Bobos in Paradise: Urban Politics and the New Economy

This paper provides some elements to explain the observed takeover in some urban areas of a new kind of elite associated with new economy jobs, also known as "bourgeois bohème" (bobos). This takeover has been associated with greater investment in urban amenities and "clean" means of transport, with adverse effects on commuting time. The model allows us to explain those developments by productivity is growth in the new economy, and by the differences in production processes between the new and old economies. The consequences of bobo takeover for house prices and employment of unskilled service workers are also discussed. A bunkerized equilibrium in which skilled workers in the old economy no longer reside in the city and have been replaced by service workers is studied. In such an equilibrium urban amenities are at their maximum and commuting flows have been eliminated. For some parameter values, bobos are better-off under bunkerization, in which case they may gain by favoring it with a "diversity" subsidy for unskilled workers to reside in the city.


Introduction
The term "bobo" stands for "Bourgeois Bohème" and was coined by David Brooks (2000) in a famous book about the rise of a new knowledge elite.
This new kind of bourgeoisie is generally considered as prevalent in globalized capital cities, and its lifestyle and political attitude stand in contrast to that of the traditional bourgeoisie. Furthermore, the bobos are generally viewed as a politically powerful group. They have been instrumental in bringing about left-wing governments in municipalities such as Berlin, Paris or San Francisco, despite the relatively high economic status of this social class.
Economically, the bobos are "symbol manipulators": teachers, intellectuals, professionals, journalists, advertisers, architects, and "connected" workers of the new economy.
In terms of consumption attitudes, the bobos promote a relaxed lifestyle where conspicuous consumption is banned. They seek human scale habitat and a "village" atmosphere, while generally living in large metropolitan areas (an early example of such conceptions is Jacobs (1961)). They insist on environmental quality and promote public transportation or bicycles. They value "arts", in particular in their most modern forms: contemporary arts, rock concerts, and so forth.
Politically, the bobos are viewed as generally supportive of environmentalists and/or socialist parties. Their takeover of major cities has taken place in the context of sharply increasing house prices from the mid-1990s to the onset of the …nancial crisis, and led to policies that recognizably di¤er from the ones implemented both by the right and by the traditional left. These policies can be summarized as follows 1 : Greater investment in collective urban amenities and socialized recreational events.
1 See Brooks (2001), Chapter 7. 1 Reduced urban space for the automobile, generally coupled with a reduction in parking space, higher taxes and more stringent regulations and constraints for personal vehicles. More investment in public transportation and in dedicated areas for bicycles, skate-boards, roller skates, and so forth. Deregulation of the use of bicyles (authorization to use wrong ways and bus corridors). Public provision of cheap bike and electrical car rental, and dedication of public space to those devices.
Promotion of "social mixity" and "diversity", by means of transfer policies and/or subsidized housing that maintain a critical mass of lower class dwellers in the city center, while intermediate classes are eliminated and relocate themselves in the outer periphery 2 .
This paper provides some elements for understanding these developments from a "pure economic perspective". By this I mean that I will attempt to explain them as a consequence of technological developments, instead of just assuming that bobos are a new kind of individuals with their own preferences.
The paper focuses on the relative roles of, and con ‡ict of interest between two kinds of bourgeoisie: The skilled workers of the old economy versus the skilled workers of the new economy (bobos) 3 . The former work in activities that are more land intensive, while still preferring to live in a city centre. As a result they derive more utility from commuting and are less willing to raise commuting costs in order to improve urban amenities than the bobos. The paper shows that as the new economy grows faster than the old economy, the bobos overtake the cadres as the politically decisive group in the city. As a result, the level of urban amenities goes up and so do transportation costs.
The consequences for house prices and the cost of services are also studied, as well as the implications for suburban unemployment of the lower classes.
House price dynamics in the transition from one regime to another are also studied. It is also shown that the date of this transition is indeterminate, as both regimes may co-exist for a range of productivity levels in the new economy.
Finally, I also show that it may be pro…table for the decisive bobo class to subsidize location of lower class unskilled workers in the city, in absence of any altruism toward them or intrinsic taste for a socially diverse makeup of the city. This is because such subsidies allow to force the economy to settle in a "bunkerized" equilibrium in which the service providers to city dwellers are located in the city, so that the price of services no longer goes up with the amenity level. As a result, ex-post there is no cost to raising the amenity level in the city, and the resulting political equilibrium involves the highest possible level of amenities and transportation cost.
The model is an application of voting equilibrium theory under interjusdictional mobility, as was studied by Rose-Ackerman (1979), Westho¤ (1977), Richter (1982), Epple et al. (1983Epple et al. ( , 1984, to the speci…c urban trends that have been oberved in the recent decades. It is also related somewhat to the large sociological literature on gentri…cation pioneered by Glass (1964) 4 . This literature, however, generally fails to identify con ‡icts of interest within the bourgeoisie, sticking instead with the traditional marxist scheme of class con ‡ict. Instead, I focus on the con ‡ict of interests between two categories of 4 There are also a number of economic studies of gentri…cation, like Rossi-Hansberg et al. (2008), Guerrieri et al. (2010), who focus on the geographical spread of increases in land prices following income growth or investment in amenities. This kind of e¤ects is also present in the current model, but the focus is on the politico-economic equilibrium, not on gentri…cation per se.
3 skilled workers that work in di¤erent types of occupation. Another relatively unusual aspect of the model is departure from the traditional assumption that all economic activity must take place in the Central Business District, as, say in, Leroy and Sonstelje's (1983) analysis of commuting gentri…cation. Here the existence of land-intensive economic activities located in the suburbs plays a key role in the analysis.
An illustration of the phenomena analyzed here in the case of Paris is the fate of the so-called "axes rouges". These policies were introduced by Paris mayors Jacques Chirac and Jean Tiberi and consisted in preventing parking along the side of a number of designated large communication ways (such as Avenue Denfert-Rochereau), in order to improve tra¢ c on those axes. In contrast, the socialist Delanoe administration, which took over in 2001, had a deliberate policy of reallocating space away from automobile tra¢ c and in favor of alternative means of transport as well as recreational activities 5 .
Consequently, the axes rouges were abolished. It is generally considered that the gentri…cation process was already well under way under the Chirac and Tiberi administrations. The introduction of axes rouges should therefore be understood as catering to the Parisian upper-middle class voter of that time, and conversely their abolition should be interpreted as a shift in the preferences of the median voter, as analyzed in this paper, not as public policies working toward gentri…cation. 6

The model
In this section, I lay out the main assumptions of the model. This is a partial equilibrium model of an area with two locations: city and periphery.
Unlike the traditional central business district models, economic activity is not constrained to take place in the city 7 .

Workers and skills
There are three categories of workers: Skilled workers specialized in the new economy, thereafter referred to as "Bobos". The total number of bobos is …xed and equal to H 1 : Each of them is endowed with one unit of specialized skilled (type 1) labor.
Skilled workers specialized in the old economy, that I will refer to as "Cadres" 8 . There are H 2 of them, each endowed again with one unit of (type 2) skilled labor.
Unskilled workers, called "workers", who are specialized in services.
There are L workers in the economy, each endowed with one unit of unskilled labor.

Goods and production
There are …ve goods: 7 For the analysis of polycentric cities, see Anas and Kim (1996), Anas et al. (1998) and Okamoto (2007). 8 This French word loosely means "executive", but it is also associated with a conventional lifestyle with a substantial emphasis on consumer's society, as opposed to the more counter-cultural lifestyle of the bobos. The cadre lifestyle is described to some extent in Barthes (1957), and its somewhat more austere U.S. equivalent is discussed in Brooks (2001), in his analysis of the "Bourgeois" versus the "Bohemians". 5 A generic consumption good which is imported, and whose price is normalized to one. This good will be used as the numéraire.
Two exported goods: -A new economy good, good 1, whose production only involves type 1 skills. The production function is where y 1 is output and h 1 the input of type-1 skill.
-An old economy good, good 2, whose production uses both type 2 skills and land. The production function is where t is the land input and h 2 the type 2 skill input. The wage of type 2 labor working in location i is therefore equal to w 2 = a 2 (1 bR i ); where R i denotes the rental cost of housing in location i: 9 Services, denoted by subscript S: These services only use labor. The production function is where l S is the input of labor. Furthermore, in order to supply a service to their customers, workers must be physically located in the residence of the customer.
Housing: at any time, one unit of land can be converted into one unit of housing at no cost. Therefore, the production fonction for housing is y H = t; but in practice we will not distinguish between housing and land.

Geography
There are two areas The center (C), or "city", which has a …xed size X in terms of land. I will assume that max(H 1 ; H 2 ) < X < 2 min(H 1 ; H 2 ): (1) This assumption implies that the entire bobo or cadre population may …t in the city, and that if it is the case, the corresponding group will be a political majority. This land is usable for housing or as an input for good 2. In addition to that, a …xed amount of additional land is allocated to public goods, that are divided between urban amenities and transportation infrastructures. As will be clear below, we do not actually need to specify that amount.
The periphery (P), or "suburb", with an in…nite supply of land. In the periphery, there is a …xed, exogenous level of amenities, which is normalized to zero. This allows us, for simplicity, to limit the political economy analysis to the city, which is the focus of the paper.
In the city, public decisions over amenities involve reallocating available space for public goods between amenities and transportation infrastructures.
As a result, there is a trade-o¤ between amenities and commuting costs. I assume that this trade-o¤ is summarized by a positive relationship between , the level of transportation cost, and ; the amenity level in the city: = ( ); 0 > 0:

Preferences
There are overlapping generations of agents who live for two periods. Each Furthermore, each individual needs exactly one unit of housing, and therefore of land, so as to survive.

8
Instead of working and consuming, people can instead live in autarky, in which case they get a reservation utility equal to u 10 : Also, I will limit the analysis to a regime where the constraint u u is binding for workers only. Consequently, only a fraction of the total mass of workers L will be employed, and the others will be "unemployed". An increase in u can also be interpreted as an increase in the generosity of welfare bene…ts.

Consumption, production, and location
In this section and the following I describe how to solve for the equilibrium.
I will solve the problem in three steps: 1. The consumption and production decisions of all three social classes when old, as a function of their residential location.
2. The locational decisions of the young of the three classes, as a function of expected amenity levels and house prices.
3. The voting decision of urban households on amenities, as a function of the sociological composition of the city.
The equilibrium concept prevailing here is essentially the same as in Epple et al. (1984): there is equilibrium in goods markets, each location is internally in a majority voting equilibrium, and no individual can gain by changing residence. 11 . 10 Unless there is a housing bubble, i.e. house prices grow at or faster than the real interest rate, such an option would make people insolvent if they live in the city, in which case they have to borrow to buy a house. But the option is viable in the suburb where the equilibrium land price is zero. Therefore, to opt for autarky one has to live in the suburb. 11 However, here voters (rationally) internalize the e¤ects of electoral outcomes on the resale value of their house, contrary to the assumptions made in Epple et al. (1984). In most of the analysis, though, this is immaterial, because house prices only depend on the expected amenity level in the subsequent period, not on the current amenity level. But this e¤ect plays some role when we consider the introduction of "diversity subsidies" in Section 9.

Consumption and production decisions
In the last period of their life, people consume by maximizing their utility function subject to c + p Sj c S = y; where y is their income net of total costs and revenues from housing, and p S is the price of services in their community, denoted by p in the periphery and by p in the city. Therefore, c = y 1+ and c S = y (1+ )p S : Consequently, indirect utility is equal to, up to a constant V (y; p S ; ; ) = (1 + ) ln y ln p S + Two social classes may potentially be commuters. Workers may commute to o¤er their service to consumers not located in their area. Cadres may commute to a production site in the other area, as land itself is not moveable. Table 1 gives us the income when old, net of the rental cost of housing, of the three social classes of the generation born at t as a function of their residential location and their work location. Note that this does not re ‡ect commuting costs that are incurred as a disutility instead of an income loss.
The rental cost of housing in the city for this generation is R t = (1+r)q t q t+1 :

Class
Work in city Work in suburb Workers in city (2) 4. Some city residents are not workers.
In the Appendix, I provide a su¢ cient condition for conditions 3 and 4 to hold in equilibrium. Finally, I also ignore equilibria where more than one group is located in both areas: that is, groups can be strictly ranked by their marginal willingness to pay to live in the city. I will …rst discuss regimes I and II and the transition between the two regimes. Then I will study the speci…c characteristics of regime III. The analysis of regime IV is left out, because it is less plausible and less relevant to this paper's focus. In particular, as long as bobos are rich enough compared to service workers, they are likely to be willing to pay more to live in the city, and any equilibrium with some workers living in the city must be such that all bobos live there. 13 In both regime I and regime II, all workers live in the suburb. Part of them commute to o¤er their services to the city. Workers must be indi¤erent between that option and that of working in the suburb. Consequently, this pins down the price of services in the city: We also need, in those regimes, that workers be below their reservation utility should they decide to live in the city, i.e.
(1 + ) ln(p t a S R t ) ln p t + < u:

Equilibrium in Regime I
In Regime I, bobos are indi¤erent between living in the city and living in the suburb. In either case, they do not pay the commuting cost. Therefore, from Table 2, the following condition must hold: (1 + ) ln(a 1 R t ) ln p t + = (1 + ) ln a 1 ln p t : Using (3), we …nd that (1 + ) [ln(a 1 R t ) ln a 1 ] = + 1 + : This determines the rental cost of housing in equilibrium: The () function captures the net utility cost of living in the city for the bobos, ignoring housing. For this regime to be possible, we need that < 0; i.e. > 1 + :

13
As implied by (4), house prices are larger, the greater the amenity level and the smaller the commuting cost. The bobos in the city, while not su¤ering directly from commuting costs, su¤er indirectly due to more expensive services in the city. Therefore, the greater the commuting cost, the lower should house prices be in the city. Also, house prices are higher, the greater the bobo's productivity. This captures the e¤ect of income on the willingness to pay for amenities of the bobos, which is re ‡ected in rental costs, since they are the marginal group of city residents.
We now turn to the cadres. Their utility is (1 + ) ln(a 2 R t ) ln p t + : They set amenities so as to maximize this utility. This decision is made after they have picked their residence and paid the house price q t ; but before selling back their real estate to the new generation. As long as amenities are not a state variable, q t+1 will depend on the amenities set by the next generation. Therefore the amenity level has no e¤ect on q t+1 ; and hence no e¤ect on R t : In this model, there are no capital gains associated with investing in greater amenities 14 . On the other hand, p goes up with transportation costs. Therefore, the cadres set amenities by just maximizing ( ) ln p t ; or equivalently, given (3),

1+2 1+
( ): Let A ; A be the corresponding amenity level and commuting cost. The corresponding utility of the cadres is equal to (1 + ) ln(a 2 R t ) ln p t + A A : For regime I to prevail, this must be larger than their utility from residing in the suburb, which is equal to (1 + ) ln a 2 ln p t : This is equivalent to We note that a 2 (1 exp( A )) is the cadre's willingness to pay for living in the city. The () function is the net utility cost of residing in the city for the cadres, ignoring housing costs. Since the cadres, unlike the bobos, have to commute, we have that ( ; ) > ( ; ) for all ; : Equation (5) therefore states that in regime I, this quantity is larger than the cost of housing, itself equal to the bobos willingness to pay for living in the city.
It is also interesting to compute the employment level in the service sector.
Denoting by R A the rental cost of housing in this regime, total income in the city is Total service demand in the city is therefore equal to Therefore, the number of service workers who work in the city (but live in the periphery) is In the periphery, the demand for services comes from the working class and the bobos who live there. Their combined income is where L P denotes the unskilled employment level in the periphery. Again we It is easy to see that @(L A P + L A C )=@a 1 > 0; although the rise in house prices associated with an increase in the new economy's productivity may well lead to a reduction in services consumption in the city.
These derivations allow us to summarize the main properties of Regime I: An equilibrium in regime I prevails if a 2 a 1 is larger than a critical threshold, which is itself greater than 1. Other things equal, bobos are willing to pay more to live in the city than cadres, because the former do not have to commute. Therefore, for cadres to dominate in the city, their income must be larger than that of the bobos by a su¢ cient margin.
In regime I, the cost of housing goes up with productivity in the new economy sector.
In regime I, employment of unskilled workers goes up with productivity in the new economy.

Regime II
Let us now turn to Regime II. The indi¤erent social group in residential choice is now the cadres, while the bobos are politically pivotal. The indi¤erence condition for the cadres reads House rental costs are now equal to For this regime to be possible, we need that < 0; i.e.
> 1 + 2 1 + : The utility of the bobos is (1 + ) ln(a 1 R t ) ln p t + : They maximize ln p t + ; or equivalently ( )=(1 + ): Let B ; B be the corresponding amenity level and commuting cost. The corresponding utility of the bobos is, in steady state, equal to (1 + ) ln(a 1 R t ) ln p t + B : For regime II to prevail, this must be larger than their utility from residing in the suburb, which is equal to (1 + ) ln a 1 ln p t : This is equivalent to where 15 We have the following Lemma: This corollary implies that there may be multiple equilibria 16 . Expecting to win the election makes it more valuable for the winning group to locate in the city, as they get an amenity level closer to their preferences. Therefore, that expectation is to some extent self-ful…lling.
Finally, we can compute unskilled employment as in the preceding section: We note that in this regime, house prices are independent of productivity in the new economy. On the other hand, productivity in the new economy has a positive e¤ect on service employment (since dL B C =da 1 > 0 because of demand e¤ects, and dL B P =da 1 > 0 because of the positive spillovers on the periphery of the additional service workers hired by the bobos in the city).
6 Comparing regime II with regime I I now establish a number of results regarding the comparison between the two regimes 17 .
Proposition 1 -Amenities, and therefore commuting costs and the price of services in the city, are larger in regime II. This result is straightforward: As the bobos do not have to commute, they incur a lower cost from increasing amenities. Therefore they vote for a greater amenity level.
Proposition 2 -House prices are larger in regime II if and only if House prices may go up as the bobos take over, because amenities make living in the city more desirable. But, at the same time, the cadres become We can also compare the employment levels of unskilled workers in the two regimes. The preceding formulas highlight that there are three e¤ects: The price of services is higher in the city in the regime where the bobos are politically decisive. This tends to reduce the demand for services and unskilled employment. Essentially, greater commuting costs are similar to a negative productivity shock a¤ecting the service sector.
If the cost of housing (R) is larger in regime II than in regime I, this depresses the demand for services in the city. The converse holds if the cost of housing actually falls in regime II compared to regime I. 18 In regime II, the bobos who live in the suburbs are replaced by cadres.
In the zone where a switch may occur, the latter are richer than the former. The cadres who live in the suburb instead of the city consume more services than the bobos they have replaced. The bobos who live in the city instead of the suburb consume fewer services than the cadres they have replaced. But, because services are more expensive in the city, the former e¤ect is stronger than the latter. On net, therefore, this change in the suburban bourgeois population tends to raise service employment.
Despite those ambiguities, we can get a su¢ cient condition for service employment to be lower in regime II than in regime I:

Proposition 3 -Assume that
A < (1 + ) ln(1 ): and Then at the margin of a transition from regime I to regime II, Therefore, if a transition from regime I to regime II is associated with higher housing costs and if the initial amenity level picked by the cadres in the city is low enough, such a transition is harmful for the employment of uskilled service workers.
7 The rise of the new economy and the transition from regime I to regime II In this section I discuss the e¤ect of an expected bobo takeover on house price dynamics.
Suppose that, due to the progress of the new economy, a 1 rises over time, while a 2 remains constant. Then the preceding analysis implies that at some stage, the composition of the city will change: the economy will shift from regime I to regime II. However, due to multiple equilibria, the date of the transition cannot be predicted. During the period such that a 2 =a 1 2 [z A ; z B ] ; multiple transitions in both directions may even occur. To simplify the analysis, let us plausibly assume that there is a unique transition date T: Therefore, the economy is in regime I before T and in regime II after.
The rental cost of housing keeps going up until date T; and stabilizes thereafter. As for house prices, before date T they evolve according to since R t = a 1t (1 e A ): We can show that house prices go up monotonically in the run-up to the bobo's takeover, provided the transition does not occur too late: then q t is monotonically increasing with time for t T; and constant thereafter.
Condition (9) means that house prices are higher after the transition than before, which, given that a 1 is growing over time, is a weaker condition than for house prices to be higher in regime II than in regime I.
From Proposition 4 we may conclude that growth in the new economy will generate an upward trend in house prices, but that it should stop once the bobo takeover is complete and once they have completed their investments in urban infrastructure. However, as we are going to see, this levelling o¤ of house prices only takes place if the city does not become bunkerized.

The bunkerized equilibrium (regime III)
In this section I characterize an equilibrium in regime III, where only workers and bobos live in the city, the latter being all located there and therefore being a political majority, and cadres are all in the suburb. Such a regime is likely to exist, for the following reason: if workers are initially located in the city, and are numerous enough to be the sole providers of services in that community, then, contrary to regimes I and II, an increase in commuting costs no longer raises the price of services in the city. This will induce city residents to elect the highest possible level of amenities, making it very costly for the cadres to locate in the city ex-ante and commute to work 19 . In such a regime, the city becomes bunkerized, in that no commuting takes place between the city and the periphery.
Let us now characterize this regime. I will limit the analysis to the zone where a regime II equilibrium also exists, i.e. a 1 > a 2 =z B :

Equilibrium determination and properties
First, it must be that workers are indi¤erent between locating in the city and the periphery. We assume (and will check that it holds in equilibrium), that workers do not commute. Therefore, we have from Table 2 that = (1 + ) ln(p t a S ) ln p t : The price of services in the suburbs is still determined by (2). However, the price of services in the city is determined by equilibrium between supply and demand. Total city income is Equilibrium in the service market in the city is such that Rearranging, we get that This de…nes a downward sloping relationship between R and p ; labeled SME. The greater the cost of housing, the lower the city dwellers'purchasing power, and the lower the equilibrium price of services.
It can be checked that Equation (10) de…nes a positive relationship between p and R; representing equilibrium in the housing market (HME). The greater p ; the greater the incentives for workers to locate in the city, and the higher the equilibrium rental cost of housing. As illustrated on Figure   1, the two relationships HME and SME uniquely determine the equilibrium values of R and p : I will label these values R C and p C : An increase in the productivity of the new economy ( Figure 2) shifts SME up and leads to an increase in the price of services and in the cost of housing; part of the rise in the bobos' purchasing power is spent on services, which raises their price and attracts new workers to the city. These workers bid the price of housing up, to the point where they are again indi¤erent between locating in the city and in the periphery. Note that this response stands in contrast to that of regime II, where the price of services was insulated from the bobo's income due to commuting of workers from the suburbs, and the price of housing also did not depend on the bobo's income because it was pinned down by productivity in the old economy, due to the cadres being the marginal city dwellers.
Furthermore, in the bunkerized regime an increase in a 1 has no e¤ect on service employment, contrary to regimes I and II. Service employment in the city is constrained by available space (there are X H 1 housing units left for the workers), and service employment in the suburb is determined by the cadre's income, which is …xed. An increase in the amenity level shifts HME up: workers have a greater incentive to locate to the city, which bids rents up, eventually depressing the demand for, and prices of services. It should be stressed that this should be an expected increase in ; as housing has to be purchased before the utility from amenities is incurred.
What amenity level will the bobos choose? Again, given our timing of events, this choice does not a¤ect q t+1 : While its expectation was already priced in q t ; the current choice of does not a¤ect q t either, since it takes place after the preceding period's housing market. Nor does a¤ect p t ; since the supply of services is frozen by the locational decisions of service workers made at t: Therefore, the bobos will simply maximize and pick the highest possible level of amenities (and therefore of commuting costs). I will denote that level by C ; and the corresponding commuting cost by C : 20

Conditions for a bunkerized equilibrium to exist
The preceding analysis discusses the properties of an equilibrium in regime III, but fails to characterize its conditions for existence. This is done in the following Proposition: Proposition 5 -An equilibrium in regime III exists if and only if the following conditions hold: (i) (1 + ) ln(a 2 R C ) ln p C + C C < (1 + ) ln a 2 ln p: (ii) (1 + ) ln(a 1 R C ) ln p C + C > (1 + ) ln a 1 ln p: (iii) (1 + ) ln(p C a S ) ln p C < (1 + ) ln(pa S ) ln p: (iv) (1 + ) ln(a 2 R C (1 + ba 2 )) ln p C + C < (1 + ) ln a 2 ln p: (

A numerical example
Given that we cannot get a closed form solution for p and R; I compute a numerical solution for the bunkerized equilibrium, checking that all the conditions in Proposition 5 hold. The key variables of interest are reported in Figures 3-5, as a function of a 1 . The range of values for a 1 is such that equilibria in both regimes II and regime III exist -below this range, an equilibrium in regime II does not exist since (8) is violated, and above this range, the simulations indicate that condition (ii) above is violated, meaning that house and service prices become so high that bobos prefer to live in the periphery 21 . The parameter values corresponding to those …gures are X = 1; H 1 = H 2 = 0:7; u = 2; a S = 1; a 2 = 1:5; = 1; ( ) = 4 , and I 21 One can check that an equilibrium, labelled Regime IIIB, with two indi¤erent groups then arises, as not all the bobo population lives in the city. Services prices are so high that the property that bobos are willing to pay more to live in the city than workers no longer holds. Regardless of the mix between workers and bobos in the city, the amenity level will be set at its maximum, since neither bobos nor workers commute.
The conditions that characterize Regime IIIB are brie ‡y discussed in the Appendix.
impose a maximum value of = 5 (which will hence prevail in regime III, along with a very high transportation cost = 625). Figure 3 plots the rental cost of housing as a function of a 1 ; while Figure 4 reports the price of services. As a comparison benchmark, their corresponding values for regime II are plotted too. As proved above, both p and R go up with a 1 : Furthermore, at least in this simulation, both are well above their regime II counterpart for the whole range of values of a 1 : This is relatively intuitive: the very high level of amenities that is voted for in regime III makes it highly desirable to reside in the city, as long as one does not commute; and services are relatively scarcer in regime III because they cannot be imported from the periphery. Figure 5 compares the bobo's utility between the two regimes. We see that for relatively low levels of a 1 ; the bobos are better-o¤ in the bunkerized equilibrium: despite higher land and service prices, they enjoy a greater amenity level. If a 1 is high, however, amenities are no longer su¢ cient to compensate the bobos for the greater prices of services and housing in the bunkerized equilibrium (and for even higher level the bobos are better-o¤ in the periphery and regime III ceases to exist).

"Diversity"
In this section I illustrate how the model may be useful to understand the reason why a city politically dominated by bobos may want to subsidize lower class service workers for residing in the city. Based upon the preceding discussion, we may think of a number of economic mechanisms through which such subsidies may raise the utility of the bobos: 1. If amenities and commuting costs are high, bringing the workers in the city may reduce urban service prices 22 . Intuitively, this e¤ect alone should 22 This is a complementarity in consumption between skilled and unskilled workers; see 26 not be enough to make it rational to subsidize service workers. Absent an externality, taxing oneself to subsidize a good cannot improve welfare.
2. If, contrary to the assumptions made above, the bobos were not numerous enough to capture political power, the presence of non-commuting workers in the city might help them build a coalition in favor of high amenities/high commuting costs.
3. A subsidy for workers to reside in the city may force the equilibrium to be in regime III, that is, it could eliminate an equilibrium in regime II.
This may be pro…table for the bobos whenever the bunkerized equilibrium delivers a higher utility to them.
4. By triggering a shift from a low amenity to a high amenity equilibrium, such subsidies may raise house prices, thus delivering capital gains to the incumbent generation of old city dwellers -indeed, we have seen that house prices are higher in regime III than in regime II. Interestingly, this e¤ect a¤ects all incumbent residents, including the cadres.
The mechanism described in point 3 can easily be analyzed within the context of the model, provided we assume that there is some way for the bobo caste as a whole to commit over such a tax policy. Let us assume that any young working class person is paid a subsidy s to reside in the city, and that this subsidy is …nanced by a tax levied on the bourgeois young. Let us assume that a 1 is high enough to rule out a regime I equilibrium. For a regime II equilibrium to exist, it must be that the young are not better-o¤ living in the city, i.e. 23 (1 + ) ln(p B a S R B + s(1 + r)) ln p B + B < u: This de…nes a maximum subsidy level beyond which regime II ceases to exist, which, given (2) and (3), is equal to 1+ e (1+ ) 2 ) 1 + r : If s > s min the economy cannot be in regime II, and a regime III equilibrium is determined by the HME and SME conditions, the former being modi…ed to take into account the subsidy: 24 (1 + ) ln(p C a S + (1 + r)s R C ) + C ln p C = u: Clearly, an increase in s shifts HME up, raising housing costs and reducing service prices. This will harm bobos 25 . However, they may bene…t from a subsidy slightly above s min if it is believed that the economy would be in regime II absent such a subsidy. For this to be the case it must be that their utility is higher in regime III under s = s min than in regime II, that is where min = s min is the tax rate associated with the minimum subsidy, given the city's budget constraint.
I have checked that condition (13) holds for the parameter values used in the simulations of Section 8.3, for a 1 4:45: This is only slightly below the value of a 1 for which the two equilibria yield the same utility to bobos absent a subsidy (see Figure 5), because the subsidy level which eliminates regime II turns out to be relatively small. 24 The SME condition is unchanged as the transfer from skilled workers to unskilled one has no e¤ect on the demand for services, given homothetic preferences. 25 Their disposable income falls because of greater taxes and higher house prices. As they spend a constant income share on each good, they must consume less of the generic good. In equilibrium, they consume the same amount of services, while the amenity level is unchanged and equal to its maximum. On net, therefore, their utility must fall.
The subsidy allows the bobos to change the sociological make-up of the city, which in turn allows them to implement a high level of amenities and commuting costs, while the pool of service workers who are located in the city because of the subsidy prevents service prices from becoming prohibitively high in response to bunkerization.
The model also predicts that an incumbent generation of old may gain from forcing the economy to be in regime III, using a subsidy to service workers, because in such a regime they sell their homes at a higher price than in regime II. 26

Evidence from French cities
In this section I provide some supportive evidence for the model. I use data for 49 of the 50 largest French urban areas 27 , which allow to study the evolution of urban transportation amenities, the sectoral composition of employment, house prices, the fraction of the population in subsidized housing, and the political orientation of the ruling municipal council 28 . I focus on the 2008-2012 period, which follows the 2008 municipal elections.
The preceding analysis shows that investment in urban amenities tends to be larger, the greater the political power of workers in the new economy, i.e. the greater the initial fraction of those workers. Furthermore, bunkerization is associated with positive comovements between amenities, subsidized housing, service employment and house prices; and to the extent that bunkerization is more likely to arise under bobo incumbency, in that regime we also expect to observe a greater than average initial fraction of employment in 26 My own computations show that this holds even in the case where the subsidy is …nanced by a tax on the old. 27 The city of Annemasse was dropped from the sample, as it is generally considered as part of the Geneva urban area.
28 See Appendix 2 for data sources.
29 the new economy. Finally, conventional wisdom suggests that bobo power is associated with a left-wing municipality, although actual outcomes depend on the nature of electoral competition: If platform convergence arises as in Downsian competition, right-wing municipalities will also pursue those policies.
In order to test those predictions, I split my sample into three groups, using an aggregate index of transportation amenities. I have data for two types of amenities: tramways ("tram") and public self-service rental bicycles ("vélib"). Both types of investment were explicitly associated with the goal of reducing the scope of car travel in urban areas. For example the Paris tramway is a substitute for a former bus line (the "petite ceinture"), but was built in order to reduce the number of entry points for cars into downtown Paris 29 . Similarly vélibs are associated with a massive reconversion of parking space into vélib delivery spots, and of car transit lanes into bicycle lanes. Overall, while these policies introduce more "ecological" means of transportation, it is plausible to assume that they tend to have adverse e¤ects on commuting costs. See, "Tramway à Paris: Delanoë est-il l'ennemi de la voiture?", L'Express, december 15 2012, http://www.lexpress.fr/actualite/politique/tramway-a-paris-delanoe-est-il-lennemi-de-la-voiture_1199483.html 30 Because many cities share the same values for AM EN ( ); however, and because it does not make sense to assign cities with the same value to di¤erent groups, the resulting each group is exogenous, due to the relatively small number of observations, we could loosely think of group I being in regime III, group II in regime II, and group III in regime I.   The numbers in Table I are overall supportive of the model, although not all di¤erences are statistically signi…cant. Cities that invested more in amenities after the 2008 elections tend to be those with a greater fraction of groups turn out to have di¤erent sizes. In particular, the bottom group is reduced to all cities for whom AM EN ( ) is equal to zero, while a large set of cities with equal scores equal to the threshold for the top third has to be assigned to group II, otherwise that group would only have three cities. As a result, group I has 11 cities. A two-group decomposition has also been tried, with similar results. 31 Only three cities change categories when comparing the assignment for = 9 to = 0:1 : Brest, Le Mans and Reims which all move from group II to group I. workers in the new economy, either in the workforce at large or among highly skilled workers, and experienced stronger growth in house prices thereafter.
They are also more likely to have raised the fraction of households in social housing ("HLM") and to have more service employment, in accordance with the above discussion on bunkerization. However, taken individually, these latter di¤erences are not statistically signi…cant. Finally, a large increase in the amenity level does not seem to be especially related to a left-wing municipality. This is consistent with the Downsian prediction of platform convergence. Indeed, the 2014 campaign of the right-wing contender for the Paris municipality, Nathalie Kosciusko-Morizet, was fully supportive of the policies that are generally associated with the Bobo establishment 32 .

Conclusion
This paper has shown that one can explain some recent trends in urban sociology and policies without referring to an evolution of the preferences of the decisive voters in the city, regarding urban amenities, transportation infrastructure, and housing subsidies for the lower class. Rather, these trends can be explained by productivity growth in the new economy goods relative to other sectors, along with the speci…city of the production process for those goods. Of course, as documented by the original book by Brooks, preferences may matter in other dimensions (such as consumption of organic food or speci…c details of home interior decoration) that are not treated by the model analyzed here. It is possible, though, that these aspects of the new urban elite's lifestyle also are a consequence of their economic characteristics, especially if one allows for endogenous preferences. This is a productive avenue for further research. 32 See "The harpist or the heiress? Image is all in the race to be …rst woman mayor of Paris", The Guardian, March 2 2014, in which it is stated that "[Nathalie Kosciusko-Morizet] was photographed using a free Vélib'bicycle(...)."

APPENDIX I: Proofs
Ruling out a con…guration where all service workers are in the city -We prove that a su¢ cient condition for ruling out such an outcome is 33 u ln a S < min(ln a 1 ; ln a 2 ): To see this, assume such a con…guration holds. Then from Table 2 we know that workers in the city provide services to both the city and the suburb, i.e.
Cleraly, from these conditions, we must have that p > p : In such an equilibrium it must be that the workers get less than u in the suburb, i.e.
u > (1 + ) ln(pa S ) ln p : From (15) it follows that (1 + ) ln pa S R pa S > ln p p + : 33 In the bunkerized equilibrium that is characterized below, cadres cannot overbid workers for living in the city, because of the very high commuting they would have to incur.
In an equilibrium where all workers are located in the city, however, they must also be commuting to the periphery, and it is enough for cadres to be richer than them to be able to underbid them.
Also note that the condition is more likely to be satis…ed, the more productive the unskilled workers. Because services are nontraded and the supply of service workers is in…nitely elastic, an increase in a S reduces the price of services more than proportionally, making it easier for the two other classes to be richer. On the other hand, the skilled workers'income always goes up with their productivity, as they produce a traded good.
Given (1), we also need that either the cadres or the bobos are better-o¤ in the suburb that in the city. Using Table 2, we see that bobos prefer to be in the city provided (1 + ) ln(a 1 R) ln p + > (1 + ) ln a 1 ln p: For this to be violated, it must be that Since > 0; it must be that a 1 pa S : Using the same steps, we can show that for the cadres not to strictly prefer the city, we need that a 2 pa S : From (17) we have that ln p < u (1 + ) ln a S : This inequality implies that if (14) holds, both (18) and (19) are violated.
It must then be that all cadres and all bobos live in the city, which contradicts assumption (1).
Ruling out a con…guration where all city residents are service workers -If that is the case, clearly some city residents must commute to supply their services to the suburb, since total city demand for services is lower than total city supply. Consequently, we must have that (1 + ) ln(pa S R) ln p + = u: At the same time, city residents cannot get strictly more than u by supplying services locally: (1 + ) ln(p a S R) ln p + u: From these two conditions it must clearly be that case that p < p: Consequently, suburban workers do not commute to the city. Then services in the city are supplied locally, implying (1 + ) ln(p a S R) ln p + = u: Since the LHS is an increasing function of p ; and since p > p ; it follows that (1 + ) ln(pa S R) ln p + > u = (1 + ) ln(pa S ) ln p: Furthermore, bobos cannot be strictly better-o¤ in the city: (1 + ) ln(a 1 R) ln p + < (1 + ) ln a 1 ln p: Since p < p; it must then be that (1 + ) ln(a 1 R) ln p + < (1 + ) ln a 1 ln p: For (20) and (21) to simultaneously hold, it must be that a 1 < pa S ; or equivalently ln a 1 < u ln a S : But this contradicts (14).
Proof of Lemma 1 -The optimization problem of the pivotal voter in each regime implies that ( ; ) is minimum in regime I, while ( ; ) is minimum in regime II.
Proof of Proposition 1 -in regime II, the bobos set and so as to maximize ( )=(1 + ): In regime I, the cadres maximize 1+2 1+ ( ): Proof of Proposition 2 -Straightforward from the expression of house prices and the fact that B > A > A > B : Proof of Proposition 3 -We have that, using the derivations in the preceding sections, Clearly, a 2 > a 1 since both regimes must exist for the transition to occur. Since one also has B > A ; all terms above are negative under the assumptions of the Proposition. QED.
Proof of Proposition 4 -Clearly, for t T; we have that q t = R B =r = a 2 (1 e B )=r: Furthermore, q T 1 = a 1T 1 (1 e A ) 1+r + R B r(1+r) : This is clearly lower than R B =r if (9) holds. Furthermore, we have that q t+1 q t = q t+1 r a 1t (1 e A ) 1 + r : We now show that this quantity is positive. Note that for t T 2 This proves that q t+1 > q t : QED.
Proof of Proposition 5 -For an equilibrium in regime III to exist, the the cadres must be better-o¤ in the periphery. This is equivalent to (i).
Second, the bobos must be better-o¤ in the city, which is equivalent to (ii).
Third, the workers in the periphery should not have an incentive to commute to the city, implying that (iii) must hold. Fourth, the cadres should not be better-o¤ locating and working in the city, i.e. (iv) should hold.
Finally, the bobos should not be better-o¤ by deviating from the equilibrium value of and picking an ex-post level of amenities that would induce the workers to commute to the city. The price that would induce them to do so is given by the RHS of (3), which we now denote by p AB ( ) 34 : If this is lower than the autarky price of services obtained from (10) and (11), then suburban workers commute to the city. This happens i¤ p AB ( ) < p ; or equivalently < (1 + )(ln p C ln p) = max : In the zone where < max ; the bobo's utility is given by (1 + ) ln(a 1 R C ) ln p AB ( ) + : 35 Therefore they maximize ( )=(1 + ); as in regime II, and pick = min( B ; 1 ( max )) = 0 : The bobos will vote for this outcome if and only if it delivers a greater utility than the maximum possible value of , that is (1 + ) ln(a 1 R C ) ln p C + C < (1 + ) ln(a 1 R C ) ln p AB ( ( 0 )) + 0 ; or equivalently, denoting by 0 = ( 0 ); C 0 < (ln p C ln p 0 1 + ): We note that if 0 = max ; the RHS is equal to zero. The LHS cannot be negative, as C is the maximum value of : Therefore, this inequality is 34 The subscript AB refers to the fact that this relationship between p and must hold in both regimes I and II. 35 Choosing an amenity level 0 6 = C ex-post has no e¤ect on R; since the resale value of the home depends on expected future amenities, while the purchase price of the home depends on expected curren amenities, given by C : 39 violated for 0 = max : It may only hold for 0 = B ; which is equivalent to (v) being violated. If that is the case, then ex-post the bobos would pick an amenity level such that workers commute from the suburbs to the city to o¤er their services. But we can then check that it cannot be rational for workers to locate to the city ex-ante. The reason is as follows: Service prices and amenity levels are the same as in regime II. But in regime II workers prefer to reside in the suburbs, i.e. would get a utility level lower than u should they live in the city. For them to locate in the city, it must therefore be that rents are lower than in regime II, that is, R t < R B : However, we know that under regime II, cadres are indi¤erent between the two areas. For them to now strictly prefer the periphery, it must be that R t > R B ; a contradiction.
Consequently, it must be that (v) holds for regime III to exist.
Conversely, if (i)-(v) hold, then clearly, the otucome computed in the preceding subsection satis…es all the equilibrium conditions. QED.
Properties of regime IIIB -In regime IIIB, both workers and bobos are located both in the city and periphery. The di¤erence between regime III is two-fold. First, condition (ii) is replaced by an equality, stating that bobos are equally better-o¤ in the city and in the periphery: (1 + ) ln(a 1 R C ) ln p C + C = (1 + ) ln a 1 ln p: Second, the service market equilibrium condition is replaced by an inequality: the demand for services in the city has to be lower than if all bobos were located in the city, implying that R t a 1 H 1 X a S p t 1 H 1 X : Consequently, the SME schedule has to be replaced by Equation (22), which is again downward sloping, while the HME schedule is unchanged.
Given the equilibrium values of R and p ; the number of bobos residing in the city,H 1 ; is determined by the city equilibrium in the service market, that isH 1 = R + p a S = a 1 + p a S = X:

APPENDIX 2 -Data sources and group assignment
The data sources used were as follows: For house prices 1998-2015 per urban areas, the professional website This was checked with independent sources: town hall web sites, press articles, and the following web site: HME SME Figure