(c) R.D. Weaver 2004 Spatial arbitrage and prices How is price determined across spatially separated markets? What are the key drivers of trade? What quantities

(c) R.D. Weaver 2004

Spatial arbitrage and prices

How is price determined across spatially separated markets?

What are the key drivers of trade?

What quantities are arbitraged?


Why it matters……….

Business managers face the challenges of Forecasting prices into the future Setting prices for products newly introduced into a

market Adjusting prices as competitors challenge their sales

with new pricing policies.


Consider any food franchise business Each store sells tens, often hundreds of products Cold Stone

How could they price products for their new State College store?

How do they update prices as economic conditions change?

What prices should they use in their proforma proposal to the bank for a working capital loan with a ten year horizon?


Review

Two levels at which we would like to consider economics of spatial trade Firm-level Markets level

Firm-level We started by considering the decision to sell a product into a new spatially

separated market.We focused on profits from the sale.

Similarly, we could consider buying from a spatially separated market.

Two decisions of interest Into which markets should sales be made?

How much should be sold into each market?


Market level issues

What is the pattern of trade flows Who is trading with whom? Where are the sources? Where are the net demand

points?

What is the pattern of prices after trade?


I. Firm-level decisionsProfits drive arbitrage…

define

Profits(i,j) = Pei dij Yj - PjYj - ACijYj

Pei price you hope to receive in market i i.e. it is our expected price

dij proportion left after deterioration in physical quantity due to shipping

Yj quantity purchased in jth market

Acij unit cost of shipping


Example: Where to sell your apples?

Price Sales &Trans

Cost

On farm $8.10/bu 0.20(suppose Cost of Production = $6.20/bu)

Local farm mkt $8.40 0.35(8 visits to sell harvest)

Local supermkt $7.80 0.10(2 deliveries)

Wholesale contract $8.10 0.08



Price Sales &Trans Net

/bu Cost

On farm $8.10-7.80 0.20 7.60-7.90(suppose Cost of Production = $6.20/bu)

Local farm mkt $8.40-8.00 0.45 7.55-7.95(20 visits to sell harvest)

Local supermkt $8.20 0.10 8.10(2 deliveries)

Wholesale contract $8.10 0.08 8.02


Example: Revisited

Would costs of transport vary with quantity?

What other issues might be relevant?

Instead of apples, think about coffee………


Decision #1:Where to sell, where to buy………Sell product Yj into market i, if

Profits(i,j) = Pei dij Yj - PjYj – Cij(Yj) > 0

Buy product Yj from market i, if

Profits(i,j) = Pei dij Yj - PjYj – Cij(Yj) < 0


dij proportion left after deterioration in physical quantity due to shipping Yj quantity purchased in jth marketAcij unit cost of shipping


Decision #2: How much to sell………is there a rule for calculating this? Let’s suppose we will ship only to one market…

Sell product Yj into market i, until the extra unit of sale is not profitable

1) ∆Profits(i,j) = Pei dij ∆Yj - Pj∆Yj - ∆Cij(Yj) = 0

Remember, as Yj is increased, costs go up….eventually

Divide 1) through by ∆Yj ∆Profits(i,j)/ ∆Yj = Pei dij - Pj - ∆Cij(Yj)/ ∆Yj = 0

Marginal change in profits= Pei dij - Pj – Marginal Cost =0


dij proportion left after deterioration in physical quantity due to shipping

Yj quantity purchased in jth market

Acij unit cost of shipping

For those of you who remember calculus, see notes on next slide..


Why does this make sense as a rule for finding the quantity to ship? We would like to ship the amount that maximizes

profits

Lets look at it graphically


Maximizing profits

Yj

$ Marginal profits= Pe i dij – Pj -∆Cij / ∆ Yj

ACij(Yj)= Cij /Yj

MCij(Yj) = ∆Cij / ∆ Yj

General idea: At Yj = 0, if profits are positive, then increase Yj . Keep increasing quantity until a further change in quantity leads to a descrease in profits.


Maximizing profits

Yj

$

Pe i dij – Pj Margin from exporting

ACij(Yj)= Cij /Yj

MCij(Yj) = ∆Cij / ∆ Yj


Allocating production across marketsSuppose your apple production Yi = 5,000 bushels

And suppose the local super-market can only take 1,000bu with certainty, and the wholesale contract is for 6,000 bu minimum.



Price Sales &Trans Net

Cost

Local supermkt $8.20 0.10 8.10(2 deliveries)

Wholesale $8.10 0.08 8.02

contract


II. Market level outcomesWhat happens when other firms do this?

At the market level, as the amount shipped increases, profit from trade for anyone will be driven to zero.

Profits(i,j) = Pei dij Yj - PjYj – Cij (Yj) 0


What will be the effect of spatial arbitrage?

Recognizing that Cij (Yj) = ACij*Yj

Profits(i,j) = Pei dij Yj - PjYj - ACij*Yj = 0

(we can divide through by Yj , why does nothing change?)

Result: Competition arbitrage locks prices together across locations

Peit dij = Pjt + ACij

We call this equation, the arbitrage equilibrium condition.


Extending our model of spatial price structure

Adding some reality


Adding reality …..and complications

Time costs Product Deterioration/Quality Change Transport costs Expected price Currencies differ Exchange rate risk Access to markets

These drive a greater wedge between prices….


Consider two markets, 1 and 2

)(

0)(/

0)(

_

)(

1212

12121212

1212112212

1212112212

YACPP

YACPPY

YCYPYP

entryfreearbitrage

YCYPYP

Arbitrage forces prices into an equilibrium relationship!


Trade Arbitrage Equilibrium

Case 2: Different currencies Define exchange rate

Eij = units ith cur/ units jth cur $/yen Entry if Profits (in exporter cur)

= Eij PejY- PiY-Cij(Y) > 0

= ($/yen) * (yen/box)*boxes-($/box)*boxes Arbitrage equilibrium if

Eij Pej- Pi-C(Y)/Y = 0

Eij Pej = Pi + AC(Yi,j)

exch rates play a role


Trade Arbitrage Equilibrium

Case 3: Taxes and subsidies Suppose importer charges tax (Tj )

Suppose exporting country pays subsidy (Si )

Entry if Profits = Eij Pe

j (1-Tj)Y- Pi (1-Si)Y-C(Y) > 0

Arbitrage equilibrium if

Eij Pej (1-Tj)- Pi (1-Si)-AC(Y) = 0


Trade Arbitrage Equilibrium Implications for prices

Arbitrage equilibrium

Eij Pej (1-Tj)- Pi (1-Si)-AC(Y) = 0

Eij Pej (1-Tj)= Pi (1-Si) + AC(Y)

Trade is distorted if exchange rates do not reflect relative value of currencies Why?

Trade is distorted by taxes and subsidiesWhy? What is the effect on trade flows?


What happens if Trade Costs are reduced?

Prices are locked together by trade

Eij Pj (1-Tj )= Pi (1-Si )+AC(Y)

Ys

Yd

Market i

Pi*

P*j

Ys

Yd

Market j


What happens if Trade Costs are reduced?Difference between prices is reduced

Amount of trade (volume) is increased

Ys

Yd

Market i

Pi*

P*j

Ys

Yd

Market j


What happens when exchange rates change? Suppose Eij decreases (one yen buys fewer $, $ “increases in value!”“Yen devalues” $ value of each unit sold in importing market (Japan) decreases less is traded, price goes down in exporting country, up in importing country

Ys

Yd

Market i

Pi*

Eij P*j

Ys

Yd

Market j


Exchange Rates Vary!

From milk.xls….. Or go to http://www.stls.frb.org/fred/data/exchange.html

Yen/$

0

50

100

150

200

250

300

350

400

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1996

1998

2000

Yen/$


Trade Links Markets Any change in one market will impact the other market! Suppose income increases in country i, what is effect?

Ys

Yd

Market i

Pi*

P*j

Ys

Yd

Market j


Trade Links Markets Any change in one market will impact the other market! Suppose production capacity expands in country j, what is effect?

Ys

Yd

Market i

Pi*

P*j

Ys

Yd

Market j


Summary: A Model of Price

Equilibrium price is determined by

Exogenous variables in both markets!

Parameters from both markets


Implications for Analysis & Forecasting

Prices from other regions can provide good predictors

No region’s prices are immune from other regions’ economic changes!

Documents

(c) R.D. Weaver 2004 Spatial arbitrage and prices How is price determined across spatially separated markets? What are the key drivers of trade? What quantities