(c) r.d. weaver 2004 spatial arbitrage and prices how is price determined across spatially separated...
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(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?
(c) R.D. Weaver 2004
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.
(c) R.D. Weaver 2004
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?
(c) R.D. Weaver 2004
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?
(c) R.D. Weaver 2004
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?
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
Example: Where to sell your apples?
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
(c) R.D. Weaver 2004
Example: Revisited
Would costs of transport vary with quantity?
What other issues might be relevant?
Instead of apples, think about coffee………
(c) R.D. Weaver 2004
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
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 marketAcij unit cost of shipping
(c) R.D. Weaver 2004
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
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
For those of you who remember calculus, see notes on next slide..
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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.
(c) R.D. Weaver 2004
Maximizing profits
Yj
$
Pe i dij – Pj Margin from exporting
ACij(Yj)= Cij /Yj
MCij(Yj) = ∆Cij / ∆ Yj
(c) R.D. Weaver 2004
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.
(c) R.D. Weaver 2004
Example: Where to sell your apples?
Price Sales &Trans Net
Cost
Local supermkt $8.20 0.10 8.10(2 deliveries)
Wholesale $8.10 0.08 8.02
contract
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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.
(c) R.D. Weaver 2004
Extending our model of spatial price structure
Adding some reality
(c) R.D. Weaver 2004
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….
(c) R.D. Weaver 2004
Consider two markets, 1 and 2
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YACPP
YACPPY
YCYPYP
entryfreearbitrage
YCYPYP
Arbitrage forces prices into an equilibrium relationship!
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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?
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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/$
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
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
(c) R.D. Weaver 2004
Summary: A Model of Price
Equilibrium price is determined by
Exogenous variables in both markets!
Parameters from both markets
(c) R.D. Weaver 2004
Implications for Analysis & Forecasting
Prices from other regions can provide good predictors
No region’s prices are immune from other regions’ economic changes!