metadata: authors: 0: author: Venables,Anthony J.
count: Africa
docna: 0: docna: Breaking into tradables : urban form and
            urban function in a developing city
docty: Policy Research Working Paper
subtopic: Urban Housing and Land Settlements,Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Labor Markets,Urban Governance and Management,Urban Housing,Municipal Management and Reform,Business Cycles and Stabilization Policies
teratopic: Industry,Communities and Human Settlements,Urban Development
abstracts: cdata!: Many cities in developing economies,
            particularly in Africa, are experiencing urbanization
            without industrialization. This paper conceptualizes this in
            a framework in which a city can produce non-tradable goods
            and -- if it is sufficiently competitive -- also
            internationally tradable goods, potentially subject to
            increasing returns to scale. A city is unlikely to produce
            tradables if it faces high urban and hinterland demand for
            non-tradables, or high costs of urban infrastructure and
            construction. The paper shows that, if there are increasing
            returns in tradable production, there may be multiple
            equilibria. The same initial conditions can support
            dichotomous outcomes, with cities either in a low-level
            (non-tradable only) equilibrium, or diversified in tradable
            and non-tradable production. The paper demonstrates the
            importance of history and expectations in determining
            outcomes. Essentially, a city can be built in a manner that
            makes it difficult to attract tradable production. This
            situation might be a consequence of low (and
            self-fulfilling) expectations or history. The predictions of
            the model are consistent with several observed features of
            African cities.
repnme: repnme: Breaking into tradables : urban form and
            urban function in a developing city
display_title: Breaking into tradables : urban form
            and urban function in a developing city
listing_relative_url: /research/2017/01/27117919/breaking-tradables-urban-form-urban-function-developing-city
topicv3: Manufacturing Sectors m1326521 1281,Land and Housing m1327648 817,Jobs m1503931 2670,Labor Supply m1504055 2751,Labor Demand m1583073 4422
publishtoextweb_dt: 2017-01-23T00:00:00Z
historic_topic: Industry,Communities and Human Settlements,Urban Development
no_of_pages: 30
author_keys: 0: author_key: 390772
model_extractions: WPS7950 Policy Research Working Paper 7950 Breaking into Tradables Urban Form and Urban Function in a Developing City _Anthony J. Venables_ Social, Urban, Rural and Resilience Global Practice Group January 2017
Policy Research Working Paper 7950

# **Abstract**

Many cities in developing economies, particularly in Africa, are experiencing urbanization without industrialization. This paper conceptualizes this in a framework in which a city can produce non-tradable goods and—if it is sufficiently competitive—also internationally tradable goods, potentially subject to increasing returns to scale. A city is unlikely to produce tradables if it faces high urban and hinterland demand for non-tradables, or high costs of urban infrastructure and construction. The paper shows that, if there are increasing returns in tradable production, there may be multiple equilibria. The same initial conditions can support dichotomous outcomes, with cities either in a low-level (non-tradable only) equilibrium, or diversified in tradable and non-tradable production. The paper demonstrates the importance of history and expectations in determining outcomes. Essentially, a city can be built in a manner that makes it difficult to attract tradable production. This situation might be a consequence of low (and self-fulfilling) expectations or history. The predictions of the model are consistent with several observed features of African cities.

This paper is a product of the Social, Urban, Rural and Resilience Global Practice Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at tony.venables@economics.ox.ac.uk.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Breaking into Tradables:**

# **Urban Form and Urban Function in a Developing City***

Anthony J. Venables University of Oxford, CEPR and International Growth Centre

**Keywords** : city, urban, economic development, tradable goods, structural transformation. **JEL classification:** O14, O18, R1, R3

* Forthcoming, Journal of Urban Economics

**Acknowledgements:** I gratefully acknowledge support from the Africa Research Program on Spatial Development of Cities at LSE and Oxford, funded by the Multi Donor Trust Fund on Sustainable Urbanization of the World Bank and supported by the UK Department for International Development.  Thanks also to referees, an editor, Paul Collier, Avinash Dixit, Vernon Henderson, Patricia Jones, Somik Lall, and seminar participants for helpful comments, and to Sebastian Kriticos for research assistance.

**Author’s Address:**

Department of Economics Manor Road Oxford OX1 3UQ, UK <u>tony.venables@economics.ox.ac.uk</u>
# **1.  Introduction**

Cities in the developing world face the challenge of accommodating a predicted 2.5 billion more people by 2050, and the fastest urbanizing region will be Sub-Saharan Africa, where urban population is predicted to treble to more than 1 billion. Urbanization is occurring at lower per capita income levels than was historically the case, sometimes referred to as ‘urbanization without growth’ (Fay and Opal, 2000; Jedwab and Vollrath 2015).<sup>1</sup> The performance of developing cities is heterogeneous, and in one area has been sharply dichotomous. Many Asian cities have been able to create jobs in tradable goods sectors and have become internationally competitive, producing large volumes of exports. African cities have failed to do this, and have instead grown on the basis of supplying local and perhaps regional markets. The phrase ‘urbanization without industrialization’ has gained currency, and Gollin et al. (2016) point to the prevalence of this phenomenon in resource rich developing countries.

The present paper analyzes the factors that shape this aspect of performance and that determine the extent to which developing cities are able to succeed in attracting high productivity tradable goods (or service) sectors, or instead remain specialized in producing non-tradables for local markets. The paper is primarily theoretical, and is based on interactions between ‘urban function’ – the economic activity that takes place in the city – and ‘urban form’ – the way in which the city is constructed and the efficiency with which it operates. To capture this, the model that is developed in the paper has several key ingredients. On the production side, we distinguish between non-tradable and tradable sectors of production. The former is likely to encounter diminishing returns because it is limited by the size of local markets, while the latter offers the prospect of increasing returns and agglomeration economies. On the residential side, urban form is captured by a standard urban model in which buildings are durable and density of construction is endogenous. The residential capital stock – and hence the size and density of the city – therefore depend on both past history and expectations of future returns.

Three sets of results are established. First, we establish conditions which are likely to lead to a city being specialized in non-tradables, as opposed to diversified into both non-tradables and tradables. Conditions include the presence of high urban and hinterland demand for nontradables, and high costs of urban infrastructure and construction. Second, we show how, if there are increasing returns in tradable production, there may be multiple equilibria. The same initial conditions can support dichotomous outcomes, with cities either in a low-level (nontradable only) equilibrium, or diversified in both tradable and non-tradable production. Third,

> 1 Jedwab and Vollrath (2015) discuss alternative reasons for this, including urban technologies, push from agriculture, politics, and natural population increase.

2
we demonstrate the importance of history and of expectations in determining outcomes. Essentially, a city can be built in a manner which makes it difficult to attract tradable production. This might be a consequence of low (and self-fulfilling) expectations or of history.

While the paper is primarily theoretical, we start by outlining three features of African cities that are illuminated by the model. The first is African cities’ failure to create jobs in internationally tradable goods or service sectors. Gollin et al. (2016) investigate this, principally at the national level, establishing the adverse effect of natural resource sectors on manufacturing employment. Natural resource dependence is only part of the story, and there are also significant regional differences. Focusing on Africa, Jones (2016) compares manufacturing shares of GDP in African and non-African economies at different stages of urbanization. In non-African economies, the manufacturing share of GDP rises from 10% to nearly 20% as the urban population share rises to 60%, above which it falls back. In Africa, the manufacturing share remains flat (or somewhat falling) at around 10% of GDP through a cross-section of urbanization rates ranging from 10% to 70%.<sup>2</sup> A more urban focus can be derived by using spatially disaggregated IPUMS data.<sup>3</sup> These are sample data collected at the individual level, with selfdeclared sector of employment. Table 1 reports the share of employment declaring to be in manufacturing in areas classified as urban. The data are presented by city (selected by size within country) and by country (in India this is urban area by state, with separate city level data unavailable). While manufacturing is not synonymous with tradable goods, the data indicate clearly the extent to which Africa is different from other regions. Simple averages across countries suggest manufacturing shares of urban employment nearly three times greater in Asia than in Africa, and increasing through time, whereas Africa’s shares have declined slightly. Accra appears as the African city with the highest share of employment in manufacturing, at 14.9%, whereas shares in Asian cities rise well in excess of 30%.<sup>4</sup>

> 2 Jones (2016).  Manufacturing shares are predicted values from a quadratic function fitted to the cross section data.

> 3 - Integrated Public Use Microdata Series (iPums) available for download at: https://usa.ipums.org/usa <u>action/variables/group</u>

> 4 Ethiopian data dates from 1994; recent manufacturing investments suggest that it could now exceed this.

3
**Table 1:  Share of employment in manufacturing:  Urban areas**

|**Africa**|||**India**|||**Other Asia**|||
|---|---|---|---|---|---|---|---|---|
||**1990s**|**2000s**|**States**|**1999**|**2004**||**1990s**|**2000s**|
|**Cameroon**|-|10.2|Maharashtra|23.4|23.8|**Thailand**|10.1|12.2|
|**Ethiopia**|7.98|-|West Bengal|24.6|27.5|Bangkok|25.2|20.3|
|Addis Ababa|18.9|-|Delhi|23.1|25.5|Samut Prakan|24.9|48.9|
|**Ghana**|14.4|12.6|Tamil Nadu|27.0|30.7|Nonthaburi|18.8|15.0|
|Accra|17.5|14.9|Karnataka|23.8|21.9|Udon Thani|9.87|6.93|
|**Liberia**|-|1.6|Andhra Pradesh|17.7|20.1|**Vietnam**|16.8|16.9|
|**Malawi**|7.19|7.09|Gujarat|25.11|37.2|Ho Chi Minh|37.5|35.1|
|Blantyre|10.7|11.4|Uttar Pradesh|22.9|26.8|Ha Noi|21.6|18.4|
|**Mali**|6.26|6.55|Rajasthan|20.6|23.3|Da Nang|21.4|20.5|
|**Mozambique**|5.3|5.1|Bihar &Jharkhand|16.2|12.6|Hai Phong|24.8|24.3|
|Maputo|9.46|6.8|Punjab|22.7|27.2|**Malaysia**|20.1|22.4|
|**Rwanda**|-|2.58|Kerala|21.2|15.7|Kuala Lumpur|25.2|20.9|
|Kigali|-|4.92|Haryana|20.3|25.9|Seberang|40.3|44.4|
|**Sierra Leone**|-|0.74|Pondicherry|28.5|20.8|**Indonesia**|9.19|8.00|
|**Sudan**|-|6.12|Chhattisgarh|17.6|19.0|Jakarta|18.9|15.5|
|**Tanzania**|-|4.96|Orissa|16.8|14.3|Bandung|20.6|23.0|
|DaresSalaam|-|8.85|Chandigarh|15.7|17.4|**Cambodia**|5.01|6.92|
|**Uganda**|-|4.82|Daman, Diu & Goa|11.5|15.8|Phnom Penh|13.2|26.9|
|Kampala|-|6.92|Himachal Pradesh|8.86|14.3|Takeo|2.43|6.84|
|**Zambia**|6.11|-|Dadra &Nagar<br>Haveli|52.5|27.9|Sihanoukville|8.02|17.5|
|Lusaka|10.4|-||||Battambang|8.25|8.16|

The second feature is the problematic ‘urban form’ of African cities. The weakness of African urban form has numerous manifestations, showing up most obviously in low stocks of key capital assets, including housing and infrastructure. While low stocks of these assets is partly a function of low income (urbanization at relatively low levels of per capita income) it is also due to market and governance failures. Lack of clarity in land-tenure is widespread, disputes between multiple claimants on land are frequent, and invasions to seize urban land are a problem. Private investment is also discouraged by inappropriately high building and land use regulations, and mortgage finance is hard to obtain (Collier and Venables 2015). Provision of public capital is low, with estimates of the infrastructure gap suggesting that as much as 20% of urban GVA needs to be spent over a period of decades to fill the gap (Foster et al. 2010). These features are captured in our modeling as high costs of building (‘costs’ including non-monetary obstacles) and of urban transport. Within the model, the consequences are low levels of residential investment and high costs of accessing jobs. This corresponds to the reality of widespread informal settlement, generally single story and constructed of mud and sheet metal.

4
Some 62% of Africa’s urban population lives in slums (UN-Habitat, 2010) and there is often a hodgepodge of land use, with slum areas persisting next to modern developments near city centers. Inefficient land use and sub-optimal stocks of residential and infrastructure capital have costs for the functioning of the city as a whole. There are direct costs as, for example, data for Nairobi suggest that land near the city center that is currently occupied by slums foregoes around two-thirds of its value compared to neighboring formal developments (Henderson et al. 2016). There are wider costs of loss of connectivity between economic agents, imposing costs on firms and manifest in some of the longest commuting times in the world.

The third feature of African cities is the apparent paradox of relatively high nominal wages and prices in many cities, despite their low real income and lack of modern sector employment. This is a feature that, as we will see, can emerge as an outcome in the model. The evidence for it comes from several sources. Jones (2016) reports that firms in African cities pay wages (at official exchange rates) about 15% higher than in non-African cities, conditional on national real GDP pc. Labor costs are estimated at up to 50% higher. Corresponding to this, sales per worker are about 25% higher than in comparable non-African cities, but this is largely in the non-traded sectors and appears to simply reflect higher prices not physical productivity.<sup>5</sup> High nominal wages are matched by high prices of goods and services. Nakamura et al. (2016) use ICP data to study the cost of living of urban households across countries and find that it is some 20- 30% higher in African countries than in other countries at similar income levels.<sup>6</sup> Part of this is due to high rents and urban transport costs (respectively 55% and 42% higher than in comparable places elsewhere) although it extends to other commodities. Prices of food and other goods are also relatively high. Henderson and Nigmatulina (2016) show that, across developing country cities, high prices are negatively associated with a measure of connectivity between people in the city.

Our model captures these features, and is developed in a series of stages. Section 2 lays out the ingredients, characterizes equilibrium and undertakes comparative statics to establish the determinants of city specialization, as well as of city size, density and rent levels. While Section 2 maintains the assumption of constant returns to scale in tradable production, Section 3 moves to environments with increasing returns, establishing the possibility of multiple equilibria and the roles of history and expectations in shaping outcomes. Section 4 concludes and offers policy implications.

> 5 These findings on labor costs and price levels are consistent with earlier work by Gelb et al. (2013, 2015), although this work does not have an urban focus.

> 6 Nakamura et al. also report findings from the Economist Intelligence Unit’s Worldwide Cost of Living Survey.  While this is produced principally for expatriates its findings are consistent, indicating African cities are 30% more costly for households than cities in low- and middle-income countries elsewhere.

5
# **2.  Production and urban form**

# **2.1 The model**

The model focuses on a single city which sells goods within and outside the city, and which is able to draw labor from the wider economy. Labor is the only input to production, and land is used for housing urban workers. Analysis is based around labor demand and labor supply. The former gives the relationship between the wage and the level of employment, depending on productive activity in the city (‘urban function’). The latter is the relationship between the wage and city population, this depending on migration and on the cost of living in the city, including costs of construction and of commuting (‘urban form’).

**_Production and labor demand:_** Labor is demanded by the production side of the city economy in which there are (potentially) two produced goods, tradables and non-tradables, with employment levels<sup>_L_</sup> _T_<sup>and</sup> _LN_ giving total city employment _L_  _LT_  _LN_ .  The wage is _w_ , the same in both sectors, and since labor is the only input the value of output produced in the city is _wL_ .<sup>7</sup> To derive the city’s labor demand function we look first at demand for labor in nontradable production, and then in tradables.

Non-tradable goods meet demands from the local market and have price _pN_ , determined endogenously by supply and demand.<sup>8</sup> They are produced under constant returns to scale so, choosing units such that one unit of labor produces one unit of output, _pN_  _w_ and the value of supply is _wLN_ . The value of demand for non-tradables is 1(  ) _wL_  _pNh_  _pN_  . In the first term, _wL_ is the city wage bill and this is spent on a composite good which is a Cobb-Douglas  aggregate of tradables with share  , and non-tradables with share 1(  ) . As we will see below, this spending takes different forms – final consumption, commuting and construction costs – but all demand the same composite, so the city’s income generates demand for non-tradables 1(  ) _wL_ . The second term, _pNh_  _pN_  , is spending on non-tradables from income generated outside the city. Such spending consists of several elements. One is spending from transfer payments to the city, such as natural resource revenues, taxes, or foreign aid. Another is

> 7 These assumptions imply full employment and an integrated labor market. It would be possible to add labor market imperfections (for example, part of non-tradable production being undertaken by an informal sector), but this is inessential for the arguments being made.

> 8 The definition of non-tradables is necessarily quite elastic.  The crucial distinction is the extent to which the price depends on supply from the city, or is set on a wider regional or international market.

6
hinterland spending on non-tradables produced in the city. We refer to _h_  _pN_  as the hinterland demand function, and take it as exogenous and decreasing in price; it is shifted upwards by higher demand from these extra-city sources. Using _pN_  _w_ and _LN_  _L_  _LT_ , the equality of supply and demand for non-tradables is  _L_  _LT_  _w_  1(   ) _wL_  _wh_  _w_ . Rearranging, This is the wage at which net urban supply of non-tradables equals hinterland demand, where _h_  1  . is the inverse hinterland demand curve. Crucially, its downwards slope captures the fact that expanding urban employment in non-tradables reduces the wage paid, since increased supply reduces the price of non-tradables.

In contrast, tradable goods face perfectly elastic world demands, have fixed world price, and will be taken as numeraire. Labor productivity in the tradable sector is _a_ <sup>_L_</sup> _T_  , and this is the wage offered in the sector. We assume that productivity is either constant or increasing in<sup>_L_</sup> _T_<sup>,</sup> increasing returns arising because of agglomeration economies external to the firm but internal to the tradable sector. The sector operates if labor productivity is greater than or equal to the market wage, _w_ , so the following relationships must hold, Together, Eqns. (1) and (2) implicitly define the city’s (inverse) labor demand schedule _w_<sup>_D_</sup> ( _L_ ) , i.e. they give the value of _w_ at which urban employment (in non-tradables and tradables) fully employs a labor force of size _L_ . This labor demand curve generally has a kink in it at the ‘trigger wage’, _a_ 0  _a_ (0) , at which tradable production commences. We summarize it as follows: If the tradable sector is inactive, then _LT_  0 and, from (1), 7
This is illustrated by the bold curve in Fig. 1 which has city employment (= population) on the horizontal axis and the wage on the vertical. The figure is drawn with constant returns to scale in tradable production so labor productivity in tradables is a constant _a_  _LT_ <sup></sup> _a_ 0 . On the downward sloping segment the entire labor force is employed in the non-tradable sector, _D_  1 _w_ ( _L_ : _LT_  0)  _h_  _L_  , downward sloping as more employment increases supply of the nontraded good, reducing price and wages. If the ensuing wage is less than _a_ 0 then tradable _D_ production is profitable, giving the horizontal segment, _w_ ( _L_ : _LT_  0)  _a_ 0 . The dividing line is where the urban population is _L_  _h_  _a_ 0  /  .

**_Urban costs and labor supply:_** Labor supply comes from the location decisions of mobile workers.  It depends on utility outside the city, set as exogenous constant<sup>_u_</sup> 0<sup>, and utility inside.</sup> This depends on the wage, the prices of goods consumed, and any further costs associated with urban living.  These include direct utility costs (and benefits) from crowding, congestion, and provision of public services.  And financial costs, arising from land and house prices and from commuting costs.

Our modeling of urban costs is in the tradition Alonso (1964) and others.<sup>9</sup> Workers are employed in the central business district (CBD) and incur commuting costs. The city is linear, and _x_ denotes distance from the CBD.<sup>10</sup> Each worker occupies a unit of housing, and housing density (hence the amount of land occupied per unit housing) is chosen by profit maximizing developers. The utility of a worker living at distance _x_ from the CBD is _v_ ( _x_ ), The term in square brackets is the wage net of housing and commuting costs. The cost of housing at distance _x_ is _p_ ( _x_ ) and commuting incurs _t_ units of the composite good per unit 1  distance, so a worker living at distance _x_ from the CBD pays commuting costs _xtw_ , where 1  _w_ is the price index of the composite good.<sup>11</sup> Income net of housing and commuting costs (i.e. the term in square brackets) is spent on the composite good, so utility is derived by deflating by the price index.<sup>12</sup>

> 9 See Duranton and Puga (2015) for full exposition and analysis of the Alonso-Muth-Mills urban model.

> 10 To minimize notation we work with a linear city with a single spoke from the CBD.

- 11 As noted above, the composite is Cobb-Douglas with tradable share _θ_ , non-tradable share 1 – _θ_ .  Since 1 

- tradables are the numeraire and the price of non-tradables is _w_ , the price index is _w_ .

> 12  If there are transfer payments spent in the city (resource rents, taxes, foreign aid) we assume that, while

8
Workers are perfectly mobile, choosing between living outside the city with utility<sup>_u_</sup> 0<sup>, or at</sup> locations _x_ in the city. For all occupied urban locations, it must therefore be the case that _v_ ( _x_ )  _u_ 0 , implying that house prices at each distance, _p_ ( _x_ ), satisfy the indifference condition The supply of housing depends on residential construction decisions, taken to maximize land rent at each point. The number of housing units – or density – built at _x_ is _N_ ( _x_ ), and rent, _r_ ( _x_ ) , is revenue from housing minus construction costs, i.e.

 1  Construction costs per unit land are _cN_ ( _x_ ) _w_ , an increasing and convex function of density (e.g. the cost of building taller).<sup>13</sup> We assume that this relationship is iso-elastic with parameter 1  _γ_ , and that costs are incurred in units of the composite good, i.e. have price _w_ . Developers choose density to maximize rent, giving first order condition and maximized rent, The edge of the city is at distance<sup>~</sup> _x_ where rent equals the exogenous outside rent _r_ 0 , i.e.

Housing capacity and total city population up to this edge are Eqns. (5) – (9) give values of three variables that vary with distance, _N_ ( _x_ ), _p_ ( _x_ ), and _r_<sup>*</sup> ( _x_ ) and two scalars, _L_ and<sup>~</sup> _x_ , as functions of parameters and the wage. They implicitly define the residential structure of the city, its built density, house prices, land rents, and total population and city edge. They also define the labor supply function – the relationship between _w_ and _L_ . An explicit form of this relationship is useful for expositional purposes and can be derived with two simplifying

> they create demand for non-tradables, they do not provide utility for urban residents.

> 13 See Henderson, Tanner and Venables (2016) for a richer modelling of construction technologies that differentiates between formal and informal housing.  Qualitative results of the present paper would be unchanged with this more general formulation.

9
> * ~ assumptions.<sup>14</sup> The first is that outside rent is zero, _r_ ( _x_ )  0 ; this implies that the edge of the ~ ~ city has _p_ ( _x_ )  _N_ ( _x_ )  0 (from (6’) and (7)), i.e. that the city converges to zero density at its edge.  It follows from (5) that the city edge is given by:

Second, we assume that construction costs increase with the square of density, _γ_ = 2, giving population This uses (7), (5) and (10) in (9); the appendix gives the case for general values of _γ_ . Inverting, the urban wage required to attract and accommodate population _L_ is This is the inverse labor supply curve, _w_<sup>_S_</sup> ( _L_ ) illustrated by the upwards sloping curves on Fig. 1, the upper one drawn for a city with higher urban costs.<sup>15</sup> Several remarks are in order. First, concavity is a general property of this supply function. Intuitively, if the wage (and hence land rent) is low the city is built at low density, so accommodates a small population.<sup>16</sup> Higher wages increase population through two margins: the city becomes larger and is built at higher density, the interaction between the two giving concavity. Second, this supply curve is derived from the fundamentals of commuting costs, construction, and land prices, but these are only part of a more general urban cost relationship. If other factors – congestion, loss of amenity – increase with city size, this too will create the upward sloping relationship as a larger city requires higher wages as compensating differential to offset these costs (see e.g. Duranton’s 2008 discussion of the ‘cost of living curve’).

> 14 These assumptions are relaxed in simulations later in the paper.

> 15 This and subsequent Figs. are derived by numerical simulation, parameters given in the appendix.

> 16 If _r_ 0 = 0 the curve is vertical at _L_ = 0, as illustrated.

10
**Figure 1:  Urban equilibrium with constant returns to scale**

<!-- Start of picture text --> w<br>wD ( L : LT  )0 w S ( L :  )<br>w S ( L )<br>E +<br>E<br>a 0<br>D<br>w ( L : LT  0)<br>1 / <br>u 0<br>L  h  a 0 /  L   a 0   u 0  2 / 4 tc L<br><!-- End of picture text -->

# **2.2  Equilibrium with constant returns in tradable production**

The urban labor demand and supply curves, Eqs. (3) and (12), give equilibrium values of the wage, city population and sectoral employment, as illustrated by points E and E<sup>+</sup> on Fig. 1. Point E<sup>+</sup> gives the equilibrium if urban costs are high, _w_<sup>_S_</sup> ( _L_ :  ) , in which case the wage exceeds _a_ 0 and city produces only non-tradables. At lower costs equilibrium is at E, with both sectors active, wage rate _w_  _a_ 0 , and hence city population and employment in tradables respectively, _L_   _a_ 0 <sup></sup> _u_ 0  2 / 4 _tc_ and _LT_   _L_  _h_ <sup>_a_</sup> 0 (from Eqs. (11) and (3b)). The message is simple. Both cases have the same real wage, _u_ 0 . However, the equilibrium without tradable production, E<sup>+</sup> , has higher nominal wages and higher non-tradable prices. High urban costs can be passed on to consumers of non-tradables, but cannot be passed on in tradable sector, meaning that the city is uncompetitive in the production of these goods.

11
What factors shape the likelihood of each of these outcomes occurring? The dividing line _S D_ between cases is where wages and employment levels satisfy _a_ 0  _w_ ( _L_ )  _w_ ( _L_ : _LT_  0) , so 1/ 2 1/  the city is specialized in non-tradables if _a_ 0   _u_ 0  2  _cth_ ( _a_ 0/)   (using Eqs. 12 and 3a). This is more likely if, from the left-hand side of the inequality, _a_ 0 is small, i.e. the productivity of workers in the tradable sector is low. This could arise because of low productivity in the sector, or transport barriers imposing additional costs on exporting. On the right hand side of the inequality four parameters enter multiplicatively, _c_ , _t_ , _H_ , 1/ _θ_ , where _H_ represents a multiplicative shift parameter in the hinterland demand function.<sup>17</sup> Before discussing the impact of these parameters, it is useful to establish their impact on other aspects of the equilibrium, in particular the area of the city, its average density, and urban land rents. Area is captured by<sup>~</sup> _x_ , Eqn. (10), and average density is _L_ /<sup>~</sup> _x_ . Total rents, _R_ , are derived by integrating over rents at each point in the city (Eqn. 6’), where the last equation uses _γ_ = 2 (see appendix for general form). The effect of parameters on endogenous variables is found by log-linearizing the equilibrium conditions, and full expressions are given in the appendix. Here we simply note the comparative static signs, with Table 2 giving the sign of an increase in each of the parameters on specialization and other endogenous variables.

The city is more likely to produce non-tradables only, _LT_ = 0, the higher are _c_ , _t_ , _H_ , and 1/ _θ_ . The last two of these capture high demand for non-tradables, either from the hinterland or from a high share of city income being spent on non-tradables. The first two capture high urban costs, of construction and commuting, respectively. While demand and costs have the same qualitative impact on city specialization and on nominal wages, they have opposite effects on city population. If _LT_ = 0, higher demand is associated with larger population, and higher costs with a smaller population. Higher values of each of these parameters increase nominal wages and the ratio of rent to wage bill. Notice however that the two cost parameters have opposite implications for city density and geographic size. High construction costs reduce density, and city size is greater despite lower population. High transport costs reduce size, raising rents and hence city density.

> 17 I.e., the demand function becomes _h_ ( _p_ )  _Hh_ ( _p_ ) 12
If the city is diversified, _LT_ > 0, then nominal wages are set by productivity in tradables, _a_ 0. Demand for non-tradables has no effect on city population – high demand is accommodated by lower tradable production. High costs do however reduce city population, because of their direct effect on density of building (for construction costs) or the extent of the city (for commuting costs).

**Table 2:  Comparative statics**

||Likelihood<br>_LT_ = 0|Population<br>_L_<sup>ˆ</sup>|Wage<br>_w_ˆ|Size<br>_x_<sup>ˆ~</sup>|Density<br>_x_<br>_L_<br>ˆ~<br>ˆ|Rent<br>_L_<br>_R_<br>ˆ<br>ˆ<br>,<br>_w_<br>_L_<br>_R_<br>ˆ<br>ˆ<br>ˆ<br><br>|
|---|---|---|---|---|---|---|
|||_LT_ = 0:_LT_ > 0|_LT_ = 0:_LT_ > 0|_LT_ = 0:_LT_ > 0|_LT_ = 0:_LT_ > 0|_LT_ = 0:_LT_ > 0|
|Δ_H_ >0|+|+0|+0|+0|+0|+0|
|Δ_c_> 0|+|- -|+ 0|+ 0|- -|+ 0|
|Δ_t_> 0|+|- -|+ 0|- -|+ 0|+ 0|
|Δ_a_0> 0|-||||||

Notes: Δ denotes a proportional change in parameter. ^ denotes a proportional change in a variable. For each variable, the first column gives comparative statics when equilibrium has _LT_ = 0 and the second when _LT_ > 0.

In summary, characteristics of the city equilibrium are determined by multiple factors, and the model gives clear predictions about the mapping between parameters and outcome variables. Of course, the model parameters are themselves just summaries of complex realities, some elements of which can be changed by policy, others not. Thus, building costs include the ad valorem equivalent of the multiple obstacles to private construction that were outlined in the introduction. Commuting costs are to do with transport investment, and also reflect income levels – cities in which most people have to walk to work. Similarly, demand for non-tradables may be driven by the distribution of tax revenues, foreign aid or natural resource revenues which may themselves be the outcome of a political economy of urban bias (Bates 1981, Lipton 1977, Ades and Glaeser 1991). Hinterland demand for non-tradables is also a function of the income and economic geography of the region in which the city is located; for example, demand will be high if there are no nearby cities offering alternative sources of supply.

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# **3.  Increasing returns, expectations, and coordination failure**

We now open up two central features of the model. The first is increasing returns to scale – agglomeration economies – in tradable production, this creating the possibility of multiple equilibria.<sup>18</sup> We show that it is possible that there is a low equilibrium in which the city produces tradables only, and also a high equilibrium in which the city is active in both sectors. The possibility of being trapped in the low-equilibrium arises because of coordination failure.<sup>19</sup> In the simplest case (section 3.1) this is an inter-firm coordination failure; potential producers of tradables do not coordinate to internalize the external economies of scale associated with agglomeration. However, given endogenous choice of the way the city is built – its size and density – the coordination failure goes deeper. Section 3.2 turns to the role of sunk costs and expectations in shaping construction decisions, and shows how (self-fulfilling) expectations may be such that the city is constructed in a way that locks it into the low equilibrium. It is possible that – even if the inter-firm coordination failure between produces of tradables were somehow resolved – the built urban form is incompatible with expanding into tradable goods production.

# **3.1 Increasing returns and multiple equilibria**

Suppose that tradable production is subject to agglomeration economies so that productivity in tradable production is increasing with the size of the sector. The left-hand segment of the labor _D_ demand curve, _w_ ( _L_ : _LT_  0) is unchanged, and the segment with tradable sector active, _wD_ ( _L_ : _LT_  0) , becomes upwards sloping. Fig. 2 illustrates for the case in which productivity is linear in tradable employment between lower and upper bounds, _a_ 0, _am_ , so _a_ ( _LT_ )  min  _a_ 0   _LT_ , _am_  ,   ,0 _a_ 0  _am_ .

As illustrated, returns to scale are strong enough for labor demand to have three intersections with labor supply. Points M and M’ are stable equilibria, while the intermediate intersection is unstable (under a dynamic in which the tradable sector expands or contracts according to whether profits are positive or negative). At the lower point, M, the city is specialized in nontradable production and wages are above the trigger point, _a_ 0 , at which tradable production commences. Entry of a small mass of tradable produces is not profitable; this point is an equilibrium if coordinated entry of a sufficiently large mass of tradable producers (who would reap the benefits of agglomeration economies) is not possible. At the upper equilibrium, M’, the tradable sector is active and is large enough for agglomeration economies to have cut in, raising

> 18 For discussion of agglomeration economies in the context of developing economies see World Bank

> (2009) and for evidence see Chauvin et al. (2016).

> 19 As in, for example Murphy et al. (1989), Henderson and Venables (2009).

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productivity. This is associated with larger city size and employment and with higher nominal wages (although real wages are held to _u_ 0 by migration and labor supply).

**Figure 2:  Increasing returns and multiple equilibria**

<!-- Start of picture text --> D<br>w w ( L : LT  )0<br>D<br>M ’ w ( L : LT  0)<br>M<br>a 0<br>w S ( L )<br>1 / <br>u 0<br><!-- End of picture text --> <!-- Start of picture text --> L<br><!-- End of picture text --> What are the conditions that support this configuration? The appendix gives conditions on parameters, and here we just make three remarks. First, point M exists if _S D a_ 0  _w_  _L_  _w_ ( _L_ : _LT_  0) , exactly as discussed in section 2.2. Second, city size must (we assume) be bounded above, so it must be the case that as _L_ becomes very large so _S D w_  _L_  _w_ ( _L_ : _LT_  0) , as illustrated. Third, a necessary condition for multiple intersections is that economies of scale in tradables are large enough that, in some range, the slope of the labor demand curve exceeds that of labor supply. Recall that, along _wD_ ( _L_ : _LT_  0), _LT_ solves _a_ ( _LT_ )  _h_  1  _L_  _LT_  , Eqn. (3b). The slope is therefore _dwdLD_  _a_ (' _LT_ ) _dLdLT_  1  _a_ ' _h_  ' _a_ ' . The slope is steeper the greater are marginal returns to scale, _a_ (' _LT_ ) , adjusted for the fact that as _L_ increases some extra jobs are created in the non-tradable sector so _dLT_ / _dL_  1. This is larger the fewer non-tradable jobs are created by demand from additional urban population (high _θ_ ), and the more 15
that the increasing wage chokes off hinterland demand for non-tradables (more elastic hinterland demand for non-tradables).

There are two further comments. First it can be shown that aggregate welfare is higher in the equilibrium M’ than M. Comparing the two, workers’ utility is, by construction, unchanged. Total city rent is higher, since along the labor supply curve it is increasing in wage and city size. There is a third element of welfare change, which is that of ‘hinterland’ consumers of the nontradable good, whose welfare depends on the price of non-tradables. We show in the appendix that the sum of these elements is increasing in the wage and hence, comparing points on the labor supply curve, welfare is higher at M’ than M. However, the distributional impact, given constant real wages in the city, is no change for workers, gain for urban landowners, and loss for outsiders consuming non-traded goods produced in the city.

Second, we suggested in the introduction that cities’ experience seemed to be dichotomous, some trapped in non-tradable production, while others have been successful in attracting tradables and have grown large clusters of tradable activities. The possibility of multiple equilibria captures this dichotomous response, showing how small initial differences can lead to quite different outcomes. However, the low equilibrium is supported by a simple inter-firm coordination failure between tradable sector producers. We now enrich this, adding interaction between the tradable sector and the way in which the city is constructed.

# **3.2  Expectations, sunk costs, and construction**

Buildings are long lived and most of the costs incurred in constructing them are sunk. This has two implications. One is that construction decisions involve forward looking expectations, and the other is that a historical legacy of urban form shapes the present urban equilibrium. It is therefore possible that cities are ‘locked-in’ to outcomes not simply because of coordination failure between firms, as we saw in the previous section, but because of a coordination failure spanning time periods and the actions of builders and firms. To capture this, a time dimension must be added to the model, and this is done simply by adding a second time period. We will show how low expectations mean that the city may be constructed at a scale and density that precludes attracting tradable sector production. High expectations can be self-fulfilling as they support construction at greater scale and density, an urban form that lowers costs, attracts tradables, and generates an outcome with higher welfare.

The extension to two periods is straightforward. Production and labor demand are as above, but residential building is durable. Buildings constructed in the first period last into the second, meaning that first period construction decisions depend on prices in period 1 and on expected prices in period 2. Time periods are indicated by subscripts 1, 2 and expectations of future 16
values by superscript _E_ , so period 1 expectations of period 2 prices of houses and labor _E E_ are, _p_ 2 ( _x_ ), _w_ 2 . Worker mobility means that house prices are expected to satisfy indifference condition (5) in both periods, so The expected present value of a house built at _x_ in period 1 is  _p_ 1( _x_ )  1(   ) _p_ 2 _E_ ( _x_ ) , where _δ_ and 1 - _δ_ are weights attached to each period, and it is this that guides period 1 construction decisions.<sup>20</sup> The expected present value of construction at density _N_ 1(<sup>_x_</sup> ) on land at _x_ in period 1, and the optimal choice of density are The edge of the city is at distance<sup>~</sup><sup>_x_</sup> 1<sup>where rent equals the exogenous outside rent</sup><sup>_r_</sup> 0<sup>, and city</sup> population follows, so These equations are analogous to Eqs (5) – (9), except that future expected prices influence construction decisions.

In the second and final period house prices satisfy the indifference condition Building takes place on land that is not previously developed so, for _x_ <sup>~</sup><sup>_x_</sup> 1 , rent, construction decisions and population are given by

> 20 We continue to use the word house ‘price’ rather than rent, although payments are made in both periods.

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Once again, these are analogous to Eqs. (5)-(9), except that they now apply only to land that is not previously developed, _x_ <sup>~</sup><sup>_x_</sup> 1 , and the housing stock (and hence population) includes that inherited from period 1.

The full equilibrium comes from the labor demand functions (as previously) and from noting that Eqs. (5a) – (9a) and (5b) – (9b), respectively, define first and second period inverse labor supply functions, _w_ 1 _S_ ( _L_ 1 : _w_ 2 _E_ ) and _w_ 2<sup>_S_</sup> ( _L_ 2 : _L_ 1) . Period 1 labor supply now depends also on expectations about period 2: and period 2 labor supply depends also on inherited residential stock and hence population<sup>_L_</sup> 1<sup>. It is not generally possible to derive explicit expressions for</sup> these supply functions, so we proceed by demonstrating some special cases, and then going to numerical simulation.

First, notice that, by construction, the two equilibria of sub-section 3.1 are stationary perfect _E_ foresight equilibria of the two-period model. Thus, if _w_ 1  _w_ 2  _w_ 2 so that _E p_ 1( _x_ )  _p_ 2 ( _x_ )  _p_ 2 ( _x_ ) then _L_ 2  _L_ 1 and the model gives stationary outcomes identical to those in section 3.1.<sup>21</sup> This is illustrated on Fig. 3, with points M, M’ and labor supply curve _w_<sup>_S_</sup> ( _L_ ) exactly as in Fig. 2. We refer to these equilibria as {M, M} and {M’, M’}, the two elements in brackets representing the outcome in the two time periods.

Second, suppose that the first period equilibrium is at M (so the city was built with stationary expectations, _w_ 2<sup>_E_</sup>  _w_ 1). What effect does this have on the set of opportunities attainable in period 2 – or more formally, what does _w_ 2<sup>_S_</sup> ( _L_ 2 : _L_ 1) look like? To answer this we assume that _r_ *(~ _x_ )  0 and _γ_ = 2, in which case the edge of the city in period 1 is ~ _x_ 1   _w_ 1   _u_ 0  / _t_ (Eqn. 10). If the same assumptions hold in period 2 then (5b) – (9b) give ~ _x_ 2   _w_  2  _u_ 0  / _t_ . This enables the integral giving city population in period 2 to be evaluated as Rearranging, the inverse labor supply curve is

> 21 With _w_ 1  _w_ 2 _E_  _w_ 2 and _p_ 1( _x_ )  _p_ 2 _E_ ( _x_ )  _p_ 2 ( _x_ ) Eqns. 5a-8a, 5b-8b and 5-8 are identical.  It follows ~ ~ that _x_ 1  _x_ 2 and _L_ 1  _L_ 2 .

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This is the dashed line _w_ 2<sup>_S_</sup> ( _L_ 2 : _L_ 1) through point M on Fig 3. The steepness of this curve close to M is apparent from Eq. (14) and reflects that fact that, if _w_ 2 is only slightly greater than _w_ 1, then the only new building undertaken will be close to the edge of the period 1 city, and low price, rent, and density, therefore accommodating few workers.<sup>22</sup> Quite generally, _w_ 2<sup>_S_</sup> ( _L_ 2 : _L_ 1) must lie on or above _w_<sup>_S_</sup> ( _L_ ) . The latter optimizes construction for each value of _L_ ; the former inherits a housing stock optimized for first period value of<sup>_L_</sup> 1<sup>, and then builds beyond. Some of</sup> the city building stock is therefore optimized for the relatively small population at M, a building stock that is not optimal for the larger population.The consequences are clear, from the fact that – as illustrated – labor supply _w_ 2<sup>_S_</sup> ( _L_ 2 : _L_ 1) does not intersect with labor demand except at M. Thus, even if inter-firm coordination failure were to be resolved, the high equilibrium is unattainable. Starting from period 1 equilibrium at M, the only equilibrium is the stationary one, remaining at M.

**Figure 3:  Multiple equilibria with sunk costs**

<!-- Start of picture text --> D<br>w w ( L : LT  )0 w 2 S ( L 2 : L 1) w 2 S ( L 2 : L 1)<br>F2<br>D<br>M’ w ( L : LT  0)<br>M<br>a 0<br>F1<br>w S ( L )<br>1 / <br>u 0<br><!-- End of picture text --> <!-- Start of picture text --> L<br><!-- End of picture text -->

> 22 See Eqn. 12 and following discussion for comparison.

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The previous case worked with period 1 equilibrium at M – as would be the case with stationary (and self-fulfilling) expectations. What if expectations are more positive, expecting tradable production in period 2? We have already seen that {M’, M’} is an equilibrium, but it is more interesting to study the transition from non-tradable specialization to tradables. We therefore _assume_ that tradable production is technologically impossible in the first period (e.g. city tradable productivity is very low), but becomes possible in the second period. The first period _D_ equilibrium therefore lies on _w_ ( _L_ : _LT_  0) but, if expectations are more positive, will not be at _E_ point M. If tradable production is expected in period 2 then _w_ 2  _w_ 2  _aM_ . This raises the returns to building in period 1 (Eqns. 5a-7a) , so there is more and denser period 1 building, accommodating a larger city population and moving the first period equilibrium along _D w_ ( _L_ : _LT_  0) to point F1. The second period labor supply curve through this point, _w_ 2<sup>_S_</sup> ( _L_ 2 : _L_ 1) , does not have a closed form solution, but is qualitatively similar to (14), as illustrated on Fig. 3, and gives the perfect foresight equilibrium pair {F1, F2}.

The essential difference between the two equilibria, {M, M} and {F1, F2} lies in expectations. Both start with _LT_  0 , but in {F1, F2} expectations are ‘optimistic’, and perfectly foresee the second period outcome with tradable production. This gives higher present value rents, more first period construction, and hence greater first period housing capacity which reduces house prices and first period nominal wages. Importantly if point F1 lies below _a_ 0, then the inter-firm coordination problem is resolved. City population and the supply of non-tradables is large enough at F1 for the wage (absent tradable production) to be less than the trigger wage, ensuring that tradable production will take place in the second period. Once again, the built structure of the city overcomes a potential inter-firm coordination failure.

# **3.3  The urban profile**

Finally, we illustrate results by developing a numerical example. This puts numbers on the arguments above and demonstrates the existence of the equilibria discussed. It also enables us to relax assumptions (in particular letting outside land rent be positive), establish welfare effects and undertake comparative statics. Perhaps most importantly, it generates illustrations of the city profile – the way in which land rent, house prices and building density varies across the city and between equilibria. The simulations use the same parameter values as underlie earlier figures, except that _r_ 0<sup></sup> 0 . Values are given in the appendix; to scale results we note that outside utility is set at unity and the two time-periods have equal weight, _δ_ = 1⁄2.

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Outcomes are illustrated in the panels of Fig. 4. Values of city-wide variables are given in the table and intra-city profiles of rent, house prices, and density are given in the three plots which have distance from the CBD on the _x_ - axis. The table reports outcomes for three equilibria: the stationary low and high equilibria, {M, M} and {M’, M’} respectively, and the equilibrium {F1,F2}. For clarity, the plots just give {M, M} (dashed lines) and {F1,F2}, for which the two time periods are subscripted.

Equilibrium {M, M} has wage in each period _w_  .165 , with a 65% premium over outside utility going to meet the urban cost of living, including commuting and housing costs. This wage is consistent with no tradable production occurring if it is greater than the trigger wage, i.e. _a_ 0<sup></sup> .165 . The intra-city profiles are given by the dashed lines on the figure. The city edge is the kink in the rent function (up to which _r_ ( _x_ )  _r_ 0 and beyond which land is undeveloped). House prices fall linearly, since commuting costs are assumed linear in distance. Density and rents decline with distance, as expected.

The solid lines, subscripted by period, are equilibrium {F1,F2} in which there is tradable production in the second period, but not the first. The example has _am_  2 , and this is the second period wage. This generates high second period house prices and land rents, and also therefore relatively high expected returns to period 1 building, _r_ 1<sup>_E_</sup> ( _x_ ) . The city is therefore built both larger and denser in the first period than is the case in equilibrium {M, M}, as is clear from the density profile _N_ 1(<sup>_x_</sup> ) . Period 2 land rents are higher again, so that there is further construction and this is at high density, curve _N_ 2(<sup>_x_</sup> ) . The relatively large amount of building in period 1 accomodates a large population, as a consequence of which period 1 wage, _w_ 1<sup></sup> .142 , and house prices, _p_ 1(<sup>_x_</sup> ) , are lower than that in equilibrium {M, M}. If the wage is less than _a_ 0 enough (in this example, requiring _a_ 0<sup></sup> .142 ) tradable production is triggered. By assumption, it does not occur in period 1, but will surely do so in period 2.

21
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increasing city population. Higher construction and commuting costs shift points {F1,F2} to the left, raising the first period wage and reducing population in both periods. The importance of future expectations can be seen by changing _δ_ , the weight on the first period relative to the second. A higher _δ_ has no effect on equilibrium {M, M} and again moves points {F1,F2} to the left, raising _w_ 1 and reducing population. Each of these parameter changes increases the likelihood that _w_ 1 exceeds _a_ 0 , in which case the city fails to attract tradable production and equilibrium of type {F1,F2} does not exist.

# **4.   Concluding comments**

The introduction to this paper sets out stylized facts about developing country cities, particularly those in Africa, indicating the presence of relatively high urban costs, a high cost of living, high nominal wages (alongside a low real wage), and failure to attract investment in tradable sectors of activity. Each of these is captured in the model developed in this paper. The analysis shows how the combination of increasing returns to scale, durable capital and sunk costs make for multiple equilibria, and the possibility – depending on parameters – that the city is built in a way that precludes establishment of the tradable goods sector.

Several broad policy messages follow. The first is the need to see the city as a whole. Policy has often been siloed, while our analysis highlights the interaction between all aspects of a city’s urban form – residential construction, infrastructure, transport – and its economic performance. The second is the high cost of policy failure. Small differences in initial conditions can – with increasing returns, sunk costs, and expectations – set cities on quite different development paths.

In terms of specific policy instruments, the paper points to the importance of efficient land use and infrastructure provision. The consequences of high building and commuting costs go far beyond their direct effects as they shape the sort of economic activity that takes place in the city. The many obstacles to residential construction that were noted in the introduction are all sources of inefficiency, which necessarily raise urban costs and thereby make the city a less attractive place for tradable goods production. Reducing these obstacles has direct benefits, and also increases the likelihood that the city will develop new sectors of activity. Expectations also matter, as the form and extent of investment in durable structures depend on the expected future prosperity of the city. Expectations need to be coordinated in some way, so that investors have confidence that the city – or a particular area within it – is likely to grow. Setting these expectations in a credible way is difficult and may require commitment in the form of investment in public infrastructure.

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Stepping outside the confines of the model, two further points can be made. While the model focuses on investment in physical capital, investment in human capital is at least as important. Acquisition of the specialist skills needed to run modern production – and to run the city – will take place only if the costs of the investment are not too high and there are expectations of positive returns. Thus, the arguments that the paper has made with respect to physical capital apply with at least equal force to human capital. The model also draws out the possibility of vicious or virtuous circles leading to multiple equilibria, and here too further forces might be at play. In particular, a fiscal feedback – not present in the model – may be important. A weak tax base is likely to lead to poor infrastructure and public services. This will raise urban costs, directly in the form of high transport and congestion costs and limited availability of power and other utilities, and indirectly via reducing the well-being of workers who require compensating wage payments. As we have seen, higher urban costs will undermine the city’s economic performance and hence its tax base (e.g. lowering rents and land values). This in turn reduces the city’s ability to provide such services, completing the vicious circle.

Finally – and for future research – this urban model needs to be placed in a wider model of urban hierarchy, within which different cities perform different functions. Some cities will specialize in non-tradables but, in all but the most natural resource abundant countries, some cities that are able to compete in non-resource tradable activities will surely be needed.

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