International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Introduction Objectives / key terms Zipf's Law Gravity equation Cumulative causation Agglomeration Multiple equilibria Stability / optimality Simulations Location Paul Krugman (1953 - ) International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Zipf's Law and the gravity equation 20 Delhi Bombay ln(size) 15 Calcutta 10 ln( populationi ) 16.94 1.048 ln( rank i ); 5 ( 528.4 ) ( 138.4 ) R 2 0.992 0 0 1 2 3 ln(rank) 4 5 6 International Trade & the World Economy; Charles van Marrewijk Zipf's Law and the gravity equation -4 ln(export)-1.033*ln(GDP) 5 Czech R. Austria Holland -6 10 Switz. Belgium -8 Japan -10 ln(distance) ln( exporti ) 0.281 1.033 ln( GDPi ) 0.869 ln( distancei ) ( 0.40) R 2 0.926 ( 34.86) ( 12.77 ) International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk T e f Farms in 1 Direction of (goods and services flows) d Spending on m 1-m manufactures Farms in 2 Direction of money flows Income (farm labor) N2 manufacturing firms N2 varieties (elasticity ) internal returns to scale monopolistic competition Spending on food b Farm workers in 2 Spending (goods) m Spending on manufactures Manufacturing workers in 2 Income Spending (goods) 1-m c N1 manufacturing firms N1 varieties (elasticity ) internal returns to scale monopolistic competition Spending on food (farm labor) a Mobility (i) (labor) Manufacturing workers in 1 Income Farm workers in 1 Consumers in 2 g (labor) Consumers in 1 Income The structure of the model International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Multiple locations and equilibrium Total number of laborers; L (1-) Laborers in the food sector (1-)L 1 Laborers in the food sector in region 1; 1(1-)L Note: 1 + 2 = 1 2 Laborers in the food sector in region 2; 2(1-)L Laborers in the manufacturing sector; L 1 Laborers in the manufacturing sector in region 1; 1L Note: 1 + 2 = 1 2 Laborers in the manufacturing sector in region 2; 2L Mobility International Trade & the World Economy; Charles van Marrewijk Multiple locations and equilibrium Short-run equilibrium; given the distribution of manufacturing labour Price index equation 1 1 1 P1 1W1 2T W2 locally imported produced Income equation I1 1W1 1 (1 ) manufacturing income Wage equation (from demand = supply in manufactures sector 1 W1 I1P1 I 2T 1 /(1 ) food income 1 1 1/ P2 International Trade & the World Economy; Charles van Marrewijk Multiple locations and equilibrium a. spreading 1 c. agglomerate in region 2 b. agglomerate in region 1 1 1 0 0 0.5 0 region 1 region 2 Three examples region 1 region 2 region 1 region 2 International Trade & the World Economy; Charles van Marrewijk Multiple locations and equilibrium Manufacturing labour force adjustment d1 1 change labor in 1 ( w1 w ); where w 1w1 2 w2 adj. wage speed difference average real wage Table 14.2 When is a long-run equilibrium reached? Possibility 1 Possibility 2 Possibility 3 If the real wage for All manufacturing workers All manufacturing workers manufacturing workers in are located in region 1 are located in region 2 region 1 is the same as the (agglomeration in region 1) (agglomeration in region 2) real wage for manufacturing workers in region 2. International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Chapter 14 tool: computer simulations relative real wage (w1/w2) 1.03 E F C 1 D B A 0.97 0 0.5 share of manufacturing workers in region 1 (lambda1) 1 International Trade & the World Economy; Charles van Marrewijk Chapter 14 tool: computer simulations relative real wage (w1/w2) 1.1 T = 2.1 T = 1.3 T = 1.7 1 T = 1.7 0.9 T = 1.3 0.0 T = 2.1 0.5 share of manufacturing workers in region 1 (lambda1) 1.0 International Trade & the World Economy; Charles van Marrewijk Chapter 14 tool: computer simulations S1 1 1 B 0.5 0 1 S0 Transport costs T Sustain points Stable equilibria Break point Unstable equilibria Basin of attraction for spreading equilibrium Basin of attraction for agglomeration in region 1 Basin of attraction for agglomeration in region 2 International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Welfare Welfare 1 0.98 0.96 0.94 0.98-1 0.96-0.98 0.92 0.94-0.96 0.92-0.94 0.9-0.92 0.9 0.88-0.9 0.833 3 2.5 2.75 transport cost T 2.25 2 1.75 0.433 1.5 1.25 1 0.88 0.033 lambda 1 International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Application: predicting the location of European cities International Trade & the World Economy; Charles van Marrewijk CHAPTER 14; GEOGRAPHICAL ECONOMICS Introduction Zipf's Law and the gravity equation The structure of the model Multiple locations and equilibrium Chapter 14 tool: computer simulations Welfare Application: predicting the location of European cities Conclusions International Trade & the World Economy; Charles van Marrewijk Conclusions Combining various international economic theories with factor mobility provides a simple theory of location and agglomeration. Distinction short-run equilibrium (given distribution of the manufacturing labour force) and long-run equilibrium (endogenously determined by equality of real wages). Distinction stable equilibrium and unstable equilibrium. Using computer simulations: • high transport costs lead to spreading of economic activity • low transport costs lead to agglomeration of economic activity • intermediate transport costs lead to multiple long-run equilibria Extensions of the basic model can explain empirical regularities, such as Zipf’s Law and the Gravity Equation.
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