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A 3-region new economic geography model in discrete time Pasquale Commendatore Ingrid Kubin Iryna Sushko 1

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NEG - Central question Long-run spatial distribution of industry 2 equally distributed agglomerated in one region unevenly distributed

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NEG – Basic structure Given amount of productive factors Distributed across two identical regions Allowed to move freely between regions according to factor rewards (dynamic law) Output sold in home region as well as in other regions (trade cost) Decisive for location decision: Cost for commodity trade between regions 3

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Where do dynamic processes play a role? -Goods and labour markets: istantaneous equilibrium -Shipping of goods: istantaneous -Factor mobility: gradual over time, adaptive process -Analytical core: One-dimensional differential equation 4

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Continuous Vs discrete time 2-R NEG in continuous time (1-D bimodal flow): Multiple equilibria; catastrophic agglomeration; hysteresis; regular local stability properties which holds within well-defined basins of attraction 2-R NEG in discrete time (1-D bimodal map): Multiple equilibria; catastrophic agglomeration; hysteresis; multiple attractors of any periodicity; chaotic dynamics; agglomeration via volatility 5

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Continuous Vs discrete time NEG models in discrete time: CP (Currie&Kubin; JEBO, 2006) [CK, 2006] FE (Commendatore, Currie&Kubin; SEA, 2008) [CCK, 2008] FC (Commendatore, Currie&Kubin; NDPLS, 2007) [CCK, 2007] FE 3-R (Commendatore&Kubin, 2012) – Local stability analysis FE 3-R (Commendatore, Kubin & Sushko, current) – Global stability analysis 6

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Footloose Entrepreneur (FE) (Forslid & Ottaviano, 2003, JEG) Factors of production - unskilled workers (immobile, variable costs) - entrepreneurs (mobile, fixed cost) Agglomeration and dispersion forces are all at work Self-reinforcing agglomeration processes preserved Entrepreneurs migrate in response to differences in real profits 7

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3-R Footloose Entrepreneur model 3 symmetric Regions (1, 2, 3) 2 Sectors (agriculture, manufacturing) 2 Factors of production (unskilled workers, entrepreneurs) 8

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Manufacturing sector Differentiated goods Produced with: 1 entrepreneur units of unskilled labour Decreasing average costs Monopolistic competition: Price: mark-up over marginal cost Iceberg transport cost, T Agricultural sector Undifferentiated good Produced with: 1 unit of unskilled labour Constant average costs Perfect competition MR = MC No transport cost (perfect trade freeness) 9

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10 Trade freeness 3 equidistant regions 1 2 3

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Number of firms = number of entrepreneurs N number of firms located in region r: Share of entrepreneurs (firms) located in region r: 11

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Istantaneous Short-run equilibrium in region r 12 Operating profit: Price index: σ : CES – taste for variety µ : share of expenditure allocated to manufacturing

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Real profit in region r 13 Operating profit per variety in region r Price index in region r

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14 Central dynamic equation: non-linear, two- dimensional in 14 Replicator dynamics but bounduary conditions

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15 Central dynamic equation: non-linear, two- dimensional in

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16 0 0.5 1 1 Core-Periphery equilibria

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17 0 0.5 1 1 3-Region symmetric equilibrium

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18 0 0.5 1 1 3-Region asymmetric equilibria

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19 0 0.5 1 1 2-Region symmetric equilibria

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20 0 0.5 1 1

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3-Region Tomahawk diagrams 21

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22 Local stability results

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Global dynamics preliminary results 23

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Global dynamics preliminary results 24

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Global dynamics preliminary results 25

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Final remarks 2-Dimensional nonlinear map: Multiple equilibria; catastrophic agglomeration; hysteresis; 2-R and 3-R stationary equilibria, possible 2-R asymmetric stable equilibria periodic and quasi-periodic multiple attractors; chaotic dynamics; strange attractors, complex basins of attraction Simple extensions: slight increase in the number of regions; asymmetric trade costs Less simple extensions: larger increase in the number of regions, endogenous trasport costs, network structure 26

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