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Chapter Nine,Buying and Selling 購買和銷售,Structure,Endowments (稟賦) Budget constraints with endowments Net demands Price offer curve Example: Labor supply Comparative statics Slutsky equation revisited,Buying 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 (稟賦). A consumers 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. What is the endowments value? For which consumption bundles may it be exchanged?,Endowments,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 endowments value.,Budget Constraints Revisited,So, given p1 and p2, the budget constraint for a consumer with an endowment is The budget set is,Budget Constraints Revisited,x2,x1,w1,w2,Budget Constraints Revisited,x2,x1,w1,w2,Budget set,Changing Endowments,x2,x1,(w1 ,w2 ),(w1 ”,w2 ”),(w1,w2 ),Changing the endowment,Changing Prices,x2,x1,w1,w2,Changing prices of the endowment,Changing Prices,x2,x1,w1,w2,Budget set,Changing Prices,x2,x1,w1,w2,The endowment point is always on the budget constraint.,So price changes pivot the constraint about the endowment point.,Net Demand,The constraint is That is, the sum of the values of a consumers net demands (凈需求) is zero.,Net Demands,Suppose and p1=2, p2=3. Then the constraint is If the consumer gross demands (毛需求)(x1*,x2*) = (7,4), then 3 good 1 units exchange for 2 good 2 units. Net demands are x1*- w1 = 7-10 = -3 and x2*- w2 = 4 - 2 = +2.,Net Demands,p1=2, p2=3, x1*-w1 = -3 and x2*-w2 = +2 so,The 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 Different Prices,x2,x1,w1,w2,x2*,x1*,At prices (p1,p2) the consumer sells units of good 1 to acquire more units of good 2.,Net seller of good 1,x2,x1,w1,w2,x2*,x1*,At prices (p1,p2) the consumer sells units of good 2 to acquire more of good 1.,Net buyer of good 1,Net Demands at Different Prices,x2,x1,x2*=w2,x1*=w1,At prices (p1”,p2”) the consumer consumes her endowment; net demands are all zero.,Autarky,Net Demands at Different Prices,Offer Curve,x2,x1,w1,w2,Price-offer curve contains all the utility-maximizing gross demands for which the endowment can be exchanged.,Net Demands,x2,x1,w1,w2,Price-offer curve,Sell good 1, buy good 2,Net Demands,x2,x1,w1,w2,Price-offer curve,Buy good 1, sell good 2,因課件太大,無法上傳。本處刪除了2張關(guān)于提供曲線和需求曲線的幾何圖形的圖片格式,請看教材圖形。cym,Some Results about Price Change,If 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. If a consumer if a net buyer of a good, when the price decreases, the consumer will remain a buyer and be better off.,因課件太大,無法上傳。本處刪除了2張關(guān)于價格變動(商品1價格下降、上升)的幾何圖形的圖片格式,請看教材圖形。cym,Labor Supply,A worker is endowed with $m of nonlabor income and R hours of time which can be used for labor or leisure. w = (R, m). Consumption goods price is pc. w is the wage rate.,Labor Supply,The workers budget constraint is where C, R denote gross demands for the consumption good and for leisure. That is,endowment value,expenditure,Labor Supply,rearranges to,Labor Supply,C,R,R,endowment,m,($),Labor Supply,C,R,R,endowment,m,Labor Supply,C,R,R,endowment,m,Labor Supply,C,R,R,endowment,m,slope = , the real wage rate,Labor Supply,C,R,R,endowment,m,C*,R*,leisure demanded,labor supplied,Labor Supply Curve,Slutskys 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 Slutskys equation?,Slutskys Equation Revisited,A change in p1 or p2 changes so there will be an additional income effect, called the endowment income effect (稟賦收入效應). Slutskys decomposition will thus have three components a pure substitution effect an (ordinary) income effect, and an endowment income effect.,Slutskys Equation Revisited,x1,w2,w1,x2,x2,x1,Initial prices are (p1,p2).,Slutskys Equation Revisited,x1,w2,w1,x2,x2,x1”,x2”,Initial prices are (p1,p2). Final prices are (p1”,p2”).,x1,Slutskys Equation Revisited,x1,w2,w1,x2,x2,x1”,x2”,Initial prices are (p1,p2). Final prices are (p1”,p2”).,How is the change in demand from (x1,x2) to (x1”,x2”) explained?,x1,Slutskys Equation Revisited,x1,w2,w1,x2,x2,x1,Initial prices are (p1,p2).,Slutskys Equation Revisited,x1,w2,w1,x2,x2,x1”,x2”,Initial prices are (p1,p2). Final prices are (p1”,p2”).,x1,Slutskys Equation Revisited,x1,w2,w1,x2,Pure substitution effect,Slutskys Equation Revisited,x1,w2,w1,x2,Pure substitution effect,Slutskys Equation Revisited,x1,w2,w1,x2,Pure substitution effect,Ordinary income effect,Slutskys Equation Revisited,x1,w2,w1,x2,Pure substitution effect,Ordinary income effect,Slutskys Equation Revisited,x1,w2,w1,x2,Pure substitution effect,Ordinary income effect,Endowment income effect,Slutskys Equation Revisited,x1,w2,w1,x2,Pure substitution effect,O

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