ECONOMIES OF AGGLOMERATION

1. ECONOMIES OF AGGLOMERATION

2. ECONOMIES OF AGGLOMERATION • Density generates costs • Higher cost of land • Greater congestion, higher commuting and transport costs • Population and economic activity are ever more concentrated in cities • There must be offsetting benefits • Higher productivity for firms • Higher wages for workers • Are these advantages due to agglomeration economies? • What are their scale and scope and causes?

3. Why is it profitable for firms to concentrate employment? • Plant-level economies of scale • Plants produce more efficiently at a larger scale • Agglomeration economies • Plants produce more efficiently when close to other plants • Urbanization economies • when close to other plants in general • Localization economies • when close to other plants in the same industry

4. MICRO-FOUNDATIONS OF AGGLOMERATION ECONOMIES • Sharing. • Matching. • Learning.

5. 1. SHARING • Sharing indivisible facilities • Simplest argument to justify the existence of a city • Example: ice hockey rink • Expensive facility with substantial fixed costs • Few individuals would hold a rink for themselves • An ice hockey rink is a an indivisible facility that can be shared by many users • Factory towns

6. Sharing the gains form the wider variety of input suppliers that • can be sustained by a larger final goods industry • C. Sharing the gains from the narrower specialisation that can be sustained with larger production • Example: Dresses and Buttons • Some competing firms locate close to one another to share a firm that supplies an intermediate input (something one firm produces that a second firm uses as an input in its production process) • Buttons produced by one firm are used by a dressmaking firm

7. Production of high-fashion dresses • Demand for dresses subject to the whims of fashion • dressmaking firms must be small and nimble • (ready to respond quickly to changes in fashion) • Varying demand for dresses causes varying demands for intermediate inputs • (e.g., buttons) • Demand for buttons changes from month to month • Important → not in the quantity demanded, but in the type of buttons • demanded • (e.g., one month square blue buttons with a smooth finish and the next month • round pink buttons with a rough finish) • Production of dresses is subject to constant returns to scale

8. Production of buttons • Subject to economies of scale. Use of indivisible inputs and specialized • labour → Cost per button decreases as the quantity increases • Scale economies large relative to button demand of individual dressmaker • Face time. • A button for a high-fashion dress is not a standardized input. • Requires interaction between dressmaker and button-maker • Dressmaker must be located close to the button-maker • Modification cost. • The dressmaker may incur a cost to modify the button to make • a perfect match (e.g., to shave the edges of a square button • to make it a hexagon)

9. Average cost of buttons from the perspective of the dressmaker • Point a → Highcost for an isolated dressmaker • Two reasons: - Low production of buttons • - Button-maker produces only one type of button

10. Point f → Low cost for the each dressmaker in a cluster Two reasons: - Sufficient demand for buttons to exploit economies of scale - Larger demand for buttons allow specialization of button-makers

11. Other example: • High-technology firms • - Rapidly changing demand → Small innovative firms • - Share suppliers of intermediate inputs (electronic components) • - Not standardized inputs → Face time

12. Sharing risk: labour pooling • Firms are subject to demand shocks • In each time period the demand for some firms grows and the demand for some other firms decreases • Unsuccessful firms will be firing workers at the same time that successful firms are hiring them • An agglomeration of firms facilitates the transfer of workers from unsuccessful firms to successful ones • The process occurs at the level of the firm, not the industry

13. A simple model • The total demand at the industry level is constant, but the demand for each firm varies from year to year • For each firm there are two possibilities equally likely: • High demand • Low demand

14. Isolated firm • A firm can be isolated • The isolated firm doesn’t face any competition for labour within its town • Labour supply is perfectly inelastic, fixed at 12 workers High demand for the product of the firm ↓ High demand for labour Equilibrium at point b → wage= $16 Low demand for the product of the firm ↓ Low demand for labour Equilibrium at point h → wage= $4

15. Firm in agglomeration • Firms in agglomeration face competition for labour (labour supply perfectly elastic, horizontal line) • For every successful firm hiring workers, there is an unsuccessful firm firing them • Total demand for labour in the agglomeration is constant A firm can hire as many workers as it wants at the market wage High demand for labour ↓ Firm hires 21 workers (point d) Low demand for labour ↓ Firm hires only 3 workers (point j)

16. Spatial equilibrium • Wage uncertain at the isolated site • high demand w=$16, low demand w=$4 • The two outcomes are equally likely: Expected wage (isolated firm) = 0.5 · $16 + 0.5· $4 = $10 • To make workers indifferent between isolated site and agglomeration → w(agglomeration) = $10

17. Firm gains from agglomeration • Expected profits will be higher in the agglomeration • Let’s suppose a firm moves from isolated site to agglomeration and then experiences one year of high demand followed by a year of low demand • Good news when demand is high (w=$10 instead of w=$16, and can hire 21 workers instead of 12 workers) Higher profit • Bad news when demand is low (w= $10 instead of w=$4) Lower profit

18. Which is larger, the good news or the bad news? • Good news dominate because a firm in the agglomeration responds to changes in the demand for its product • Expected profit in agglomeration > Expected profit in isolated site (0.5 · adf) + (0.5· gjf) > (0.5 · abc) + (0.5 + ghi) (0.5 · $147) + (0.5 · $3) > (0.5 · $48) + (0.5 + $48) $75 > $48

19. 2. MATCHING. • Improving the quality of matches between employers and employees • Usual assumption → workers and firms are matched perfectly • Each firm can hire workers with the skills the firm requires • In real world workers and firms are not always perfectly matched • Mismatches require costly worker training • A large city can improve the matching of workers and firms in the real world

20. A simple model • Assumptions • Each worker has a unique skill described by a position or “address” on a circle with a one-unit circumference • There are 4 workers and skills evenly spaced on • the circle • The address of a worker is the distance between her • skill position and the “north pole” of the circle • Each firm enters the market by picking a product to • produce and an associated skill requirement. • S=1/8 S=5/8 • Training costs. Workers incurs the cost associated to • mismatch

21. Competition for workers. • Each firm offers a wage to any worker who meets its • skill requirement • Each worker accepts the offer with the highest net wage • net wage = wage offered by the firm - training costs • Each firm will hire two workers

22. Equilibrium • Each firm is the single employer in the skill interval surrounding its skill requirement • Equilibrium with 4 workers (skill types) and 2 firms • Equilibrium mismatch is 1/8 (workers at 0 and 2/8 work in firm at 1/8, so each worker has a skills gap of 1/8) Each firm pays a gross wage equal to the value of output produced by a perfectly matched worker. Net wage = Gross wage – Skills gap·Unit training cost Net wage = $12 – 1/8 · $24 = $9

23. Introducing agglomeration • We represent an increase in the size of the labour force by increasing the number of workers on the unit circle • Now we have 6 workers (skill types) and 3 firms enter the market • Each worker has a mismatch of 1/12 • Workers incur lower training cost • Net wage increases Net wage = $12 – 1/12 · $24 = $10

24. An increase in the number of workers decreases mismatches and training costs • The presence of a large number of workers attracts firms that compete for workers, generating better skill matches and higher net wages • This is an incentive for workers to live in large numbers in cities, so the attraction between frims and workers is mutual

25. 3. LEARNING The Obligatory Marshall Quotation When an industry has thus chosen a locality for itself, it is likely to stay there long: so great are the advantages which people following the same skilled trade get from near neighbourhood to one another. The mysteries of the trade become no mysteries; but are as it were in the air, and children learn many of them unconsciously. Good work is rightly appreciated, inventions and improvements in machinery, in processes and the general organization of the business have their merits promptly discussed: if one man starts a new idea, it is taken up by others and combined with suggestions of their own; and thus it becomes the source of further new ideas. Alfred Marshall. 1890. Principles of Economics. London: Macmillan. Book IV, Ch. X, § 3: The advantages of localized industries; hereditary skill.

26. Three Types of Externalities (Glaeser et al. 1992) 1. Marshall-Arrow-Romer Local knowledge spillovers between firms in the same industry Specialization and concentration promote growth • Local monopoly helps growth by internalizing externalities 2. Porter Innovation in competitive industry clusters with many small firms Specialization and fragmentation promote city growth • Local competition requires firms to innovate or die 3. Jacobs Local knowledge transfers across industries Diversification and fragmentation promote city growth • “Cross-fertilization” of ideas across different lines of work

27. Evidence not conclusive • Glaeser et al. (1992) find evidence of Jacobs externalities explain the employment growth of sector-city • Henderson et al (1995) find that new industries appear in diverse cities but mature industries grow in specialized cities.

28. Nursery cities (Duranton and Puga, 2001) • Consider a firm that is looking for the ideal production process for a new product • By experimenting with different processes, the firm will find the ideal process • Once found the ideal process, the firm will switch to mass production and start earning a profit • Question is: where should the firm experiment, in a diverse city or a specialized city?

29. Cost and Benefits of both options (model) • First option → experiment in a diverse city and then move to a specialized city after discovering the ideal process • An experiment entails producing a prototype of the firm’s new product with a particular production process • Suppose there are six processes in the diverse city • Once the prototype from the ideal process is finished, the firm will immediately recognize that it has discovered the ideal process • Assume that it takes on average three years • Once discovered the ideal, the entrepreneur will move to a specialized city and start making profits

30. Cost of each prototype = $4 (losses of the firm each year of the 3 year) • Year 4 the firm moves to specialized city. Moving cost = $7 • Assume firm operates 6 years • Last 3 years the firm earns a gross profit = $12 • Firm’s lifetime profit is Net profit = Gross profit – Prototype cost – Moving cost Net profit = $36 – $12 – $7 = $17

31. Second option → search for the process in the specialized city • Advantage → lower prototype cost Each specialized city has the specialized inputs for one production process Suppose, prototype cost = $3 · 3 years = $9 • Disadvantage → Higher moving cost The search for the ideal process would require moves from one specialized city to another An average of three moves, moving costs = $7 · 3 years = $21 Net profit = $36 - $9 - $21 = $6 • Profit is lower when experimenting in specialized cities • Different roles of diverse and specialized cities

32. Establishment relocations in France, 1993-1996

33. The Geography of Innovation and Production • Innovative activity tends to cluster spatially • Geographic concentration of innovation varies by industry • Does not coincide with geographic concentration of production • Traditional arguments for concentration of production • Dependency on natural resources • Low transportation costs • Large economies of scales • Clustering of innovation when new knowledge is particularly important • Industry expenditure on R&D relative to sales • Share of skilled workers in industry employment • University research relevant to the industry • Indirect evidence of knowledge spillovers

35. Externalities of human capital • The productivity of individual workers is enhanced by an environment of high human capital • Labor and education policy • Social returns to skill > private returns to skill • Education as a public good • Rationale for vast government intervention • Endogenous growth theory • Lucas (1988) allows a country’s average human capital to increase TFP

36. Standard approach to the analysis of human capital externalities An economy with workers i or j, living in cities a. The social output of worker i with human capital hi and living in city a is given by: A is a technological parameter independent of location and Ba is a city specific parameter. The earnings of this worker are: Reciprocal externality

37. The cost of human hi:

38. Lucas (1988): “Most of what we know we learn form other people. We pay tuition to only a few of these teachers, either directly or indirectly by accepting lower pay so we hang around them, but most of it we get for free, and often in ways that are mutual- without distiction between student and teacher”

39. Assume that worker i’s human capital directly benefits N other workers in the city by an amount At the same time, worker i also benefits from the human capital investment made by all other workers in the interaction group. Summing across all workers j part of the interaction group of worker i: Where is the average human capital in city a and N is the size of the interaction group. So we can write now:

40. This equation can be estimated by means of regression analysis Rauch (1993) is the first i individual j city There exist human capital externalities is Rauch finds between 0.03-0.05

41. HOW TO MEASURE ECONOMIES OF AGGLOMERATION • Production function: Q = f(K,L) Q = units of output L = units of labour K = units of capital • Suppose a production function has the form (Cobb-Douglas) If , then there is constant returns to scale. If , then there are economies of scale

42. Example: Suppose K and L both double. Then we have: So output increases by This means output more than doubles if . The elasticity of output with respect to L equals and the elasticity of output with respect to K equals . (Elasticity is the percentage change in output that occurs when labor or capital increases by one percent.)

43. How to incorporate agglomeration economies into the production function? The idea of agglomeration economies is that economies of scale Also depend on the size of the city. Change the production function to: where N is the population of the city or the number of firms in the city The elasticity of output with respect to the population of the city N is If there are no agglomeration economies, then =0. Then if the population of the city doubles (substitute 2N for N), then output will be multiplied by , i.e., it won’t change If there are agglomeration economics, then . This means that firms are more efficient if they are located in larger cities. (Could alternately define N as the number of firms in the city.)

44. Example: suppose . Then if the population of the city doubles, output will be multiplied by , i.e., output rises by 7%. How to test this? Ideally, this would be tested for particular industries. Get data on number of workers who work in the (say) shoe industry in each city (L) and the amount of capital in the shoe industry in each city (K) and the number of shoe manufacturing firms in each city (N), and the number of pairs of shoes produced in each city.

45. This gives us a dataset of values of Q, K, L, and N for each city in the U.S. Then run a regression that explains Q using K, L, and N. It gives us estimates of . If , then there are agglomeration economies in the shoe industry. (Note: regression analysis next time.) This type of function has been estimated: Results: for the electrical machinery industry, 0.02 for the pulp and paper industry, 0.11 for the petroleum industry. 0.27 in the office industry. These effects are small, but they can be important in giving large cities an advantage over small ones.

47. Wages • In competitive markets labour is paid the value of its marginal product • Larger employment size/density Higher productivity Higher wage Urban wage premium

48. But not the only possible reason for higher wages in larger cities • 1. Sorting of the skilled into cities? • 2. Human capital accumulation? • So • Two basic questions: • Is it that most skilled sort into cities or that cities improve productivity? • Is the effect important when people get to the city or do wages grow over • time faster?

49. Sorting • Most skilled might sort into cities because: • Information flows are relatively more valuable to them • Consumption amenities might be more attractive for skilled people • If wages are higher cities, why workers do not flock to higher wage cities? • If wages are higher cities, why firms do not flee the higher wage cities?

50. Labour supply • In order to have a spatial equilibrium real wages per unit of skill equalize: • needs to be constant across cities i • units of skill wage in city i price index in city i • Implies that • So if , there are no ability differences across cities