Anderson’s Model of Heartland-Hinterland Trade
- See: F. J. Anderson Ch. 2
F.J. Anderson Regional Economic Analysis Ch. 2, 3
- Interest: Heartland-Hinterland structure
Focus on the hinterland economy
Role of resources
Suggests factors underlying regional disparities.
- Setup: Two regions
Competitive markets
Labour is immobile between regions
Capital and materials are mobile.
Multiple sectors: Export sector
Home sector (produces for
Hinterland consumption: non-base)
Expanded version: adds a resource
sector
Heartland has cost advantages in producing the
manufactured export good.
- Hinterland and Heartland are not equals.
- Heartland has a cost advantage in manufactured goods
(hinterland export sector)
- Source of cost advantage:
- via: economies of scale (via market size)
transportation cost and nearness of markets.
- To be competitive hinterland wages must be lower to
overcome the cost advantage of the heartland.
- low wages only necessary if the hinterland must export
manufactured goods to fully employ its workforce).
- Hinterland region is small compared to the heartland:
- too small to affect heartland input or output prices.
- Notation:
Output Prices:
px hinterland price of hinterland exports (x)
pm hinterland price of imports (m)
pH hinterland price of home sector (H) goods
px heartland price of hinterland exports (x)
pm heartland price of hinterland imports (m)
pH heartland price of home goods (H)
Input prices:
w wage rate
r (rental) price of capital
m price of materials
Transportation costs:
tm cost per unit of bringing imports to hinterland
tx cost per unit of shipping exports to heartland
Input-output coefficients: (in physical units)
aij amount of input i per unit of sector j output
i=L labour j = m import sector
i=K capital j= x export sector
i=m materials j= H home sector
- treat input-output coefficients as constants.
- inverse of coefficients: productivities.
- Prices in the Hinterland and Heartland:
- Input prices:
- Materials and capital are mobile.
- prices: r, m same in hinterland as heartland.
hinterland too small to affect them.
- Labour: immobile between regions
- hinterland wage adjusts to ensure hinterland workforce
is employed.
- labour is mobile between hinterland industries: ensures
same wage in each industry.
- Competition (free entry of new firms) ensures economic profits =0
so:
px = aLx w + aKx r + amx m
pH = aLH w + aKH r + amH m
RHS = cost per unit of export (home sector) output produced.
- Competition and trade between regions ensures:
Hinterland exports:
px = px - tx heartland price is higher by transport
costs.
Hinterland too small to affect px
(so its price is tied to px)
Hinterland imports:
pm = pm + tm hinterland price is higher by transport
costs.
(hinterland too small to affect pm)
Home sector only produces for hinterland consumption if:
pH - tH < pH < pH + tH
otherwise: better to import if pH + tH < pH
better to export if pH - tH > pH
- Wage Determination in the hinterland:
- Wage (w) must be low enough to ensure that exports are
cheap enough to sell in the heartland.
px = px - tx
so:
px - tx = aLx w + aKx r + amx m
- everything in the equation is known except w.
i.e., technology (a’s), capital and materials prices
(r,m) and transport costs are all given.
solve for w:
w = (px - tx - aKx r - amx m)/ aLx
- at this wage rate unit costs just match price received in
heartland for export goods.
- hinterland wage is lower:
- lower is heartland price of export goods
- higher transport costs
- higher is aLx (lower labour productivity)
- higher is aKx, amx (lower productivity of other
inputs).
- Having determined the hinterland wage it is possible to determine whether
a home sector will exist.
- w determines unit cost of producting H in the hinterland
- this gives PH
- then can see if :
pH - tH < pH < pH + tH
Adding A Resource Sector to the Hinterland
- Another possible sector of employment: treat as a possible export industry.
- “R “ denotes resource sector, Re is resource rent per unit, there is a limited
quantity of the resource (N).
- the resource is in fixed supply: if demand <supply then Re=0.
- Like the export sector:
pR = pR - tR (pR determined outside hinterland)
so:
pR - tR = aLR w + aKR r + amR m + aReR Re
- This sector will only be economical if it can attract labour away from other
sectors.
- It must be able to pay more than the wage derived above for export sector:
(pR - tR - aKR r - amR m – aReR Re)/ aLR > (px - tx - aKx r - amx m)/ aLx
now Re is determined locally: no resource sector it equals 0.
So if inequality above holds when Re=0 the resource sector will
be economical.
Labour Demand for the Hinterland:
- Basically three segments (assuming no resource sector): one for each
sector (R, X and H).
- Anderson’s model it is assumed that R sector is viable at the highest
wage, then the H sector and lastly the X sector.
i.e. hinterland’s advantage lies in R sector.
- Tracing out the demand curve:
- High wage: - no labour demanded in the hinterland
- neither resource nor export sectors are viable
given the output prices.
- no home sector: it is non-base activity.
- At:
w = (pR - tR - aKR r - amR m)/ aLR
- wage is low enough that the resource sector is now
viable.
- resource sector hires until resource is fully utilized: (output = N/aReR so labour demand is: aLR N/aReR)
- N is the total amount of the resource available.
- At:
w = (pH + tH - aKH r - amH m)/ aLH
- hinterland firms can compete with heartland imports
- labour demand is flat at this wage until all heartland
imports are replaced by home production.
- further fall in the wage will lead to additional expansion
of H sector as consumers substitute cheaper H
goods for other goods (downward sloping portion)
- If wages fall sufficiently far:
- Export sector is viable.
- Hinterland can export to heartland.
- Assuming Heartland is large vs. hinterland demand
remains flat at this wage.
- Possibilities?
- could be that the home sector becomes an export
sector .
- or an entirely new export sector.
- Diagram (as in Anderson Fig. 2.4).
Equilibrium outcomes in the Hinterland economy:
- Assume a fixed hinterland labour supply.
- small supply (£ aLRN/ aReR)
- wage: w = (pR - tR - aKR r - amR m)/ aLR
- all employment is in the resource sector.
- note: Re=0 not all the resource is used.
- expanding labour supply:
- wage eventually falls to: w = (pH + tH - aKH r - amH m)/ aLH
- two sectors in the hinterland economy:
resource sector (now Re>0)
home sector.
- expand labour supply further:
- wage begins to fall still further: home sector continues to
expand.
- expand labour supply still more:
- wage falls until an export sector is economical
e.g. w = (px - tx - aKx r - amx m)/ aLx
- three sectors now: resource, home and export sector.
- wage stays constant for further expansions, export sector
absorbs additional workers.
Changing the size of the Resource Base
- Say the hinterland has more resources:
- labour demand shifts right (first flat segment is longer)
- Effects depend on position of labour supply:
- if all employment is in resource sector to start: no effect.
- if some employment is in other sectors (larger labour supply):
- resource sector employment, output and exports expand
- wages may rise (but not if supply=demand on same old
flat segment)
- large enough rise in resource base will raise
hinterland wages.
Implications for Regional Disparity and Regional Wage Differentials:
- See Anderson p.54 for a summary statement of the model’s implications.
- Say that labour supply is large enough (or resource endowment small
enough) that the hinterland has an export sector:
Hinterland wage: w = (px - tx - aKx r - amx m)/ aLx
Heartland wage: w* = (px – a*Kx r – a*mx m)/ a*Lx
* - denotes heartland
Why might w* > w ?
- transport costs (tx): hinterland must have lower wages to
counter cost of exporting to heartland.
(locational disadvantage)
- differences in input-output coefficients:
- assuming that heartland has a cost advantage suggests:
a*<a inputs are more
productive in heartland
(technological disadvantage)
- The model also suggests that a large enough resource endowment
could outweigh these disadvantages
- given the demand curve above a large resource endowment
relative to labour supply gives a higher wage, resource-
dominated hinterland economy.
e.g., Alberta
- Earlier demand curve assumed that the resource sector could
support the highest wage (it was the highest segment on
the demand curve)
- this is most likely to be true if:
- resource prices are high
- productivity in resources is high (a’s low)
- cost of transporting resource output to the
heartland are low.
(especially relative to values of the same variables
in the (possible) export sector sector)
- Possible sources of lower Atlantic Canada wages:
- locational and technological disadvantages
- smaller resource base.
- low relative prices for its resources.
- The labour demand curve consisted of several flat segments in Anderson’s
model.
- A less unusual labour demand curve can be obtained by assuming:
- many resource industries or resources of differing quality
- many home sector goods, home goods that are not perfect
substitutes for heartland goods.
- many export industry goods.
i.e. many small industries becoming at slightly different
wages.
Anderson’s Framework and Heckscher-Ohlin (HO):
- Hinterland industrial structure and trade has roots in resource endowments.
- large resource endowment: many employed in resource industry
output largely exported.
- this is like HO.
- Technological assumptions:
Heckscher-Ohlin: both regions have same technologies (a’s)
Anderson: hinterland at a technological disadvantage.
- Transportation costs and market location:
Heckscher-Ohlin: ignores transport costs
Anderson: hinterland at a disadvantage: far from markets,
transport costs matter.
- Disadvantages of the hinterland region result in lower wages in Anderson.
i.e., no factor price equalization result as in HO.
- Labour immobile in both models.
- no migration in face of disparities (unlike staples model).
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