Increasing Returns and Economic Geography © Allen C. Goodman, 2002.

Increasing Returns and Economic Geography

© Allen C. Goodman, 2002

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?

Utility

All individuals have utility function:

1AM CCU (1)

where CA is consumption of agricultural good, and CM is

consumption of manufactured good.

Manufacturing

Manufacturing aggregate is defined by:

(2)

)1/(

1

/)1(

N

iiM cC

where N is the number of potential products and > 1 is the elasticity of substitution among the products

Labor force

Peasant population is completely immobile between regions, with a given peasant supply (1 – )/2 in each region.

Thus, workers in each region add up to:

L1 + L2 = . (3)

IRTS

Key feature of manufacturing is:

LMi = + xI (4)

This gives us increasing returns to scale since:

xi/LMi = [1 – (/LMi)]/.

Output per person increases as L increases.

Free Entry

With free entry of firms into mfg., then profits must = 0. So:

(p1 – w1)x1 = w1 (7)

(p2 – w2)x2 = w2

Using (6) and (7),

)1(

21

xx (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:

n

n

L

L1

2

1

2

(9)

Neary on Fujita-Krugman-Venables (FKV)

© A. Goodman, 2002

Costs

Wages = w

Fixed costs = Fw

Variable costs = 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

Transport cost = (T-1) * Producer Price

So, if T = 1, transport cost is 0.

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

111 pq ][ 1122

1111

TPYPY (8)

122

111

11 )( TpnpnP

n1 domestic varieties cost p1

n2 imported varieties cost p2T

Since each firm sells in both markets the price index is decreasing in the numberof firms in both markets (because greater variety benefits consumers), andincreasing in trade costs

(9)

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

• When will eq’m exhibit diversification with manufacturing taking place in both countries, 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

2

3

Three Effects of Entry

1 Price Index EffectDemand and MR

2 Demand or Backward LinkageDemand and MR

3Costor Forward LinkageAC and MC

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.

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.

Three effects (3)

Third effect – Since migration is driven by differentials in real wages, entry by a new firm tends to raise real wages (because P1 in Country 1. This further increases migration. This is arrow 3.

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.