Abstract
This paper constructs a model of endogenous location of entrepreneurs with preference heterogeneity between individuals. Two main results are found. First, agglomeration and partial dispersion can be simultaneously stable but preference heterogeneity reduces the possibility of multiple equilibria. Secondly, measuring individual welfare in terms of equivalent income we show that in the case of agglomeration, the worst-off workers would prefer a dispersed equilibrium.
Notes
Murata (2003) and Tabuchi and Thisse (2002) integrate taste heterogeneity by assuming that mobile people are attached to their regions (for non-market attributes such as local or social amenities: climate, culture, family etc.). Then, by using a probabilistic migration dynamic borrowed from discrete choice theory, these authors show that a gradual or partial agglomeration arises from the dispersion of activities and then gives rise to a gradual re-dispersion when trade is liberalized. Murata (2007), assuming that tastes heterogeneity impacts on returns to scale, shows that an increase in heterogeneity renders the market more segmented in terms of product but more unified in terms of space. Lastly Zeng (2008) assumes that there are two kinds of mobile workers that differ in their preferences on manufactured goods, which leads them to form geographically separated clubs (the market yields a persistent residential segregation).
For a survey of the NEG see Candau (2008).
However by introducing land rent and urban costs, Candau (2009) shows that a unanimous preference for dispersion emerges.
The upper-tier utility a logarithmic quasi-linear function rather than a Cobb–Douglas function in the former and a quadratic quasi-linear function in the latter.
In the core, firms find bigger outlets (backward linkage) but also intermediate inputs at a lower price (forward linkage).
Having zero profits in the long run is a standard assumption in the Dixit–Stiglitz framework of monopolistic competition, however Picard et al. (2004) relax this condition of free entry and show that standard results hold, they also shows that it is imperfect competition (existence of a positive mark-up) more than increasing returns that matters for the formation of agglomeration in economic geography.
Parameters: μ h = 0.6, λ = 1, ρ = 4. The parameter β is absent from Ω (see end of section).
In the following we also use the phrase “partial agglomeration” to describe this equilibrium.
For high trade costs the market crowding effect is greater than the market access effect, therefore northern relative nominal wage decreases with h. A proof of this result is available on request.
The derivative has the same sign as \(\left( \phi ^{2}-1\right) \left( \rho -\mu _{h}\right) .\)
Indeed one computes that \(\frac{\partial \sigma ^{s}}{\partial \phi }\) has the same sign as
$$ \phi ^{\frac{\mu _{h}}{1-\rho }-1}\left( 1+\frac{\mu _{h}}{1-\rho }\right) +\phi ^{\frac{\mu _{h}}{1-\rho }+1}\left( 1-\frac{\mu _{h}}{1-\rho }\right) -2, $$which is positive for ϕ < 1 and equal to zero for ϕ = 1.
Configuration (1) does not occur because the left-hand expression in Eq. 15 tends to zero from above when ϕ→1. Observe that when ϕ→1 one has Ω > 1 for all h and when ϕ = 1 one has Ω ≡ 1.
In the word of Baldwin et al. (2003) catastrophic agglomeration is one of “the most celebrated feature” of the new economic geography. Such a result can however be view as a theoretical curiosity by many economists not specialized in the field and thus we build in Appendix a model where agglomeration is not catastrophic but gradual (we show that all our results hold). One can notice that gradual agglomeration can also be obtained by introducing migration costs (as in Murata 2003) or inter sectoral mobility of workers as in Puga (1999). To fully understand why catastrophic agglomeration occurs in the NEG see Pflüger and Südekum (2008a) and to find empirical tests of this radical change and of multiple equilibria see Davis and Weinstein (2002).
Parameters are again μ h = 0.6, λ = 1, ρ = 4.
Since we analyse the welfare of each individual under different spatial equilibria (there is no comparison between individuals), we can drop this term without loss of generality.
Parameters: β = 1, λ = 1, μ h = 0.6, ρ = 4, L = 2.4, v = 3/4.
Parameters: β = 1, λ = 1, μ h = 0.6, ρ = 4, L = 2.4, v = 3/4.
This liberal approach to social justice has been famously defended by Rawls (1971) and Dworkin (2000).
It corresponds to a particular case of money-metric utility function (Samuelson 1974).
See, for instance, Charlot et al. (2006).
Parameters: μ h = 0.6, ρ = 3, σ = 0.99, λ = 1 and L = 2.4. Stable equilibria are represented by black rounds.
Note that when λ = 1.05, an allocation of activities in proportion to the worker populations would have h = .488. On the basis of simulations we conjecture that for λ = 1 (equal populations of workers in the two regions), the market equilibrium always displays too much agglomeration from the point of view of the worst-off workers.
The result in term of welfare may be robust to the introduction of many industries, but location choices would certainly be altered. Zeng (2008) in particular introduces two kinds of sectors and shows that trade liberalization leads to an agglomeration of each sector in a different region. By using an utilitarian social welfare function, Zeng concludes with the literature that full agglomeration is the better outcome. Taking into account the situation of the worst-off as we have done here would certainly change the conclusion.
The results in terms of welfare may be robust to the introduction of many industries, but location choices would certainly be altered. Zeng (2008) in particular introduces two kinds of sectors and shows that trade liberalization leads to an agglomeration of each sector in a different region. By using an utilitarian social welfare Zeng concludes with the literature that full agglomeration is the better outcome. Taking into account the situation of the worst-off as we have done here would certainly change the conclusion.
Parameters: μ h = 0.3, ρ = 6, f = 1 and L = 1.
Parameters: μ h = 0.5, ρ = 3, f = 0.5, L = 2.6 and β = 1.
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Appendix: Spatial equilibria and welfare with a quasi-linear demand
Appendix: Spatial equilibria and welfare with a quasi-linear demand
Ottaviano et al. (2002) and Pflüger (2004) propose models without income effect, indeed in the former the upper-tier utility is a quadratic quasi-linear function while in the latter the upper-tier utility is a logarithmic quasi-linear function. We propose here to study this last function with the same taste heterogeneity as in the text:
Then we get:
The supply side is not modified (q = (ρ − 1)fw/vw A ) thus we get:
Migration is now driven by the following equation:
In order to keep the analysis as simple as possible, we assume that L = L* (i.e. λ = 1). Sustain points are given by:
Then β has the same impact on sustain points as σ, an increase in it increases ϕ s and reduces ϕ s ∗ .
However a difference exists between these two kinds of taste heterogeneity, indeed a decrease in σ (compare Fig.Footnote 28 6a, c) generates an upward translation of the relative real wage, which makes the symmetric equilibrium unstable (see Fig. 6b), while a decrease in β (with σ = 1) makes the dispersed equilibrium stable for a wider range of trade costs (see Fig. 6d).
In order to perform welfare analysis based on equivalent income on the Pfluger model with taste heterogeneity, we plot Fig. 7.
When trade costs are high or low, the results found are very similar to those obtained in the text. Indeed in Fig. 7,Footnote 29 we can observe that agglomeration and partial dispersion are detrimental to southern immobile workers in term of equivalent income in the case of a northern agglomeration. When the agglomerated equilibrium in the South is chosen, the poorest people are located in the North and there is over agglomeration in the South from their point of view. Having said that a new result is found for intermediate trade freeness: indeed in that case the partial agglomeration in the region where individuals have the weaker preference for the industrial goods is the best stable outcome for the worst off. However dispersion is still the unattainable (i.e., unstable) optimal equilibrium in the light of egalitarian principles.