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Experiment with an Auction to create a Demand Function

Experiment with an Auction to create a Demand Function. Berufsakademie Eisenach Staatliche Studienakademie Thüringen University of Cooperative Education. Prof . Dr. Stephan Rometsch. Demand Function. EXPERIMENT. Auctions and the Theory of Demand

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Experiment with an Auction to create a Demand Function

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  1. Experiment with an Auctiontocreate a Demand Function Berufsakademie EisenachStaatliche Studienakademie Thüringen University ofCooperative Education Prof. Dr. Stephan Rometsch

  2. Demand Function

  3. EXPERIMENT AuctionsandtheTheoryof Demand • PART I• Second priceclosedsealbidauction • English auction •First priceclosedsealbidauction •Dutchauction • PART II• Demand Functionandimplications

  4. Second priceclosedsealbidauction ASSUMPTIONS AND INTRODUCTION • A bidderknows not thebidofothers • Person withthehighestbidgetsthe item • But he/shepaysthepriceofthesecondhighestbid • Whyisitsensefulltorevealthetruewillingnesstopay? • Simple:Becausethereisnoregret! • Every otherdecisiondoesn´tgainanyadvantage!

  5. Background ? • I wanttoknowYourtruewillingnesstopay! • Therefore, I wanttoknowYourtrueevalutionofthegoodtocreateYourtruedemandfunction • The truewillingnesstopayforthe item ofpersoniiszi

  6. Example • A person i evaluates the item with € 25,- (zi=25) cs = 5 p = gj= 20 gi= zi= 25 • If person i bids gi=ziand no one bids more – then he/she gets the item and has to pay p=gj=20, the price of the second highest bid (of person j) and igets a consumer surplus of 5.

  7. Well ?1. • Would person ibetter off if he does anything else? cs = 5 p = gj= 20 zi= 25 ĝi= 28 • The result is the same. He gets the item and has to pay p=gj=20, the price of the second highest bid and gets a true consumer surplus of 5. Therefore, gi=zi=25 was high enough.

  8. Well ?2. • Would person ibetter off if he reduces the bid? cs = 5 p = gj= 20 ği= 23 zi= 25 • The result is the same. He gets the item and has to pay p=gj=20, the price of the second highest bid and gets a true consumer surplus of 5. Therefore, gi=zi=25 was ok.

  9. gi = zi = 25was high enough

  10. But… • Be careful, if gi<gj, then person j gets the item… p = gk = 18 ği= 17 gj= 20 zi= 25 • Now person j gets the item and has to pay p=gk=18, the price of the second highest bid (of person k) and person i is very angry.

  11. Person i is very angry, because he wants to have the item, because his true willingness to pay was zi=25.

  12. ResultsIf person ihas the highest evaluation • To higher the price over zi doesn´t gain any advantage. • To lower the price under zi doesn´t gain any advantage. • If you lower the price, be careful, there is an increasing probability that another person j with the bid gj has the highest bid and gets the item. • And then person i is very angry, because he wants to have the item, because his true willingness to pay was zi=25.

  13. Results • Therefore, reveal your true willingness to pay with your true bid and you get the item for the price p, which is not higher then ziand you realize some positive consumer surplus. • Note: The probability that the price p equals your bid giand your willingness to payzi is close to zero: • probability (p = gj = gi= zi) = 0

  14. Another person has a higher bid 1. zj= gj= 28 • Would person ibetter off if he bids ĝi=30 and not gi=zi=25? cs = -3 zi= 25 p = gj= 28 ĝi= 30 • Person igets the item and has to pay a price which is higher than his true willingness to pay zi=25 < p=gj=28. • Then he gets the item…. --- But, why ?

  15. Another person gets the item 2. zj= gj= 28 • Would person ibetter off if he does not bid gi=zi=25? zi= 25 p = ĝi= 27 gj= 28 • Person i doesn´t get the item and person j has to pay a higher price as before p=ĝi=27 < gj=28. Reduced cs for j – but what is the advantage for person i?

  16. Another person gets the item 3. zj= gj= 28 • Would person ibetter off if he bids ği<ziand not gi=zi=25? large csfor j p = ği= 21 zi= 25 gj= 28 • Person i doesn´t get the item and person j has to pay • a lower price as before p=ği=21 < zi=25 < gj=28. • Persons i and j are friends? – Again: what is the • advantage for i?

  17. Another person gets the item • If your bid is higher than your true willingness to pay, there is an increasing probability that you get the item for the price p, which is higher then ziand you have to pay more than your true evaluation and you realize some negative consumer surplus. • If another guy gets the item, then he has to pay the price of the second highest bid. • Be careful and don´t try to influence the price of others! • Don´t try to influence the consumer surplus of others!

  18. Second price auction is equal to an ”English auction” • The auctioneerstarts with a reserve priceand bidders successively offer higher prices - bids. Each bid exceed the previous by some minimal bid increment. • When no participant is willing to increase the bid further, then the item is awarded to the highest bidder. • Normally the auction stops below the willingness to pay of the highest bidder. • Therefore, he pays the second highest bid!

  19. Result is the same1. • Would person ibetter off if he does anything else? cs = 5 12 15 17 18 20 gi gj gi gj p = gi zi= 25 • The result is the same. He gets the item and has to pay p=gi=20, the price of the second highest bid and gets a true consumer surplus of 5. Therefore, gi=zi=25 was high enough.

  20. First price auction is equal to an ”Dutch auction” • The auctioneerstarts with a high priceand lowers the price successively until the first bidder rises his finger. • When no participant rises his finger he reduces the price more and more. • The auction stops until the first bidder shouts: “ Mine! ” • Then he pays the price were the auction stops, when he rises his finger. • This is the first price!

  21. Another Result 1. • The auctioneer begins with highest price, say 100. 60 60 70 80 90 100 „MINE !“ p = zi • Person igets the itemand has to pay his bid! p = 60 = zi

  22. What´s the problem for person i? 1. • The auctioneer begins with highest price, say 100. 40 60 70 80 90 100 gj p = zi • Person igets the itemand has to pay his bid! • But: What is in between the gap to the next highest bid? • Person i wants to wait until the auctioneer achieves a border

  23. Create the data firstidea: averageprice = 7,08 secondproposal: p = 10 and 3 customers

  24. Create the data

  25. Create the data

  26. Create the data

  27. y = -0,7863x + 15,536 R² = 0,9857 estimation: p(q) = 15 - ¾ q R = p*q = 9*9 = 81

  28. REVENUE

  29. consumerssurplus =zi– p 6 = (15-9) + 2(14-9) + (12-9) + 3(10-9) + 2(9-9) = 22 5 5 3 1 1 1 0 0 p=9 R = p * q = 81 q=9

  30. profit = revenue- costs costs per unit: c = 6 price ↑ p = 10 quantity ↓q = 7 revenue↓ r = 70 profit ↓ π= 28

  31. profit = revenue + subsidy Subsidy per unit s = 7 price↓ p = 5 quantity ↑ q = 13 revenue↓ r = 65 profit↑ π = 156 But: priceis not zero! Additional costs per unitorsubsidyinfluencesthe marginal behaviour. pricereducing: p = 5 quantityincreasing:q =13

  32. T-shirtas a presentforeveryparticipant– logicalequivalenttothe total pricediscriminatingmonopolist. consumerssurplus= zi– p= (15-0) + 2(14-0) + … + 2(0-0) = 138 =monopolisticprofit p = 0

  33. Compare Theory vs. Experiment I ! ! EXP: q= 9

  34. Compare Theory vs. Experiment II EXP: p= 9 ! !

  35. Compare Theory vs. Experiment III EXP: q = 7 EXP: p = 10 EXP: π= 28

  36. Literatur A. ROTT, Die Nachfragefunktion: Ein ökonomisches Experiment für die Lehre, Dortmunder Diskussionsbeiträge zur Wirtschaftspolitik, Nr. 92, Juli 1999 H. VARIAN, Intermediate Microeconomics - A modern Approach, Norton, Chapter 17: Auctions T. Bergstrom, J. Miller, Experiments with Economic Principles, McGraw-Hill, 1998. (http://zia.hss.cmu.edu/miller/eep/eep.html) Thankyouforattention! Vielen Dank für Ihre Aufmerksamkeit Prof. Dr. Stephan M. Rometsch Berufsakademie Eisenach Staatliche Studienakademie Thüringen

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