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1、Chapter NineBuying and Selling购买和销售购买和销售StructureuEndowments（禀赋）禀赋）uBudget constraints with endowmentsuNet demandsPrice offer curveuExample:Labor supplyComparative staticsuSlutsky equation revisitedBuying and SellinguTrade involves exchange-when something is bought something else must be sold.uWhat
2、will be bought?What will be sold?uWho will be a buyer?Who will be a seller?Buying and SellinguAnd how are incomes generated?uHow does the value of income depend upon commodity prices?uHow can we put all this together to explain better how price changes affect demands?EndowmentsuThe list of resource
3、units with which a consumer starts is his endowment（禀赋）禀赋）.uA consumers endowment will be denoted by the vector (omega).EndowmentsuE.g.states that the consumer is endowed with 10 units of good 1 and 2 units of good 2.uWhat is the endowments value?uFor which consumption bundles may it be exchanged?En
4、dowmentsup1=2 and p2=3 so the value of the endowment isuQ:For which consumption bundles may the endowment be exchanged?uA:For any bundle costing no more than the endowments value.Budget Constraints RevisiteduSo,given p1 and p2,the budget constraint for a consumer with an endowment isuThe budget set
5、is Budget Constraints Revisitedx2x1w w1 1w w2 2Budget Constraints Revisitedx2x1w w1 1w w2 2Budget setChanging Endowmentsx2x1(w1,w2)(w1”,w2”)(w1,w2)Changing the endowmentChanging Pricesx2x1w w1 1w w2 2Changing prices of the endowmentChanging Pricesx2x1w w1 1w w2 2Budget setChanging Pricesx2x1w w1 1w
6、w2 2The endowment point is always on the budget constraint.So price changes pivot theconstraint about the endowment point.Net DemanduThe constraintisuThat is,the sum of the values of a consumers net demands（净需求）净需求）is zero.Net DemandsuSuppose and p1=2,p2=3.Then the constraint is uIf the consumer gro
7、ss demands(毛需毛需求）求）(x1*,x2*)=(7,4),then 3 good 1 units exchange for 2 good 2 units.Net demands are x1*-w w1=7-10=-3 andx2*-w w2=4-2=+2.Net Demandsp1=2,p2=3,x1*-w w1=-3 and x2*-w w2=+2 soThe purchase of 2 extra good 2 units at$3 each is funded by giving up 3 good 1 units at$2 each.Net Demands at Diff
8、erent Pricesx2x1w w1 1w w2 2x2*x1*At prices(p1,p2)the consumersells units of good 1 to acquiremore units of good 2.Net seller of good 1x2x1w w1 1w w2 2x2*x1*At prices(p1,p2)the consumersells units of good 2 to acquiremore of good 1.Net buyer of good 1Net Demands at Different Pricesx2x1x2*=w w2 2x1*=
9、w w1 1At prices(p1”,p2”)the consumerconsumes her endowment;netdemands are all zero.AutarkyNet Demands at Different PricesOffer Curvex2x1w w1 1w w2 2Price-offer curve contains all theutility-maximizing gross demands for which the endowment can be exchanged.Net Demandsx2x1w w1 1w w2 2Price-offer curve
10、Sell good 1,buy good 2Net Demandsx2x1w w1 1w w2 2Price-offer curveBuy good 1,sell good 2Some Results about Price ChangeuIf a consumer is a net seller of a good,when the price of the good decreases,if she remains a buyer then the consumer is worse off.uIf a consumer if a net buyer of a good,when the
11、price decreases,the consumer will remain a buyer and be better off.Labor SupplyuA worker is endowed with$m of nonlabor income and R hours of time which can be used for labor or leisure.w w=(R,m).uConsumption goods price is pc.uw is the wage rate.Labor SupplyuThe workers budget constraint iswhere C,R
12、 denote gross demands for the consumption good and for leisure.That isendowment valueexpenditureLabor Supplyrearranges toLabor SupplyCRRendowmentm($)Labor SupplyCRRendowmentmLabor SupplyCRRendowmentmLabor SupplyCRRendowmentmslope=,the real wage rateLabor SupplyCRRendowmentmC*R*leisuredemanded labors
13、uppliedLabor Supply CurveSlutskys Equation RevisiteduSlutsky:changes to demands caused by a price change are the sum ofa pure substitution effect,andan income effect.uThis assumed that income y did not change as prices changed.But does change with price.How does this modify Slutskys equation?Slutsky
14、s Equation RevisiteduA change in p1 or p2 changes so there will bean additional income effect,called the endowment income effect（禀赋收入效应）禀赋收入效应）.uSlutskys decomposition will thus have three componentsa pure substitution effectan(ordinary)income effect,andan endowment income effect.Slutskys Equation R
15、evisitedx1w w2w w1x2x2x1Initial prices are(p1,p2).Slutskys Equation Revisitedx1w w2w w1x2x2x1”x2”Initial prices are(p1,p2).Final prices are(p1”,p2”).x1Slutskys Equation Revisitedx1w w2w w1x2x2x1”x2”Initial prices are(p1,p2).Final prices are(p1”,p2”).How is the change in demandfrom(x1,x2)to(x1”,x2”)e
16、xplained?x1Slutskys Equation Revisitedx1w w2w w1x2x2x1Initial prices are(p1,p2).Slutskys Equation Revisitedx1w w2w w1x2x2x1”x2”Initial prices are(p1,p2).Final prices are(p1”,p2”).x1Slutskys Equation Revisitedx1w w2w w1x2Pure substitution effectSlutskys Equation Revisitedx1w w2w w1x2Pure substitution
17、 effectSlutskys Equation Revisitedx1w w2w w1x2Pure substitution effectOrdinary income effectSlutskys Equation Revisitedx1w w2w w1x2Pure substitution effectOrdinary income effectSlutskys Equation Revisitedx1w w2w w1x2Pure substitution effectOrdinary income effectEndowment income effectSlutskys Equati
18、on Revisitedx1w w2w w1x2Pure substitution effectOrdinary income effectEndowment income effectSlutskys Equation RevisitedOverall change in demand caused by achange in price is the sum of:(i)a pure substitution effect(ii)an ordinary income effect(iii)an endowment income effectSlutsky Equation with EndowmentsOr(-)(+)(+)