Market Boundary

If all producers ship homogeneous units of the same commodity to a single central market, there is no market boundary because there is only one market.

In this case, the price each producer receives under perfectly competitive conditions is the central market price less the transfer costs.

Central Market$10

Market Boundary

Suppose there are two markets instead. Producers will ship to the market offering higher net price (i.e., net of transfer costs).

Thus, some producers supply one market, while others supply the other.

But some producers may be located at points where the price is the same whether they ship to one market or the other.

The boundary between two markets can be identified by finding the points at which prices paid to producers, net of transfer costs, are the same whether they ship to one market or the other.

Example Suppose the two markets are 6 miles apart.

Price at A Price at B

A 1 2 3 4 5 6B123456

The prices are $6/unit in Market A and $5/unit in market B. The transfer costs are $0.5/unit for each mile.

$6

$5

The boundary point is located at the intersection of the two price lines.

4 miles from market A, and2 miles from market B.

The price at the boundary is $4 per unit.

$4

Price at A Price at B

A 1 2 3 4 5 6B123456

The boundary will shift if the price rises in one market relative to the other or if transfer costs change.

$6

$5

Say, the price in market B rises to $6 per unit.

$4

Also, due to an improvement in market B's warehouse loading system, the transfer cost to market B is reduced from $0.50 to $0.40 per unit.

$6Wrong!

Thus, the price line for market B shifts up in a nonparallel way.

flatter!

$6

$4.67

2.26

So, the new boundary is to the left of the old boundary.

Spatial Equilibrium Models

Consider the orange industry:

The area east of the Mississippi is one region with its supply centered in Florida.

The other region is that area west of the Mississippi with its supply centered in California.

Assume that the oranges of the two regions are completely substitutable as far as the consumers are concerned.

The cost of moving oranges between the two regions is assumed to be known and can be approximated by an average cost per unit of product that moves between the two regions.

The supply and demand curves for the two regions are plotted in the figures below.

Western Market

SW

DW

Eastern Market

SE

DE

Consider first the case where no trade is permitted: the autarky equilibrium.

PW a

QW a

PE a

QE a

Since no trade can occur between regions, each region is an isolated market with its price and quantity determined solely by its supply and demand. The two regions are completely independent.

Excess Supply and Excess Demand

Now consider the situation in which trade is permitted between the two regions. To study the trade equilibrium, we construct the excess supply and excess demand curves of the regions.

The excess supply curve of a region describes the quantity by which supply in the region exceeds the demand at each price level. In particular, we are interested in the excess supply

curve of an exporting region.

The excess demand curve of a region describes the quantity by which demand in the region exceeds the supply at each price level. In particular, we are interested in the excess demand

curve of an importing region.

Western Market

SW

DW

PW a

QW a

Interregional Market

Since the Western region is the low price region, we examine its excess supply curve.

ESW

Thus, we have identified the excess supply curve of the West. This supply curve gives the export schedule of the West.

Next slide, we will identify the import schedule of the East. That is, the excess demand curve of the East.

Interregional Market

Since the Eastern region is the high price region, we examine its excess demand curve.

Eastern Market

SE

DE

PE a

QE a

EDE

Next slide, we will put together the excess supply curve of the West and the excess demand curve of the East.

We will then examine the trade equilibrium.

To simplify the exposition, we will first assume that the transfer cost is zero. Next Slide

Western Market

SW

DW

Eastern Market

SE

DEPW a

QW a

PE a

QE a

Interregional Market

EDE

ESW

The equilibrium in the interregional market is determined by the intersection of the ESW and EDE curves.

Given the ESW and EDE curves, the trade equilibrium price is P and the trade volume is Q.

P

Q

Trade Equilibrium

Interregional Market

EDE

ESW

Given the interregional price, P, what is the associated price and quantity in the domestic markets? Let’s examine the Western market first.

P

Q

Since the transfer cost is zero, the domestic price is the same as the interregional price.

P

Given the domestic price, the domestic supply is QW

s and domestic demand is QW

d.

QWd QW

s

The difference between QWs and QW

d is the exports, which equal the trade volume Q in the interregional market.

Western Market

SW

DW

PW a

QW a

Eastern Market

SE

DE

PE a

QE a

Interregional Market

EDE

ESW

P

Q

Now, given the interregional price, P, what is the associated price and quantity in the Eastern market?

Since the transfer cost is zero, the domestic price is the same as the interregional price. P

Given the domestic price, the domestic demand is QE

d and domestic supply is QE

s.

QEs QE

d

The difference between QEd and QE

s is the imports, which equal the trade volume Q in the interregional market.

Eastern Market

SE

DE

PE a

QE a

Interregional Market

EDE

ESW

P

Q

Thus, a complete description of the interregional trade equilibrium is the following:

P

QEs QE

d

Western Market

SW

DW

PW a

QW a

P

QWd QW

s

A Complete Picture

Exporting Region

Importing Region

Positive Transfer Cost

With the introduction of a positive transfer cost (t), we will be able to examine the effect on equilibrium of a transfer cost increase.

With a positive transfer cost, the price differential between the two regions, at the equilibrium, must equal to the transfer cost.

P P t

P and P

E W

E W

' '

' '

,

where are the equilibrium prices

for the East and West, respectively.

WHY?

Eastern Market

SE

DE

Interregional Market

EDE

ESW

P

Q

What would be the effects of the introduction of a positive transfer cost on the prices in the two regions and the trade volume?

P

QEs QE

d

Western Market

SW

DW

P

QWd QW

s

Exporting Region

Importing Region

Effects of Transfer Cost Increase With a positive transfer cost:

the equilibrium price in the West falls from P to PW'

the equilibrium price in the East rises from P to PE'

the price wedge between the two regions equals t

With a falling price in the exporting region, the supply in the West drops and its demand rises. Thus, there is a drop in the Western region's excess supply quantity. (export less)

With a rising price in the importing region, the supply in the East rises and its demand falls. Thus, there is a drop in the Eastern region's excess demand quantity. (import less)

Accordingly, the trade volume drops.

See the graphical analysis in the next slide.next slide

P P tE W' ' P P PE W

Eastern Market

SE

DE

Interregional Market

EDE

ESW

P

Q

P

QEs QE

d

Western Market

SW

DW

P

QWd QW

s

In the middle panel, find the price for the East and the price for the West such that their difference equals the transfer cost.

Say, the transfercost is this much: t

PW'

PE'

P P tE W' '

Sharing the Burden of Transfer Cost Increase

With an increase in the transfer cost, the price in the surplus region decreases whereas the price in the deficit region increases.

The differential impact on prices in each of the two regions depends on the slope of the respective excess supply and excess demand curves.

If ESW is steeper (i.e., more price inelastic) than EDE, the price in the West will fall more than the price rise in the East.

Conversely, if EDE is steeper (i.e., more price inelastic) than ESW, the price in the East will increase more than the price fall in the West.

Interregional Market

ESW

EDE

Inelastic Excess SupplyElastic Excess Demand

PPE

PW

Exporting region takes the hit.

Interregional Market

ESW

EDE

Elastic Excess SupplyInelastic Excess Demand

P

PE

PW

Sharing the Burden: Elasticity Matters

Importing region takes the hit.

The Underlying Curves Matter

How do the slope of excess supply curve and the slope of excess demand curve get determined?

The slope of ES curve depends on the slopes of supply and demand curves in the surplus region.

The steeper these regional supply and demand curves, the steeper is the excess supply curve.

The slope of ED curve depends on the slopes of supply and demand curves in the deficit region.

The steeper these regional supply and demand curves, the steeper is the excess demand curve.

Prohibitive Transfer Costs

If the transfer costs should further increase, the price difference will widen and trade volume fall.

If the transfer costs should increase up to or beyond the difference in the autarky prices, trade will shrink to zero.

EDE

ESW

Interregional Market

Q

Effects of Demand and Supply Shifters

The spatial equilibrium model can be used to assess the effect of changes in regional supply and demand shifters (such as: income, weather, etc.)

Any shift in the regional supply or demand curve in the West will shift the excess supply curve of that region.

Likewise, any shift in the regional supply or demand curve in the East will shift the excess demand curve of that region.

Obviously, a shift in the excess supply or excess demand curve will, in turn, result in changes in prices and quantities of the trading equilibrium.

Effect of Income Increase in the Surplus Region

An increase in the income level of a surplus region will cause a rightward shift in the region's demand curve.

Western Market

SW

DW

Interregional Market

EDE

ESW

Hence, a leftward shift in the region's excess supply curve (i.e., it will export less).

Surplus Region

Now, given the new excess supply curve, you can figure out the rest. For example, let’s focus on the surplus region.

price risestrade volume, ES (& ED) fall

Effect of Income Increase in the Deficit Region

An increase in the income level of a deficit region will cause a rightward shift in the region's demand curve.

Eastern Market

SE

DE

Interregional Market

ESW

Deficit Region

EDE

Hence, a rightward shift in the region's excess demand curve (i.e., it will import more).

Now, given the new excess demand curve, you can figure out the rest. Let’s focus on the deficit region.

price risestrade volume, ED (& ES) rise

In-Class Exercise 4d

Consider the effect of a supply shock (say, extraordinary good weather) in the surplus region.

The regional supply curve will shift to the right which, in turn, will cause a rightward shift in the region's excess supply curve.

Graphically illustrate the new equilibrium (for all three markets).

Consider the effect of a supply shock in the deficit region.

The regional supply curve will shift to the right which, in turn, will cause a leftward shift in the region's excess demand curve.

Graphically illustrate the new equilibrium (for all three markets).

Work Space for Exercise 4d: Surplus Region

Western Market

SW

DW

Interregional Market

EDE

ESW

Surplus Region

A good weather in the surplus region will cause a rightward shift in the region's supply curve.

Hence, a rightward shift in the region's excess supply curve (i.e., it will export more).

Now, given the new excess supply curve, you can figure out the rest. Focus on the surplus region.

price fallstrade volume, ES (& ED) rise

Eastern Market

SE

DE

Interregional Market

ESW

Deficit Region

EDE

A good weather in the deficit region will cause a rightward shift in the region's supply curve.

Hence, a leftward shift in the region's excess demand curve (i.e., it will import less).

Work Space for Exercise 4d: Deficit Region

Now, given the new excess demand curve, you can figure out the rest.

price fallstrade volume, ED (& ES) fall