Lab 6: Fish on Two Beaches
Textbook reading: Kreps, Chapter 13, especially 13.3 (when the picture works) and 13.4 (the Kerala fish market), plus the Class 11 page. This lab assumes you have had Class 11.
Problem of the Day
Groups of three at a whiteboard. The TA presents the market and the board notes. Groups work for forty minutes; the last ten minutes are a room-wide comparison of each group’s prices and counts.
Board notes
The fish market. Six boats and six restaurants on a coast with two beaches. Each boat lands one basket of fish; each restaurant wants one basket for tonight. A captain who cannot sell on the beach sells to the cannery truck, which pays by grade.
| North Beach | |||
|---|---|---|---|
| Restaurant, a basket is worth | Ana $40 | Cy $32 | Eli $12 |
| Captain, the cannery pays | Pat $4 | Quinn $8 | Rosa $16 |
| South Beach | |||
|---|---|---|---|
| Restaurant, a basket is worth | Ben $36 | Dee $28 | Fay $8 |
| Captain, the cannery pays | Sam $24 | Tom $32 | Uma $40 |
Rules. Everyone knows the table. Any captain and any restaurant on the same beach may agree a price, one basket per deal. Nobody trades at a loss: a restaurant never pays more than a basket is worth to it, and a captain never takes less than the cannery pays.
North Beach
Only North Beach is open today: Ana, Cy and Eli buy from Pat, Quinn and Rosa. Captains shop around for the highest price they can get, and restaurants shop around for the lowest price they can pay. The beach is in equilibrium when the price has stopped moving: no captain and no restaurant can earn more by changing what they do, whether that is asking a different price, switching partners, or walking away.
Suppose the going price on the beach is $8. Who wants to buy at that price, and who wants to sell? Is there excess demand or excess supply, and which way does that push the price? Now suppose the going price is $20, and answer the same questions.
Where does the price settle? In equilibrium, how many baskets change hands, how many go to the cannery, and which restaurants go home without one?
Eli reaches Pat first and offers $6, more than the cannery pays him. Is that deal part of an equilibrium?
South Beach
Now only South Beach is open: Ben, Dee and Fay buy from Sam, Tom and Uma. Try a going price of $20, then $36: who buys, who sells, and which way does the price move?
Where does the price settle, how many baskets change hands, and how many go to the cannery?
One Beach
A road opens along the coast, and all six boats land on one beach where all six restaurants buy. Try a going price of $16, then $32.
Where does the price settle, how many baskets change hands, and how many go to the cannery? Compare with the two beaches apart: what happened to the prices, and where did the extra basket come from?
Review
In one sentence: why does one more basket reach a restaurant when the beaches are joined, even though the same boats landed the same fish?
Solutions
Published after the last section has met.
North Beach. At $8. Ana, Cy and Eli would all buy (each values a basket at $8 or more); only Pat and Quinn would sell (Rosa needs $16). Three buyers for two baskets: excess demand, and the restaurant left out bids higher. At $20. Ana and Cy would buy (Eli stops at $12); Pat, Quinn and Rosa would all sell. Three baskets for two buyers: excess supply, and the captain left out undercuts. Where it settles. Between $12 and $16, two restaurants will pay and two captains will sell, and nobody left out can move the price: Eli will not pay more than $12 and Rosa will not take less than $16. Two baskets change hands, Ana and Cy buying from Pat and Quinn; Rosa’s basket goes to the cannery; Eli goes home without. Gains (40 + 32) − (4 + 8) = $60, however the price splits them. Eli’s $6. Pat would take it, but Cy, with no boat of his own, earns more by offering Pat $8 than by going without, and Pat earns more by taking it; the bidding does not stop until Eli drops out at $12. The deal is not part of an equilibrium: at $6 a restaurant left on the beach still has a better move, and so does Pat.
South Beach. At $20. Ben and Dee would buy; nobody would sell (Sam needs $24). Excess demand, price rises. At $36. Only Ben would still buy; Sam and Tom would sell. Excess supply, price falls. Where it settles. Between $28 and $32 one restaurant (Ben) will pay and one captain (Sam) will sell: below $28 Dee joins the bidding and two restaurants chase one basket; above $32 Tom’s boat joins and two baskets chase one restaurant. One basket changes hands, Ben buying from Sam, at $28 to $32. Tom’s and Uma’s baskets go to the cannery; Dee and Fay go home without. Gains 36 − 24 = $12. The two beaches apart: three baskets to restaurants, three to the cannery, $72 of gains, at prices about $16 apart.
One Beach. At $16. Ana, Ben, Cy and Dee would buy; Pat, Quinn and Rosa would sell. Four for three: excess demand, price rises. At $32. Ana, Ben and Cy would buy; Pat, Quinn, Rosa, Sam and Tom would sell. Three for five: excess supply, price falls. Where it settles. Between $24 and $28 four restaurants (Ana, Ben, Cy, Dee) will pay and four captains (Pat, Quinn, Rosa, Sam) will sell; Dee will not pay more than $28 and Tom will not take less than $32, so neither side left out can move it. Four baskets change hands at $24 to $28; Tom’s and Uma’s go to the cannery; Eli and Fay go home without. Gains (40 + 36 + 32 + 28) − (4 + 8 + 16 + 24) = $84, against $72 apart. The comparison. The North price rose from about $14 to about $26 and the South price fell from about $30 to the same figure. The extra basket is Rosa’s: on North it went to the cannery for $16 because the only buyer left there was Eli at $12, while on South Dee went home because the cheapest boat left wanted $32. On one beach Rosa and Dee find each other, a deal worth $12 to the pair, and that is the whole gain from joining the beaches.
Review. Apart, the basket that went unsold and the restaurant that went unfed were on different beaches; joined, the price falls far enough for Dee and rises far enough for Rosa, and the two of them trade.