1 1 Deep Thought BA 210 Lesson II.2 Bargaining and Impatience Why can’t the ant and the caterpillar just get along? One eats grass, the other eats Caterpillars

1 1

Deep ThoughtDeep Thought

BA 210 Lesson II.2 Bargaining and ImpatienceBA 210 Lesson II.2 Bargaining and Impatience

Why can’t the ant and the caterpillar Why can’t the ant and the caterpillar just get along? One eats grass, the just get along? One eats grass, the other eats Caterpillars … Oh, I see other eats Caterpillars … Oh, I see now. ~ Jack Handeynow. ~ Jack Handey..

(Translation: Today is another lesson teaching you how to get the (Translation: Today is another lesson teaching you how to get the best deal for yourself from bargaining.)best deal for yourself from bargaining.)

2 2BA 210 Lesson II.2 Bargaining and ImpatienceBA 210 Lesson II.2 Bargaining and Impatience

OverviewOverview

OverviewOverview

3 3

OverviewOverview

BA 210 Lesson II.2 Bargaining and Impatience

Lesson II.1 Strategic BargainingLesson II.1 Strategic Bargaining

Lesson II.2 Bargaining and ImpatienceLesson II.2 Bargaining and Impatience

Example 1: Best Alternative to No AgreementExample 1: Best Alternative to No AgreementExample 2: Mutual Alternatives to No AgreementExample 2: Mutual Alternatives to No AgreementExample 3: Manipulating Alternatives to No AgreementExample 3: Manipulating Alternatives to No AgreementExample 4: Bargaining with ImpatienceExample 4: Bargaining with ImpatienceExample 5: Relative ImpatienceExample 5: Relative ImpatienceLesson II.3 Sequential Quantity CompetitionLesson II.3 Sequential Quantity CompetitionSummarySummaryReview QuestionsReview Questions

4 4BA 210 Lesson II.2 Bargaining and Impatience

Lesson II.2 formulates and solves Lesson II.2 formulates and solves the following games:the following games:Examples 1, 2, 3, 4, 5: Examples 1, 2, 3, 4, 5: Sequential Bargaining Games.Sequential Bargaining Games. Have Have

unique rollback solutions. The solution favors the first mover, unique rollback solutions. The solution favors the first mover, and so favors aggressors; favors those with better outside and so favors aggressors; favors those with better outside alternatives to an agreement; and favors those with more alternatives to an agreement; and favors those with more patience.patience.

OverviewOverview


Example 1: Best Alternative to No Example 1: Best Alternative to No AgreementAgreement

Example 1: Best Alternative to No AgreementExample 1: Best Alternative to No Agreement


Comment: When Comment: When solving any Bargaining Game, solving any Bargaining Game, a bargainer’s a bargainer’s share of the fshare of the fixed positive gain from an agreement is added to ixed positive gain from an agreement is added to their their Best Alternative To No Agreement (BATNA)Best Alternative To No Agreement (BATNA). In . In particular, a bargainer can increase their total payoff from an particular, a bargainer can increase their total payoff from an agreement by increasing their BATNA. agreement by increasing their BATNA.



Question: Suppose Buyer Bob Question: Suppose Buyer Bob values the bag of fresh beans in values the bag of fresh beans in front of him at 1 dollar and front of him at 1 dollar and Seller SabithaSeller Sabitha, in an effort to improve , in an effort to improve her bargaining position, has taken the time to find an alternative her bargaining position, has taken the time to find an alternative buyer would would pay $0.60. That drops the gains from a trade buyer would would pay $0.60. That drops the gains from a trade between Bob and Sabitha from $1.00 to $0.40. between Bob and Sabitha from $1.00 to $0.40.

As before, suppose there is only enough time before his tour bus As before, suppose there is only enough time before his tour bus leaves for Buyer Bob to make one offer to Seller Sabitha for the leaves for Buyer Bob to make one offer to Seller Sabitha for the bag of beans. Seller Sabitha must either accept or reject that bag of beans. Seller Sabitha must either accept or reject that offer, and if Sabitha rejects then she can sell to the alternative offer, and if Sabitha rejects then she can sell to the alternative buyer for $0.60. buyer for $0.60. Will trade occur between Bob and Sabitha? If Will trade occur between Bob and Sabitha? If so, at what price to Bob? so, at what price to Bob?



Answer: Answer: The gain from Bob trading with Sabitha is $0.40. To The gain from Bob trading with Sabitha is $0.40. To consider all possible price offers (offers by Bob to buy or consider all possible price offers (offers by Bob to buy or counteroffers by Sabitha to sell), consider a counteroffers by Sabitha to sell), consider a bargaining payoff bargaining payoff table.table. The game lasts only one round, and gains are measured as The game lasts only one round, and gains are measured as a percentage of the $0.40 gain from Bob trading with Sabitha.a percentage of the $0.40 gain from Bob trading with Sabitha.

As before, Sabitha should accept anything as being better than As before, Sabitha should accept anything as being better than nothing. So, Bob can get away with 100 percent of the gains nothing. So, Bob can get away with 100 percent of the gains minus a pittance. That leaves Bob with $0.40 gains from trade, minus a pittance. That leaves Bob with $0.40 gains from trade, and Sabitha with $0.00, meaning Bob pays $1.00-$0.40 = $0.60 and Sabitha with $0.00, meaning Bob pays $1.00-$0.40 = $0.60 to Sabitha, and Sabitha receives $0.60+$0.00 = $0.60 from Bob. to Sabitha, and Sabitha receives $0.60+$0.00 = $0.60 from Bob.

Rounds to Game End

Offer byTotal Gain to Divide

Bob's GainOffered

Sabitha's Gain

Offered

1 Bob 100 ? ?



Comment: In any Bargaining Game, Comment: In any Bargaining Game, a bargainer’s shares of the a bargainer’s shares of the fixed positive gain from an agreement depends solely fixed positive gain from an agreement depends solely on the on the sequence of who makes offers and on any depreciation of the sequence of who makes offers and on any depreciation of the gains from an agreement over the bargaining rounds. In gains from an agreement over the bargaining rounds. In particular, the particular, the bargainers’ shares are independent of the level of bargainers’ shares are independent of the level of the gain from an agreement, and of the BATNAs of the the gain from an agreement, and of the BATNAs of the bargainers.bargainers.

Rounds to Game End


Bob's GainOffered

Sabitha's Gain

Offered

1 Bob 100 100 0



Example 2: Bilateral Alternatives to Example 2: Bilateral Alternatives to No AgreementNo Agreement

Example 2: Bilateral Alternatives to No AgreementExample 2: Bilateral Alternatives to No Agreement


Question 1. Question 1. Consider union-management negotiations over wages Consider union-management negotiations over wages for workers during Easter Weekend at Medieval Times Dinner for workers during Easter Weekend at Medieval Times Dinner Theatre. The weekend lasts Saturday and Sunday. Each day Theatre. The weekend lasts Saturday and Sunday. Each day Medieval Times operates with union labor, it makes a profit of Medieval Times operates with union labor, it makes a profit of $10,000. On the Friday night before the weekend, the $10,000. On the Friday night before the weekend, the employee’s union confronts the management over wages. The employee’s union confronts the management over wages. The union presents its demand. The management either accepts or union presents its demand. The management either accepts or rejects it and returns the next day with a counteroffer. Each day rejects it and returns the next day with a counteroffer. Each day without an agreement with the union, Medieval Times makes a without an agreement with the union, Medieval Times makes a profit of $3,000 after paying for expensive scab (non-union) profit of $3,000 after paying for expensive scab (non-union) labor, and union labor earns $2,000 from outside employment.labor, and union labor earns $2,000 from outside employment.

What initial wage demand should the union make? Should What initial wage demand should the union make? Should management accept that demand?management accept that demand?

Review QuestionsReview Questions



Answer 1: Answer 1: To consider all possible wage offers (offers by the To consider all possible wage offers (offers by the Union to sell labor or offers by Management to buy labor), Union to sell labor or offers by Management to buy labor), consider another consider another bargaining payoff tablebargaining payoff table. The game ends if an . The game ends if an offer is accepted or if the weekend ends without an accepted offer is accepted or if the weekend ends without an accepted offer. Gains are measured as a percentage of the 2offer. Gains are measured as a percentage of the 2xx(10-3-2) = 10 (10-3-2) = 10 thousand gain from accepting the Union’s offer at the beginning.thousand gain from accepting the Union’s offer at the beginning.

Rounds to End of Game


Union's GainOffered

Mgmt's GainOffered

1 Mgmt. 50 ? ?

2 Union 100 ? ?

13 13

Starting 1 bargaining round from Starting 1 bargaining round from the end of the game,the end of the game, when a when a contract has 50 percent of its contract has 50 percent of its original value, the Union should accept anything as being better original value, the Union should accept anything as being better than nothing. So, Management can get away with the whole 50 than nothing. So, Management can get away with the whole 50 percent minus a pittance, leaving the Union with the pittance. percent minus a pittance, leaving the Union with the pittance.

Rolling back to the beginning of the game, 2 bargaining rounds Rolling back to the beginning of the game, 2 bargaining rounds from the end, when a contract has 100 percent of its original from the end, when a contract has 100 percent of its original value, Management could reject any offer and get 50 percent in value, Management could reject any offer and get 50 percent in the next round. So, the Union’s best acceptable offer leaves the next round. So, the Union’s best acceptable offer leaves Management with 50 percent plus a pittance, and the union with Management with 50 percent plus a pittance, and the union with 25 percent minus a pittance.25 percent minus a pittance.





Union's GainOffered

Mgmt's GainOffered

1 Mgmt. 50 0 50

2 Union 100 50 50

14 14



Union's GainOffered

Mgmt's GainOffered

1 Mgmt. 50 0 50

2 Union 100 50 50



The Union’s initial wage demand should be for 50% of the The Union’s initial wage demand should be for 50% of the $10,000 profits, or $5,000, and management should accept that $10,000 profits, or $5,000, and management should accept that demand. Since the BATNA for Medieval Times is $3,000demand. Since the BATNA for Medieval Times is $3,000xx2 = 2 = $6,000 profit from scab labor and the BATNA for union labor is $6,000 profit from scab labor and the BATNA for union labor is $2,000$2,000xx2 = $4,000 from outside employment, the initial wage 2 = $4,000 from outside employment, the initial wage demand by the union should be $4,000+$5,000 = $9,000, and demand by the union should be $4,000+$5,000 = $9,000, and management should accept that demand, and so earn $20,000-management should accept that demand, and so earn $20,000-$9,000 = $11,000 profit.$9,000 = $11,000 profit.


Example 3: Manipulating Alternatives Example 3: Manipulating Alternatives to No Agreementto No Agreement

Example 3: Manipulating Alternatives to No AgreementExample 3: Manipulating Alternatives to No Agreement


Comment: Comment: When a strategic bargainer observes that a better When a strategic bargainer observes that a better outside opportunity translates into a better share in a bargain, he outside opportunity translates into a better share in a bargain, he will look for strategic moves that improve those outside will look for strategic moves that improve those outside opportunities. And he will notice that what matters is his outside opportunities. And he will notice that what matters is his outside opportunity relative to that of his rival. He will do better in the opportunity relative to that of his rival. He will do better in the bargaining even if he makes a commitment or a threat that lowers bargaining even if he makes a commitment or a threat that lowers both parties’ outside opportunities, as long as that of the rival is both parties’ outside opportunities, as long as that of the rival is damaged more severely.damaged more severely.



Question: Question: Reconsider the outcome of the original union-Reconsider the outcome of the original union-management wage bargaining for Thanksgiving Weekend at management wage bargaining for Thanksgiving Weekend at Medieval Times Dinner Theatre, where each day Medieval Times Medieval Times Dinner Theatre, where each day Medieval Times operates with union labor, Medieval Times makes a profit of operates with union labor, Medieval Times makes a profit of $10,000 before paying union wages, and each day without an $10,000 before paying union wages, and each day without an agreement with the union, Medieval Times makes profit $3,000 agreement with the union, Medieval Times makes profit $3,000 from scab labor and union labor earns outside income $2,000.from scab labor and union labor earns outside income $2,000.

Compute how outcomes changeCompute how outcomes change if the union gives up $500 per if the union gives up $500 per day of outside income to intensify their picketing and, thereby, day of outside income to intensify their picketing and, thereby, reduces Medieval Times profit from scab labor by $1,000 per reduces Medieval Times profit from scab labor by $1,000 per day. day.



Answer: Answer: The The bargaining payoff tablebargaining payoff table is not affected by changing is not affected by changing the BATNA for each bargainer.the BATNA for each bargainer.

In particular, the Union and Management reach an agreement on In particular, the Union and Management reach an agreement on the first round, and each get half of the gains from an agreement.the first round, and each get half of the gains from an agreement.




Union's GainOffered

Mgmt's GainOffered

1 Mgmt. 50 0 50

2 Union 100 50 50


Originally, the Union’s initial wage demand should give it 50% Originally, the Union’s initial wage demand should give it 50% of the $10,000 gains from trade, or $5,000, and management of the $10,000 gains from trade, or $5,000, and management should accept that demand. Since the BATNA for Medieval should accept that demand. Since the BATNA for Medieval Times is $3,000Times is $3,000xx2 = $6,000 profit from scab labor and the 2 = $6,000 profit from scab labor and the BATNA for union labor is $2,000BATNA for union labor is $2,000xx2 = $4,000 from outside 2 = $4,000 from outside employment, the initial wage demand by the union should be employment, the initial wage demand by the union should be $4,000+$5,000 = $9,000, and management should accept that $4,000+$5,000 = $9,000, and management should accept that demand, and so earn $20,000-$9,000 = $11,000 profit.demand, and so earn $20,000-$9,000 = $11,000 profit.

But with intensified picketing, the BATNA for Medieval Times But with intensified picketing, the BATNA for Medieval Times is $2,000is $2,000xx2 = $4,000 and the BATNA for union labor is 2 = $4,000 and the BATNA for union labor is $1,500$1,500xx2 = $3,000 and the gains from trade is $13,000. So, the 2 = $3,000 and the gains from trade is $13,000. So, the initial wage demand by the union should be $3,000+$6,500 = initial wage demand by the union should be $3,000+$6,500 = $9,500, and management should accept that demand, and so earn $9,500, and management should accept that demand, and so earn $20,000-$9,500 = $10,500 profit. $20,000-$9,500 = $10,500 profit. The Union does better.The Union does better.



Example 4: Bargaining with ImpatienceExample 4: Bargaining with Impatience

Example 4: Bargaining with Example 4: Bargaining with ImpatienceImpatience


Comment: Comment: Now consider a different kind of cost of delay in Now consider a different kind of cost of delay in reaching an agreement. Suppose the actual monetary value of the reaching an agreement. Suppose the actual monetary value of the total gains from an agreement does not depreciate, but bargainers total gains from an agreement does not depreciate, but bargainers have a “time value of money” and therefore prefer early have a “time value of money” and therefore prefer early agreement to later agreement. agreement to later agreement.



Question: Compute a bargaining payoff table Question: Compute a bargaining payoff table for Bargainers A for Bargainers A and B making alternating offers over 3 bargaining rounds, with and B making alternating offers over 3 bargaining rounds, with Bargainer A making the first offer, A discounting 10% between Bargainer A making the first offer, A discounting 10% between each period, and B also discounting 10% between each period.each period, and B also discounting 10% between each period.That is, both bargainers believe that having only 90 cents right That is, both bargainers believe that having only 90 cents right now is as good as having $1 one round later.now is as good as having $1 one round later.





A's GainOffered

(10% dis.)

B's GainOffered

(10% dis.)

1 A 100 ? ?

2 B 100 ? ?

3 A 100 ? ?


Answer: A bargaining payoff table Answer: A bargaining payoff table for Bargainers A and B for Bargainers A and B making alternating offers over 3 bargaining rounds, with making alternating offers over 3 bargaining rounds, with Bargainer A making the first offer:Bargainer A making the first offer:




A's GainOffered

(10% dis.)

B's GainOffered

(10% dis.)

1 A 100 100 0

2 B 100 90 10

3 A 100 91 9

Starting 1 bargaining round from Starting 1 bargaining round from the end,the end, B should accept B should accept anything as being better than anything as being better than nothing. After deducing that, A’s nothing. After deducing that, A’s best acceptable offer to B is a pittance, leaving A with 100.best acceptable offer to B is a pittance, leaving A with 100.

Rolling back to 2 rounds from the end, Rolling back to 2 rounds from the end, A could reject any offer A could reject any offer and get 100 in the next round, which after A’s 10% discount is and get 100 in the next round, which after A’s 10% discount is worth 90 in the current round. After deducing that, B’s best worth 90 in the current round. After deducing that, B’s best acceptable offer to A is 90 plus a pittance, leaving B with 10.acceptable offer to A is 90 plus a pittance, leaving B with 10.

Rolling back to the beginning of the game, Rolling back to the beginning of the game, B could reject any B could reject any offer and get 10 in the next round, which after B’s 10% discount offer and get 10 in the next round, which after B’s 10% discount is worth 9 in the current round. . After deducing that, A’s best is worth 9 in the current round. . After deducing that, A’s best acceptable offer to B is 9 plus a pittance, leaving A with 91.acceptable offer to B is 9 plus a pittance, leaving A with 91.





(10% dep.)

A's GainOffered

B's GainOffered

1 A 81 81 0

2 B 90 81 9

3 A 100 91 9

Comment: Comment: When both bargainersWhen both bargainersdiscountdiscount the same percent, the the same percent, thedivision of the gains from tradedivision of the gains from tradeis the same as if the object itself is the same as if the object itself were were depreciatingdepreciating by that percentage. by that percentage.

In the current problem, on the one hand, if there are 3 bargaining In the current problem, on the one hand, if there are 3 bargaining rounds and if A and B each discount 10%, then A’s best rounds and if A and B each discount 10%, then A’s best acceptable offer to B is 9 plus a pittance, leaving A with 91. On acceptable offer to B is 9 plus a pittance, leaving A with 91. On the other hand, if there are 3 bargaining rounds and the object the other hand, if there are 3 bargaining rounds and the object itself depreciates 10% per round, then A’s best acceptable offer itself depreciates 10% per round, then A’s best acceptable offer to B is, again, 9 plus a pittance, leaving A with 91.to B is, again, 9 plus a pittance, leaving A with 91.



Example 5: Relative ImpatienceExample 5: Relative Impatience



Comment: Comment: We now see that more patience (less discounting) We now see that more patience (less discounting) translates into a better share in a bargain. So a strategic bargainer translates into a better share in a bargain. So a strategic bargainer will learn patience.will learn patience.

The Chinese symbol for patience can also mean restraint and The Chinese symbol for patience can also mean restraint and control. It is formed by 2 different characters with the image of control. It is formed by 2 different characters with the image of blade on the heart.blade on the heart.

The word connotes how difficult it is to practice patience. The word connotes how difficult it is to practice patience.



Question: Question: Compare outcomes from 3 rounds of bargaining in Compare outcomes from 3 rounds of bargaining in three different scenarios:three different scenarios:

1)1)Both bargainers discount the money payoff from an agreement Both bargainers discount the money payoff from an agreement 10 percent each round. 10 percent each round. 2)2)The first mover (the first to make an offer) discounts the The first mover (the first to make an offer) discounts the money payoff from an agreement 10 percent each round, but the money payoff from an agreement 10 percent each round, but the second mover discounts 20 percent. second mover discounts 20 percent. 3)3)The first mover (the first to make an offer) discounts the The first mover (the first to make an offer) discounts the money payoff from an agreement 20 percent each round, but the money payoff from an agreement 20 percent each round, but the second mover discounts 10 percent. second mover discounts 10 percent.



Answer: A bargaining payoff table Answer: A bargaining payoff table for Bargainers A and B, with for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, Bargainer A making the first offer, with 3 bargaining rounds, with A discounting 10% between each period, and with B with A discounting 10% between each period, and with B discounting 20% between each period. discounting 20% between each period.



A's GainOffered

(10% dis.)

B's GainOffered

(20% dis.)

1 A 100 ? ?

2 B 100 ? ?

3 A 100 ? ?





A's GainOffered

(10% dis.)

B's GainOffered

(20% dis.)

1 A 100 100 0

2 B 100 90 10

3 A 100 92 8



Rolling back to the beginning, Rolling back to the beginning, B could reject any offer and get 10 B could reject any offer and get 10 in the next round, which after B’s 20% discount is worth 8 in the in the next round, which after B’s 20% discount is worth 8 in the current round. . After deducing that, A’s best acceptable offer to current round. . After deducing that, A’s best acceptable offer to B is 8 plus a pittance, leaving A with 92.B is 8 plus a pittance, leaving A with 92.



A bargaining payoff table A bargaining payoff table for Bargainers A and B, with Bargainer for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, with A A making the first offer, with 3 bargaining rounds, with A discounting 20% between each period, and with B discounting discounting 20% between each period, and with B discounting 10% between each period. 10% between each period.



A's GainOffered

(20% dis.)

B's GainOffered

(10% dis.)

1 A 100 ? ?

2 B 100 ? ?

3 A 100 ? ?





A's GainOffered

(20% dis.)

B's GainOffered

(10% dis.)

1 A 100 100 0

2 B 100 80 20

3 A 100 82 18



Rolling back to the beginning, Rolling back to the beginning, B could reject any offer and get 20 B could reject any offer and get 20 in the next round, which after B’s 10% discount is worth 18 in in the next round, which after B’s 10% discount is worth 18 in the current round. . After deducing that, A’s best acceptable the current round. . After deducing that, A’s best acceptable offer to B is 18 plus a pittance, leaving A with 82.offer to B is 18 plus a pittance, leaving A with 82.



Summary: Summary: Compare outcomes from 3 rounds of bargaining in Compare outcomes from 3 rounds of bargaining in three different scenarios. three different scenarios. 1)1)Both bargainers discount the money payoff from an agreement Both bargainers discount the money payoff from an agreement 10 percent each round. Outcome: First mover A’s best 10 percent each round. Outcome: First mover A’s best acceptable offer to B is 9%, leaving A with 91%. acceptable offer to B is 9%, leaving A with 91%. 2)2)The first mover (the first to make an offer) discounts the The first mover (the first to make an offer) discounts the money payoff from an agreement 10 percent each round, but the money payoff from an agreement 10 percent each round, but the second mover discounts 20 percent. Outcome: A’s best second mover discounts 20 percent. Outcome: A’s best acceptable offer to B is 8%, leaving A with 92%.acceptable offer to B is 8%, leaving A with 92%.3)3)The first mover (the first to make an offer) discounts the The first mover (the first to make an offer) discounts the money payoff from an agreement 20 percent each round, but the money payoff from an agreement 20 percent each round, but the second mover discounts 10 percent. Outcome: A’s best second mover discounts 10 percent. Outcome: A’s best acceptable offer to B is 18 plus a pittance, leaving A with 82.acceptable offer to B is 18 plus a pittance, leaving A with 82.A does best when his is more patient (discounts less) than B. A does best when his is more patient (discounts less) than B.



Comment: Comment: When a strategic bargainer observes that more When a strategic bargainer observes that more patience (less discounting) translates into a better share in a patience (less discounting) translates into a better share in a bargain, he will seek partners less patient than himself and avoid bargain, he will seek partners less patient than himself and avoid those more patient.those more patient.



SummarySummary

SummarySummary


SummarySummary

A bargainer’s shares A bargainer’s shares of the fof the fixed positive gain from an agreement ixed positive gain from an agreement depends solely on the sequence of who makes offers and on any depends solely on the sequence of who makes offers and on any depreciation of, or discounting of, the gains from an agreement depreciation of, or discounting of, the gains from an agreement over the bargaining rounds. In particular, the over the bargaining rounds. In particular, the bargainers’ shares bargainers’ shares are independent of the level of the gain from an agreement. are independent of the level of the gain from an agreement.


A bargaining payoff table A bargaining payoff table for Bargainers A and B, with Bargainer for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, with A A making the first offer, with 3 bargaining rounds, with A discounting 30% between each period, and with B discounting discounting 30% between each period, and with B discounting 40% between each period. 40% between each period.



A's GainOffered

(30% dis.)

B's GainOffered

(40% dis.)

1 A 100 100 0

2 B 100 70 30

3 A 100 82 18



A bargaining payoff table A bargaining payoff table for Bargainers A and B, with Bargainer for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, with A A making the first offer, with 3 bargaining rounds, with A discounting 40% between each period, and with B not discounting 40% between each period, and with B not discounting. (If A did not discount, he would have 100% of the discounting. (If A did not discount, he would have 100% of the gains from an agreement.) gains from an agreement.)



A's GainOffered

(40% dis.)

B's GainOffered

(0% dis.)

1 A 100 100 0

2 B 100 60 40

3 A 100 60 40


39 39



Review QuestionsReview Questions You should try to answer some of the following questions You should try to answer some of the following questions before the next class. before the next class. You will not turn in your answers, but students may request You will not turn in your answers, but students may request to discuss their answers to begin the next class. to discuss their answers to begin the next class. Your upcoming Exam 1 and cumulative Final Exam will Your upcoming Exam 1 and cumulative Final Exam will contain some similar questions, so you should eventually contain some similar questions, so you should eventually consider every review question before taking your exams.consider every review question before taking your exams.



Review Question 1Review Question 1


Comment: Comment: TheFasterTimes.Com posts an account of bargaining TheFasterTimes.Com posts an account of bargaining for a tiny glass bottle covered in a landscape painting at for a tiny glass bottle covered in a landscape painting at Shanghai’s Yuyuan market.Shanghai’s Yuyuan market.

The games began at a whopping 380RMB, or about $56US. Over The games began at a whopping 380RMB, or about $56US. Over the course of 20 minutes, the buyer brought the price down by the course of 20 minutes, the buyer brought the price down by pointing out design flaws and pretending to be distracted by a pointing out design flaws and pretending to be distracted by a porcelain doll in a red silk dress. When the shopkeeper refused to porcelain doll in a red silk dress. When the shopkeeper refused to go below 80RMB, the buyer walked away, slowly. “Come back,” go below 80RMB, the buyer walked away, slowly. “Come back,” the saleswoman cried, racing after her. “You can have it for 60.” the saleswoman cried, racing after her. “You can have it for 60.” Deal, at just under $9US, or about 1/6 of the asking price. Deal, at just under $9US, or about 1/6 of the asking price.

Bargaining in China is an art form that requires a lot of patience, Bargaining in China is an art form that requires a lot of patience, and a willingness of the buyer to signal their patience by and a willingness of the buyer to signal their patience by spending time. spending time.



Question 1. Question 1. Consider negotiations over the price of a tiny glass Consider negotiations over the price of a tiny glass bottle covered in a landscape painting at Shanghai’s Yuyuan bottle covered in a landscape painting at Shanghai’s Yuyuan market. Buyer Betty values the bottle at $65, and Seller Shen’s market. Buyer Betty values the bottle at $65, and Seller Shen’s cost of supplying the bottle is $5. S makes the first offer, with 2 cost of supplying the bottle is $5. S makes the first offer, with 2 bargaining rounds of alternating offers, and with S discounting bargaining rounds of alternating offers, and with S discounting 2% between each period. 2% between each period.

Compare bargaining outcomes when B discounts 10% between Compare bargaining outcomes when B discounts 10% between each period with B discounting only 1% between each period, each period with B discounting only 1% between each period, and with B discounting 100% between each period (which is and with B discounting 100% between each period (which is absolute impatience). absolute impatience).



Answer 1: A bargaining payoff table Answer 1: A bargaining payoff table for Bargainers B and S, for Bargainers B and S, with Bargainer S making the first offer, with 2 bargaining rounds, with Bargainer S making the first offer, with 2 bargaining rounds, with B discounting 10% between each period, and with S with B discounting 10% between each period, and with S discounting 2% between each period. discounting 2% between each period.



B's GainOffered

(10% dis.)

S's GainOffered

(2% dis.)

1 B 100 100 0

2 S 100 90 10



A bargaining payoff table A bargaining payoff table for Bargainers B and S, with Bargainer for Bargainers B and S, with Bargainer S making the first offer, with 2 bargaining rounds, with B S making the first offer, with 2 bargaining rounds, with B discounting only 1% between each period, and with S discounting only 1% between each period, and with S discounting 2% between each period. discounting 2% between each period.



B's GainOffered

(1% dis.)

S's GainOffered

(2% dis.)

1 B 100 100 0

2 S 100 99 1



A bargaining payoff table A bargaining payoff table for Bargainers B and S, with Bargainer for Bargainers B and S, with Bargainer S making the first offer, with 2 bargaining rounds, with B S making the first offer, with 2 bargaining rounds, with B discounting 100% between each period, and with S discounting discounting 100% between each period, and with S discounting 2% between each period. 2% between each period.



B's GainOffered

(100% dis.)

S's GainOffered

(2% dis.)

1 B 100 100 0

2 S 100 0 100



Summary: Summary: In the first case, when B discounts 10% between each period, B In the first case, when B discounts 10% between each period, B captures 90% of the $60 gains from trade, or $54, leaving S with $6. Buyer captures 90% of the $60 gains from trade, or $54, leaving S with $6. Buyer Betty thus makes an acceptable offer of $65-$54 = $11, leaving Seller Shen Betty thus makes an acceptable offer of $65-$54 = $11, leaving Seller Shen with gain $11-$5 = $6. with gain $11-$5 = $6.

On one extreme, when B discounts only 1% between each period, B captures On one extreme, when B discounts only 1% between each period, B captures 99% of the $60 gains from trade, or $59.40, leaving S with $0.60. Buyer 99% of the $60 gains from trade, or $59.40, leaving S with $0.60. Buyer Betty thus makes an acceptable offer of $65-$59.40 = $5.60, leaving Seller Betty thus makes an acceptable offer of $65-$59.40 = $5.60, leaving Seller Shen with gain $5.60-$5 = $0.60.Shen with gain $5.60-$5 = $0.60.

On the other extreme, when B discounts 100% between each period, B On the other extreme, when B discounts 100% between each period, B captures 0% of the $60 gains from trade, or $0, leaving S with $60. Buyer captures 0% of the $60 gains from trade, or $0, leaving S with $60. Buyer Betty thus makes an acceptable offer of $65, leaving Seller Shen with gain Betty thus makes an acceptable offer of $65, leaving Seller Shen with gain $65-$5 = $60. $65-$5 = $60. It is just as if Seller Shen made a take-it-or-leave-it offer.It is just as if Seller Shen made a take-it-or-leave-it offer.

Buyer Betty does better when she is more patient. In an extreme, she gets no Buyer Betty does better when she is more patient. In an extreme, she gets no gains when she has no patience.gains when she has no patience.


47 47

End of Lesson II.2End of Lesson II.2


BA 210 Introduction to BA 210 Introduction to MicroeconomicsMicroeconomics

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1 1 Deep Thought BA 210 Lesson II.2 Bargaining and Impatience Why can’t the ant and the caterpillar just get along? One eats grass, the other eats Caterpillars