(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 decisions Profits drive arbitrage… define Profits(i,j) = P e i d ij Y j - P j Y j - AC ij Y j P e i price you hope to receive in market i i.e. it is our expected price d ij proportion left after deterioration in physical quantity due to shipping Y j quantity purchased in jth market Ac ij unit cost of shipping

(c) R.D. Weaver 2004 Example: Where to sell your apples? Price Sales &Trans Cost On farm$8.10/bu0.20 (suppose Cost of Production = $6.20/bu) Local farm mkt$ (8 visits to sell harvest) Local supermkt$ (2 deliveries) Wholesale contract$

(c) R.D. Weaver 2004 Example: Where to sell your apples? Price Sales &Trans Net /buCost On farm$ (suppose Cost of Production = $6.20/bu) Local farm mkt$ (20 visits to sell harvest) Local supermkt$ (2 deliveries) Wholesale contract$

(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 Y j into market i, if Profits(i,j) = P e i d ij Y j - P j Y j – C ij (Y j ) > 0 Buy product Y j from market i, if Profits(i,j) = P e i d ij Y j - P j Y j – C ij (Y j ) < 0 P e i price you hope to receive in market i i.e. it is our expected price d ij proportion left after deterioration in physical quantity due to shipping Y j quantity purchased in jth market Ac ij 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 Y j into market i, until the extra unit of sale is not profitable 1) ∆Profits(i,j) = P e i d ij ∆Y j - P j ∆Y j - ∆C ij (Y j ) = 0 Remember, as Y j is increased, costs go up….eventually Divide 1) through by ∆Y j  ∆Profits(i,j)/ ∆Y j = P e i d ij - P j - ∆C ij (Y j )/ ∆Y j = 0 Marginal change in profits= P e i d ij - P j – Marginal Cost =0 P e i price you hope to receive in market i i.e. it is our expected price d ij proportion left after deterioration in physical quantity due to shipping Y j quantity purchased in jth market Ac ij 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= P e i d ij – P j -∆C ij / ∆ Y j AC ij (Y j )= C ij /Y j MC ij (Y j ) = ∆C ij / ∆ Y j General idea: At Y j = 0, if profits are positive, then increase Y j. Keep increasing quantity until a further change in quantity leads to a descrease in profits.

(c) R.D. Weaver 2004 Maximizing profits Yj $ P e i d ij – P j Margin from exporting AC ij (Y j )= C ij /Y j MC ij (Y j ) = ∆C ij / ∆ Y j

(c) R.D. Weaver 2004 Allocating production across markets Suppose your apple production Y i = 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$ (2 deliveries) Wholesale $ contract

(c) R.D. Weaver 2004 II. Market level outcomes What 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) = P e i d ij Y j - P j Y j – C ij (Y j )  0

(c) R.D. Weaver 2004 What will be the effect of spatial arbitrage? Recognizing that C ij (Y j ) = AC ij *Y j Profits(i,j) = P e i d ij Y j - P j Y j - AC ij *Y j = 0 (we can divide through by Y j, why does nothing change?) Result: Competition  arbitrage locks prices together across locations P e it d ij = P jt + AC ij 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 Arbitrage forces prices into an equilibrium relationship!

(c) R.D. Weaver 2004 Trade Arbitrage Equilibrium Case 2: Different currencies Define exchange rate E ij = units ith cur/ units jth cur $/yen Entry if Profits (in exporter cur) = E ij P e j Y- PiY-C ij (Y) > 0 = ($/yen) * (yen/box)*boxes-($/box)*boxes Arbitrage equilibrium if E ij P e j - P i -C(Y)/Y = 0 E ij P e j = P i + AC(Y i,j )  exch rates play a role

(c) R.D. Weaver 2004 Trade Arbitrage Equilibrium Case 3: Taxes and subsidies Suppose importer charges tax (T j ) Suppose exporting country pays subsidy (S i ) Entry if Profits = E ij P e j (1-T j )Y- P i (1-S i )Y-C(Y) > 0 Arbitrage equilibrium if E ij P e j (1-T j )- P i (1-S i )-AC(Y) = 0

(c) R.D. Weaver 2004 Trade Arbitrage Equilibrium Implications for prices Arbitrage equilibrium  E ij P e j (1-T j )- P i (1-S i )-AC(Y) = 0 E ij P e j (1-T j )= P i (1-S i ) + AC(Y) Trade is distorted if exchange rates do not reflect relative value of currencies Why? Trade is distorted by taxes and subsidies Why? 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 E ij P j (1-T j )= P i (1-S i )+AC(Y) Ys Yd Market i Pi*Pi* P*jP*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*Pi* P*jP*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*Pi* E ij P * j Ys Yd Market j

(c) R.D. Weaver 2004 Exchange Rates Vary! From milk.xls….. Or go to

(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*Pi* P*jP*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*Pi* P*jP*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!