Increasing Returns and Economic Geography © Allen C. Goodman, 2009 NO CLASS Tuesday, 2/10 NO CLASS Tuesday, 2/10

IRTS Fundamental basis for urban areas is increasing returns to scale in something. You can’t have gathering of activities unless you have IRTS. Strangely, urban economists didn’t do much with this for many years. Krugman used some of his international trade models to gain some useful insights. How does the model work?

Leads to a lot of questions Do cities look the same, or different? Do wages and/or prices converge, as we might expect them to, or to they diverge if IRTS are important? What roles do transportation costs have? Think of this in terms of NY, LA and the Great In-Between Does either specialize? Do wages equilibrate? Do they trade?

Utility All individuals have utility function: (1) where C A is consumption of agricultural good, and C M is consumption of manufactured good.

Manufacturing Manufacturing aggregate is defined by: (2) where N is the number of potential products and  > 1 is the elasticity of substitution among the products When  is high, differentiated goods are nearly perfect substitutes for each other, while as  is low, the desire to consume a greater variety of manufactured goods increases, due to the fact that the varieties are less then perfect substitutes and consumers wishing to satisfy their preference for variety, will be spending on more of the available varieties.

IRTS Key feature of manufacturing is: L Mi =  +  x I (4) This gives us increasing returns to scale since: x i /L Mi = [1 – (  /L Mi )]/ . Output per person increases as L increases.

Free Entry With free entry of firms into mfg., then profits must = 0. So: (p 1 –  w 1 )x 1 =  w 1 (7) (p 2 –  w 2 )x 2 =  w 2 Using (6) and (7), (8)

Output/firm So, output/firm is the same in each region irrespective of wage rates, relative demand, etc. This implies that the number of mfg. goods produced in each region is proportional to the number of workers such that: (9)

Neary on Fujita-Krugman-Venables (FKV) © A. Goodman, 2002

This is complicated Depends on a lot of normalizations. Solvable, and not even easily solvable with a set of CES functions. Neary provides some of the essentials.

Costs Wages = w Fixed costs = Fw Variable costs per unit = cw Total costs = Fw + cqw Marginal cost = cw

cw AC MR D  cw/(  (  F/c Equilibrium (1) MR = MC (2) Profits = 0 (2') Price = AC

Transport Costs – Iceberg Key assumption The assumptions we use in the central place model make things intractable, so think of transport as an iceberg. Some portion of the good melts away in transit. Transport cost = (T-1) * Producer Price So, if T = 1, transport cost is 0. If T = 2, you must ship 2x 1 in order for x 1 to arrive. The higher T is, relative to 1, the more is lost, and the higher the transport cost. It costs $ to transport manufactured goods; it costs 0 to transport agricultural goods.

Impacts of Trade – Price Index n 1 domestic varieties cost p 1 n 2 imported varieties cost p 2 T Since each firm sells in both markets the price index is decreasing in the number of firms in both markets (because greater variety benefits consumers), and increasing in trade costs (9) Since every firm sells in both markets, the price index is decreasing in the number of firms in both markets (because greater variety benefits consumers) and is increasing in trade costs.

Impacts of Trade – Demand Ftn. (8) n 1 domestic varieties cost p 1 n 2 imported varieties cost p 2 T Since each firm sells in both markets the price index is decreasing in the number of firms in both markets (because greater variety benefits consumers), and increasing in trade costs First, the demand function facing a typical firm located in country 1 must be extended to incorporate exports. Note however, that firms are oblivious to all these complications: the perceived demand function is identical to the simpler one without trade. Total demand depends positively on the industry price index (P 1 and P 2 ) and on the level of manufacturing expenditure (μY 1 and μY 2 ) in both markets, and negatively on the level of trade costs T.

Home Market Effect Country with higher demand has a proportionately larger share of manufacturing. It assumes rather than explains international differences in incomes, since we (as yet) haven’t explained agglomeration.

Assume Labor Mobility Workers can work in NY or in LA When will eq’m exhibit diversification with manufacturing taking place in both countries (regions), and when will it exhibit agglomeration? Assume a new mfg. firm enters in Country (region) 1 (and a firm exits in Country 2). If  1 falls, firm leaves and initial eq’m returns. If  1 rises, initial equilibrium is unstable. There are three effects of entry.

cw AC MR D  cw/(  (  F/c 1 Three Effects of Entry 1 Price Index Effect Demand and MR

Three effects (1) Price index – An extra firm lowers the industry price index which reduces the demand facing each existing firm. This is arrow 1. This is always stabilizing.

cw AC MR D  cw/(  (  F/c 1 2 Three Effects of Entry 1 Price Index Effect Demand and MR 2 Demand or Backward Linkage Demand and MR

Three effects (2) Demand (backward linkage) – An extra firm raises demand for labor in Country 1. This puts upward pressure on local money wages, which encourages foreign workers to migrate. This in turn raises demand for local varieties. This is arrow 2 and tends to  ,  more inmigration, etc. Agglomeration is more likely when share of mfg in national income is high and transportation costs are low.

cw AC MR D  cw/(  (  F/c Three Effects of Entry 1 Price Index Effect Demand and MR 2 Demand or Backward Linkage Demand and MR 3 Cost or Forward Linkage AC and MC

Three effects (3) Third effect – Remember that P 1  in Country 1. This tends to raise real wages As people come in, the supply of labor increases and money wage w may fall, increasing profitability. This further increases migration. This is arrow 3. It leads to more instability.

In sum With high transport costs, you get local agglomeration, but expensive foreign goods. Local wages may fall  to regional convergence. With low transport costs, you get local agglomeration, and cheaper foreign goods. Local wages may rise  regional divergence.

Putting them together Stability is affected by: T – transportation costs m - share of nominal income spent on mfg.  – elasticity of substitution between varieties Higher T always encourage stability. For sufficiently low T, diversification is always unstable since the countries are ex ante identical. Somewhere in between is a threshold level of trade costs, a “break” point at which the diversified equilibrium is on the brink of instability.

In sum With high transport costs, you get local agglomeration, but expensive foreign goods. Local wages may fall  to regional convergence. With low transport costs, you get local agglomeration, and cheaper foreign goods. Local wages may rise  regional divergence.

Example Start with a pattern in which activities are equally split between the two regions, meaning that the share of the manufacturing sector is 1/2 in each region. At the other extreme of the spectrum, low transport costs foster the agglomeration of activities within a single region, hence implying that the share is either 0 or 1. For intermediate values, both configurations are stable equilibria, in which case the actual spatial pattern heavily depends on history. Those spatial patterns of production, as well as the conditions under which they emerge, provide a crude, but accurate, description of some general trends.

Transport costs and industry share when labor is mobile Size of local markets changes with labor migration. For such self-reinforcing changes to occur, it must be that trading between regions becomes sufficiently cheap. Putting all these results together shows that lowering transport costs first leaves the location of economic activity unchanged, and then gives rise to a snowball effect that stops only when an extreme form of economic agglomeration is obtained. Transport Costs Stable Eq’m Unstable Eq’m 1 0 ½