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Chapter NineBuying and SellingStructureuEndowmentsuBudget constraints with endowmentsuNet demandsuLabor supplyBuying and SellinguTrade involves exchange-when something is bought something else must be sold.uWhat 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 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.(,)(,)1210 2EndowmentsuE.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?(,)(,)1210 2Endowmentsup1=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.(,)(,)1210 2 pp11222103226 Budget Constraints RevisiteduSo,given p1 and p2,the budget constraint for a consumer with an endowment isuThe budget set is(,)12p xp xpp1 12 21 122 .(,),.xxp xp xppxx121 12 211221200 Budget Constraints Revisitedx2x1 1 1 2 2p xp xpp1 12 21 122 Budget Constraints Revisitedx2x1 1 1 2 2p xp xpp1 12 21 122 Budget set (,),xxp xp xppxx121 12 211221200 Budget Constraints Revisitedx2x1(1,2)(1”,2”)(1,2)Changing the endowmentBudget Constraints Revisitedx2x1 1 1 2 2p xp xpp1 12 21 122 p xp xpp1 12 21 122 Changing prices of the endowmentBudget Constraints Revisitedx2x1 1 1 2 2p xp xpp1 12 21 122 p xp xpp1 12 21 122 Budget setBudget Constraints Revisitedx2x1 1 1 2 2p xp xpp1 12 21 122 The endowment point is always on the budget constraint.p xp xpp1 12 21 122 Budget Constraints Revisitedx2x1 1 1 2 2p xp xpp1 12 21 122 The endowment point is always on the budget constraint.p xp xpp1 12 21 122 So price changes pivot theconstraint about the endowment point.Budget Constraints RevisiteduThe constraintisuThat is,the sum of the values of a consumers net demands（净需求）净需求）is zero.pxpx1112220()().p xp xpp1 12 21 122 Net DemandsuSuppose and p1=2,p2=3.Then the constraint is uIf the consumer gross 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*-1=7-10=-3 andx2*-2=4-2=+2.(,)(,)1210 2 p xp xpp1 12 2112226 .Net Demandsp1=2,p2=3,x1*-1=-3 and x2*-2=+2 sopxpx11122223320()()().The purchase of 2 extra good 2 units at$3 each is funded by giving up 3 good 1 units at$2 each.Net Demandsx2x1 1 1 2 2pxpx1112220()()x2*x1*At prices(p1,p2)the consumersells units of good 1 to acquiremore units of good 2.Net seller of good 1Net Demandsx2x1 1 1 2 2p xp xpp1 12 21 122 x2*x1*At prices(p1,p2)the consumersells units of good 2 to acquiremore of good 1.Net buyer of good 1Net Demandsx2x1pxpx1112220()()x2*=2 2x1*=1 1At prices(p1”,p2”)the consumerconsumes her endowment;netdemands are all zero.p xp xpp1 12 21122 AutarkyNet Demandsx2x1 1 1 2 2pxpx1112220()()Price-offer curve contains all theutility-maximizing gross demands for which the endowment can be exchanged.Net Demandsx2x1 1 1 2 2pxpx1112220()()Price-offer curveSell good 1,buy good 2Net Demandsx2x1 1 1 2 2pxpx1112220()()Price-offer curveBuy good 1,sell good 2Labor SupplyuA worker is endowed with$m of nonlabor income and R hours of time which can be used for labor or leisure.=(R,m).uConsumption goods price is pc.uw is the wage rate.Labor SupplyuThe workers budget constraint iswhere C,R denote gross demands for the consumption good and for leisure.That isp Cw RRmc ()p CwRwRmc endowment valueexpenditureLabor Supplyp Cw RRmc ()rearranges toCwpRmwRpcc .Labor SupplyCRRendowmentm($)Labor SupplyCRRendowmentCwpRmwRpcc mLabor SupplyCRRendowmentCwpRmwRpcc mwRpc mLabor SupplyCRRendowmentCwpRmwRpcc mwRpc mslope=,the real wage rate wpcLabor SupplyCRRendowmentCwpRmwRpcc mwRpc mC*R*leisuredemanded laborsuppliedLabor 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?ypp 1 122 Slutskys Equation RevisiteduA change in p1 or p2 changes so there will bean additional income effect,called the endowment income effect.uSlutskys decomposition will thus have three componentsa pure substitution effectan(ordinary)income effect,andan endowment income effect.ypp 1 122 Slutsky Equation with Endowments1111111111111(,()()(,)(,)sxp m pxpxp mxp mxppmm11111111111(,()()(,)()sxp m pxpxp mxppmOr(-)(+)(+)Slutskys Equation Revisitedx1 2 1x2x2x1Initial prices are(p1,p2).Slutskys Equation Revisitedx1 2 1x2x2x1”x2”Initial prices are(p1,p2).Final prices are(p1”,p2”).x1Slutskys Equation Revisitedx1 2 1x2x2x1”x2”Initial prices are(p1,p2).Final prices are(p1”,p2”).How is the change in demandfrom(x1,x2)to(x1”,x2”)explained?x1Slutskys Equation Revisitedx1 2 1x2x2x1Initial prices are(p1,p2).Slutskys Equation Revisitedx1 2 1x2x2x1”x2”Initial prices are(p1,p2).Final prices are(p1”,p2”).x1Slutskys Equation Revisitedx1 2 1x2Pure substitution effectSlutskys Equation Revisitedx1 2 1x2Pure substitution effectSlutskys Equation Revisitedx1 2 1x2Pure substitution effectOrdinary income effectSlutskys Equation Revisitedx1 2 1x2Pure substitution effectOrdinary income effectSlutskys Equation Revisitedx1 2 1x2Pure substitution effectOrdinary income effectEndowment income effectSlutskys Equation Revisitedx1 2 1x2Pure 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 effect
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