut (lYY5) also has proposed many RCE spatial mod&. Krugman’s spatial writings from late 190 1 to the end of 1’904 arc discussed in the next section. Krugman remarks that the Weber-Christaller model is

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Critical Reviews

“exasperatingly blurry about who was making what decisions, and almost completely silent on the question of how decisions of individuals might affect one another” (p. 39), and that the ‘
21.

22.

23. 24.

25.

26.

27.

28.

29. 30.

31.

trajectories. Batty and Longley (1994) use techniques of fractal geometry to characterize urban growth. In a related model, Zenou and Smith (1995) show how asymmetric information in the labour market may lead to unequal spatial rates of unemployment in equilibrium. This literature, summarized by Durlauf (1994), arose as a way of explaining the link between income inequality and economic growth. The evolution of general equilibrium analysis is summarized by Ingrao and Israel (1990). Mainstream I analyses typically do not rest on all the assumptions required for a WGE; however, they are conducted as if the WGE is a meaningful point of reference-that is, as if markets left on their own reach social optima. Similarly, multiple equilibria are also triggered by production nonconvexities, which are inherent in the sort of increasing-returns production Krugman discusses. Geanakoplos (1990) and Magi11 and Quinzii (1996) discuss the problem of market incompleteness in general equilibrium. Akerlof and Yellen (1986) and Stiglitz and Weiss (1992). respectively, present analyses of labour and credit markets under asymmetric information. Missing markets exist in these models for two reasons: firms and/or lenders would prefer to make separate contracts with different types of workers and/or borrowers (hard workers vs slackers, good risks vs poor ones) but cannot tell the ‘types’ apart. The workers and borrowers in question know their types, but those who would be hurt by truthfully revealing this information have an incentive to lie. Dymski (forthcoming) explores the methodological underpinnings of contemporary models of asymmetric information. Mainstream II models do not invariably conclude that public policies and regulations can improve allocational efficiency and hence social welfare; as noted, it is a matter of parameters and specification in every case as to whether policy interventions can improve on market outcomes. Recall Macmillan (1994); and Barnes writes that “interest in nonlinear models of spatio-temporal change has resulted in conceptualizations that better capture the historical, evolutionary, path-dependent, and unpredictable nature of real societies. [. .] Although much of the theoretical work has been very technical, it is gradually enabling a break from the neoclassical thinking that for so long has dominated [spatial theory].” (1990, p. 293). Also see Pollard and Storper (1996). Scott traces agglomeration economies in Southern California to intra-regional networks of contracts and subcontracts generated by NASA prime contracts; over the 198Os, these contracts pumped over $2 billion annually into this regional economy. Barnes and Sheppard (1992) authors argue that when agents cannot be abstracted from their spatial contexts, rational-choice models often lead to fallacies of composition wherein actions have consequences opposite those intended. Also see the work by Y. Papageorgiou mentioned in Note 10. Webber (1994) points out that not only that macro-structural forces are moulded by state action, but also that the basis of state policies lies in each nation’s internal class characteristics. His conelusion, of Korea and Taiwan, that “places differ, and so, therefore, must policies” (p. 71) could be reinter-

Critical preted here as ‘places differ, and so, therefore, must microfoundations.’ 32. The recent volume by Sheppard and Barnes (1990) presents a superb example of ‘trade’ between formal theory and political economy. These authors investigate the significance of spatiality for class conflict and exploitation using rigorous formal methods (the Sraffian model). 33. Concerning asymmetric power, try this experiment: list the ‘top ten’ departments around the world both in economics and in geography, do a simple count of the number of tenured RCE theorists and political economists in each, cross-tabulate, and compare.

451

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