Chapter NineBuying and SellingSlide 3EndowmentsSlide 5Slide 6Slide 7Budget Constraints RevisitedSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Net DemandsSlide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Labor SupplySlide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slutsky’s Equation RevisitedSlide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Chapter NineBuying and SellingBuying and SellingTrade involves exchange -- when something is bought something else must be sold.What will be bought? What will be sold?Who will be a buyer? Who will be a seller?Buying and SellingAnd how are incomes generated?How does the value of income depend upon commodity prices?How can we put all this together to explain better how price changes affect demands?EndowmentsThe list of resource units with which a consumer starts is his endowment.A consumer’s endowment will be denoted by the vector (omega).EndowmentsE.g.states that the consumer is endowed with 10 units of good 1 and 2 units of good 2.   ( , ) ( , )1 210 2EndowmentsE.g.states that the consumer is endowed with 10 units of good 1 and 2 units of good 2.What is the endowment’s value?For which consumption bundles may it be exchanged?   ( , ) ( , )1 210 2Endowmentsp1=2 and p2=3 so the value of the endowment isQ: For which consumption bundles may the endowment be exchanged?A: For any bundle costing no more than the endowment’s value.( , ) ( , ) 1 210 2p p1 1 2 22 10 3 2 26      Budget Constraints RevisitedSo, given p1 and p2, the budget constraint for a consumer with an endowment isThe budget set is ( , ) 1 2p x p x p p1 1 2 2 1 1 2 2   .( , ) ,, .x x p x p x p px x1 2 1 1 2 2 1 1 2 21 20 0    Budget Constraints Revisitedx2x1p x p x p p1 1 2 2 1 1 2 2   Budget Constraints Revisitedx2x1p x p x p p1 1 2 2 1 1 2 2   Budget set( , ) ,,x x p x p x p px x1 2 1 1 2 2 1 1 2 21 20 0    Budget Constraints Revisitedx2x1p x p x p p1 1 2 2 1 1 2 2   p x p x p p1 1 2 2 1 1 2 2' ' ' '   Budget Constraints Revisitedx2x1p x p x p p1 1 2 2 1 1 2 2   p x p x p p1 1 2 2 1 1 2 2' ' ' '   Budget setBudget Constraints Revisitedx2x1p x p x p p1 1 2 2 1 1 2 2   The endowment point is always on the budget constraint.p x p x p p1 1 2 2 1 1 2 2' ' ' '   Budget Constraints Revisitedx2x1p x p x p p1 1 2 2 1 1 2 2   The endowment point is always on the budget constraint.p x p x p p1 1 2 2 1 1 2 2' ' ' '   So price changes pivot theconstraint about the endowment point.Budget Constraints RevisitedThe constraintisThat is, the sum of the values of a consumer’s net demands is zero.p x p x1 1 1 2 2 20( ) ( ) .    p x p x p p1 1 2 2 1 1 2 2   Net DemandsSuppose and p1=2, p2=3. Then the constraint is If the consumer demands (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.( , ) ( , ) 1 210 2p x p x p p1 1 2 2 1 1 2 226    .Net Demandsp1=2, p2=3, x1*-1 = -3 and x2*-2 = +2 sop x p x1 1 1 2 2 22 3 3 2 0( ) ( )( ) .        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p x p x1 1 1 2 2 20( ) ( )    x2*x1*At prices (p1,p2) the consumersells units of good 1 to acquiremore units of good 2.Net Demandsx2x1p x p x p p1 1 2 2 1 1 2 2' ' ' '   x2*x1*At prices (p1’,p2’) the consumersells units of good 2 to acquiremore of good 1.Net Demandsx2x1p x p x1 1 1 2 2 20( ) ( )    x2*=x1*=At prices (p1”,p2”) the consumerconsumes her endowment; netdemands are all zero.p x p x p p1 1 2 2 1 1 2 2" " " "   Net Demandsx2x1p x p x1 1 1 2 2 20( ) ( )    Price-offer curve contains all theutility-maximizing gross demands for which the endowment can be exchanged.Net Demandsx2x1p x p x1 1 1 2 2 20( ) ( )    Price-offer curveSell good 1, buy good 2Net Demandsx2x1p x p x1 1 1 2 2 20( ) ( )    Price-offer curveBuy good 1, sell good 2Labor SupplyA worker is endowed with $m of nonlabor income and R hours of time which can be used for labor or leisure.  = (R,m).Consumption good’s price is pc.w is the wage rate.Labor SupplyThe worker’s budget constraint iswhere C, R denote gross demands for the consumption good and for leisure. That isp C w R R mc  ( )p C wR wR mc  endowment valueexpenditureLabor Supplyp C w R R mc  ( )rearranges toCwpRm wRpc c .Labor SupplyCRRendowmentm($)Labor SupplyCRRendowmentCwpRm wRpc c mLabor SupplyCRRendowmentCwpRm wRpc c m wRpcmLabor SupplyCRRendowmentCwpRm wRpc c m wRpcmslope = , the ‘real wage rate’wpcLabor SupplyCRRendowmentCwpRm wRpc c m wRpcmC*R* leisuredemanded laborsuppliedSlutsky’s Equation RevisitedSlutsky: changes to demands caused by a price change are the sum of–a pure substitution effect, and–an income effect.This assumed that income y did not change as prices changed. But does change with price. How does this modify Slutsky’s equation?y p p 1 1 2 2 Slutsky’s Equation RevisitedA change in p1 or p2 changes so there will bean additional income effect, called the endowment income effect.Slutsky’s decomposition will thus have three components–a pure substitution effect–an (ordinary) income effect, and–an endowment income effect.y p p 1 1 2 2 Slutsky’s Equation Revisitedx121x2x2’x1’Initial prices are (p1’,p2’).Slutsky’s Equation Revisitedx121x2x2’x1”x2”Initial prices are (p1’,p2’).Final prices are (p1”,p2”).x1’Slutsky’s Equation Revisitedx121x2x2’x1”x2”Initial prices