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1、6.均衡与拍卖,1,6.1 市场均衡(Market Equilibrium),A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.在某价格下，市场需求量等于市场供给量。此时的价格为市场均衡价格，此时的数量为均衡数量。,2,6.1.1 均衡的确定,p,q,q=D(p),Marketdemand,Marketsupply,q=S(p),p*,q*,D(p*)=S(p*);the marketis in equilibrium.,3,Ma
2、rket Equilibrium,S(p),D(p)S(p);an excessof quantity supplied overquantity demanded.,p*,p,D(p),Market price must fall towards p*.,4,Market Equilibrium,D(p”),D(p”)S(p”);an excessof quantity demandedover quantity supplied.,p”,S(p”),Market price must rise towards p*.,p*,5,Two special cases,when quantity
3、 supplied is fixed,independent of the market price,andwhen quantity supplied is extremely sensitive to the market price.,6,6.1.2 比较静态学,需求变动对市场均衡的影响供给变动对市场均衡的影响需求和供给同时变动对市场均衡的影响,7,均衡的变动,8,供求同时变动对均衡的影响,9,6.2 税负与Pareto最优,6.2.1 从量税与市场均衡从量税收对市场均衡有何影响？如何影响价格？对均衡数量有何影响？由谁来负担税收？税收对社会福利有何影响？,10,从量税,税率为 t，买者支
4、付的价格为 pb,卖者得到的价格为 ps，则有,在征收税收的情况下，市场均衡条件变为：,11,从量税与市场均衡,均衡价格增加，均衡数量降低卖者只得到了 ps=pb-t.,$t,pb,qt,ps,12,6.2.2 谁承担了税收？,Tax paid by buyers,Tax paid by sellers,13,弹性与税收的转嫁,税收的负担比例与该产品的需求弹性和供给弹性的大小相关。假定：需求曲线 p=a-bq供给曲线 p=c+dq每销售一单位产品需付税 t销售者和购买者各负担多少？,14,q,O,P,S,S,D,D,q*,p*,ST,ST,A,B,C,$t,D,D,A,B,C,D,D,B,C,
5、A,弹性与税收的转嫁,15,q,O,P,S,S,D,D,q*,p*,ST,ST,A,B,C,$t,S,S,ST,ST,$t,A,B,C,S,S,ST,ST,$t,A,B,C,弹性与税收的转嫁,16,6.2.3 税收的福利损失,税收对社会福利的影响：即消费者剩余变动和生产者剩余变动之和。,17,税收的福利损失和自价格弹性,如果 eD=0 或 eS=0，则社会福利损失为零,18,税收的福利损失和自价格弹性,p,市场需求,市场供给,p*,q*,不征税的情形,q,19,无税收时的福利,CS,PS,20,税收的福利损失,CS,PS,Tax,福利损失,21,税收的福利损失,22,税收的福利损失和自价格弹性
6、,p,q,p*,q*,$t,pb,qt,ps,23,税收的福利损失和自价格弹性,p,q,p*,q*,$t,pb,qt,ps,24,税收的福利损失和自价格弹性,p,q,ps=p*,$t,pb,qt=q*,25,6.3 Auctions,Who Uses Auctions?Owners of art,cars,stamps,machines,mineral rights etc.Why auction?Because many markets are imperfect and it is hard to discover potential buyers true valuations of y
7、our asset.Auctions help to discover this information.,26,6.3.1 Types of Auctions,English auction:bids are public announcementsbid price rises until there are no further bidshighest bid wins winner pays his bid.,通常以保留价格起拍；每一个出价都要超出前一个出价某个最小的竞价增量。,27,网上英式拍卖,传统拍卖对每件拍卖品来说，不需要事先确定拍卖时间，一般数分钟即可结束拍卖；而对于网上拍卖
8、来说，则需要事先确定拍卖的起止时间，一般是数天或数周。例如，在eBay拍卖站点，拍卖的持续时间一般是7天。,28,网上拍卖中的“狙击”,由于网上拍卖的持续时间较长，这使得许多网上竞买人具有“狙击”（Sniping）情况，即直到拍卖结束前的最后数分钟才开始出价，试图提交一个能击败所有其他竞买人的出价，并使得其他竞买人没有时间进行反击。,29,如何解决？,解决在拍卖的最后时刻出价的一种方式是在固定的时期内增加“扩展期”。例如，扩展期设定为五分钟，这意味着如果在最后五分钟内有出价，则拍卖的关闭时间自动延长五分钟。这一过程一直持续下去，直到五分钟以内没有出价，拍卖才终止。这种方式有效地解决了“狙击”现
9、象。,30,另一种解决方法,另一种方法是实施“代理竞价”机制。例如，eBay解释它的代理系统为“每一个竞买人都有一个代理帮助出价，竞买人只需告诉代理希望为该物品支付的最高价格，代理会自动出价，直到达到最高价格”。,31,英式拍卖的缺点,英式拍卖的缺点是：既然获胜的竞买人的出价只需比前一个最高价高一点，那么每个竞买人都不愿马上按照其预估价出价。另外，竞买人要冒一定的风险，他可能会被令人兴奋的竞价过程吸引，出价超出了预估价，这种心理现象称为“赢者诅咒（Winners Curse）”。,32,Types of Auctions（2）,Sealed-bid first-price auction（首价
10、密封投标拍卖）:bids are private informationbids are made simultaneouslyhighest bid wins winner pays his bid.,33,多个物品单位的拍卖,当同时拍卖多个物品时，这种拍卖形式被称做歧视性价格拍卖(discriminatory auction)，又称做多价拍卖(multiple-price auction)。决定获胜者的规则：密封的投标从高到低排序，被拍卖的物品从最高的投标价格开始依次分配，直到物品卖完。每个获胜者支付的价格就是自己的投标值。,34,Types of Auctions（3）,Sealed-b
11、id second-price auction（次价密封投标拍卖）:bids are private informationbids are made simultaneouslyhighest bidder wins winner pays second-highest bidalso known as a Vickrey auction.,35,多个物品单位的拍卖,当多个物品单位的拍卖时，这种拍卖形式被称做同价拍卖，又称为竞争拍卖或者边际价格拍卖。决定获胜者的规则：密封的投标从高到低排序，被拍卖的物品从最高的投标价格开始依次分配，直到物品卖光。所有的获胜者将支付同样的价格。,36,支付什么
12、价格？,这个价格可以等于获胜者中的最低投标此时称为N价拍卖；也可以等于失败者中的最高投标此时称为N+1价拍卖。,37,Types of Auctions（4）,Dutch auction（荷兰式拍卖）:auctioneer announces a high bid and then gradually lowers the bidfirst buyer to accept wins and pays that price.荷兰式拍卖亦称“减价拍卖”，它是指拍卖标的的竞价由高到低依次递减直到第一个竞买人应价（达到或超过底价）时击槌成交的一种拍卖。,38,Reserve Price,A selle
13、r specified bid level below which no sale is made.,39,6.3.2 Economists Classification of Auctions,（个人价值拍卖）Private-value auctions:every potential buyer knows for sure her own valuation of the item for saleall these individual valuations are independent of each other.例如艺术品的拍卖。,40,Economists Classifica
14、tion of Auctions,（共同价值拍卖）Common-value auctions:item for sale has the same value to every potential buyerpotential buyers differ in their own estimates of this common value例如，拍卖一个里面装了一定数量钱的钱袋。,41,赌石头,一块未经开窗的原石，除形状和重量外谁也说不清里面是什么。即使到了科学发达的今天，也没有一种仪器能通过其外壳判断出其内是“宝玉”还是“败絮”，唯有切割剖开才知道。赌石人凭着自己的经验，根据外皮的颜色、纹理
15、，猜测里面玉石的成色，然后竞价购买。,42,6.3.3 拍卖设计,Goals:帕累托有效出售者利润最大化,43,Auction Design,帕累托有效the item must sell to the buyer with the highest valuation of the item.Which auctions are Pareto efficient?,44,Auctions and Efficiency,不具有保留价格的英国式拍卖能够保证帕累托有效率结果的实现；荷兰式拍卖通常并没有保证评价最高的人一定会赢得商品；Sealed-bid first-price auction nee
16、d not be efficient.No buyer knows other buyers valuations,so the highest valuation buyer may bid too low and lose to another bidder.Sealed-bid second-price auction is Pareto efficient,45,Why Use a Reserve Price?,Suppose there are 2 buyers.The seller believes each buyers valuation is$20 with chance 1
17、/2 and$50 with chance 1/2.i.e.with chance 1/4 each,the seller believes she faces buyer valuations($20,$20),($20,$50),($50,$20)and($50,$50).,46,Why Use a Reserve Price?,Use an English auction.Bids must be raised by at least$1.With chance 1/4 each,winning bids will be$20,$21,$21 and$50 if there is no
18、reserve price.Sellers expected revenue is($20+$21+$21+$50)/4=$28with no reserve price.,47,Why Use a Reserve Price?,With chance 1/4 each,the seller believes she faces buyer valuations($20,$20),($20,$50),($50,$20)and($50,$50).Set a reserve price of$50.With chance 1/4 there will be no sale.With chance
19、3/4 the winning bid will be$50.Sellers expected revenue is,48,Reserve Price and Efficiency,The reserve price causes an efficiency loss since,with chance 1/4,there is no trade.,49,Second-Price,Sealed-Bid Auction,bids are private informationbids are made simultaneouslyhighest bidder wins winner pays s
20、econd-highest bidalso known as a Vickrey auction.,50,Second-Price,Sealed-Bid Auction,No bidder knows any other bidders true valuation of the item for sale.Yet,it is individually rational for each bidder to state truthfully his own valuation.Why?E.g.two bidders with true valuations v1 and v2.,51,Seco
21、nd-Price,Sealed-Bid Auction,E.g.two bidders with true valuations v1 and v2.Bids are b1 and b2.Expected gain to bidder 1 is,52,Second-Price,Sealed-Bid Auction,How is this maximized?If v1 b2,then maximize the prob.of winning;i.e.set b1=v1.If v1 b2,then minimize the prob.of winning;i.e.set b1=v1.Either
22、 way,telling the truth is best!,53,Second-Price,Sealed-Bid Auction,Since truth-telling is best for every bidder,the highest valuation bidder will win.Hence the second-price,sealed-bid auction is Pareto-efficient.,54,Common-Value Auctions,The item for sale has the same value to every potential buyer.
23、Potential buyers differ in their own estimates of this common value.Bidder is estimate is vi=v+i,where v is the common value and i is bidder is estimation error.,55,Common-Value Auctions,If every bid is truthful,the winner is the bidder with the largest estimation error i so a truthful winner on average pays more than the true value v-the winners curse.,56,
