北京大学国家发展研究院2014年秋季学期 本科双学位课程 中级微观经济学 2班 第六讲 购买和销售 任课教师 李力行 第9章 购买和销售 Endowments 禀赋 禀赋 Budget constraints with endowments Net demands Price offer curve Example Labor supply Comparative statics Slutsky equation revisited Buying and Selling How is income generated 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 How does the value of income depend upon commodity prices Endowments The list of resource with which a consumer starts is his endowment A consumer s endowment will be denoted by the vector 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 12 10 2 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 endowment s value 12 10 2 pp 1122 2103226 Budget Constraints Revisited So given p1 and p2 the budget constraint for a consumer with an endowment is The budget set is 12 p xp xpp 11221122 xxp xp xpp xx 121 12 21122 12 00 Budget Constraints Revisited x2 x1 1 1 2 2 p xp xpp 11221122 Budget set xxp xp xpp xx 121 12 21122 12 00 Budget Constraints Revisited x2 x1 1 1 2 2 p xp xpp 11221122 p xp xpp 1 1221122 Budget set Budget Constraints Revisited x2 x1 1 1 2 2 p xp xpp 11221122 The endowment point is always on the budget constraint p xp xpp 1 1221122 So price changes pivot the constraint around the endowment point Budget Constraints Revisited The constraint is That is the sum of the values of a consumer s net demand is zero pxpx 111222 0 p xp xpp 11221122 Net Demands Suppose and p1 2 p2 3 Then the constraint is If the consumer demands x1 x2 7 4 then 3 units of good 1 exchange for 2 units of good 2 Net demands are x1 1 7 10 3 and x2 2 4 2 2 12 10 2 p xp xpp 11221122 26 Net Demands p1 2 p2 3 x1 1 3 and x2 2 2 so pxpx 111222 23320 The purchase of 2 extra units of good 2 at 3 each is funded by giving up 3 units of good 1 at 2 each Net Demands x2 x1 1 1 2 2 pxpx 111222 0 x2 x1 At prices p1 p2 the consumer sells units of good 1 to acquire more units of good 2 Net Demands x2 x1 1 1 2 2 p xp xpp 1 1221122 x2 x1 At prices p1 p2 the consumer sells units of good 2 to acquire more of good 1 Net Demands x2 x1 pxpx 111222 0 x2 2 2 x1 1 1 At prices p1 p2 the consumer consumes her endowment net demands are all zero p xp xpp 11221122 Net Demands x2 x1 1 1 2 2 pxpx 111222 0 Price offer curve contains all the utility maximizing gross demands for which the endowment can be exchanged Net Demands x2 x1 1 1 2 2 pxpx 111222 0 Price offer curve Sell good 1 buy good 2 Net Demands x2 x1 1 1 2 2 pxpx 111222 0 Price offer curve Buy good 1 sell good 2 19 20 21 Some Results about Price Change If a consumer is a net seller of a good when the price of that good decreases if she remains a seller then the consumer is worse off However if she switches to a net buyer then she may be better off If a consumer is a net buyer of a good when the price decreases the consumer will remain a buyer and be better off 22 A net seller facing falling price 23 A net buyer facing falling price Labor Supply A worker s non labor income endowment is m and time endowment is R hours of time which can be used for labor or leisure R m Consumption good C price is pc w is the wage rate Labor Supply The worker s budget constraint is pcC wL m where C R denote gross demands for the consumption good and for leisure p Cw RRm c p Cw Rw Rm c endowment value expenditure Labor Supply p Cw RRm c rearranges to C w p R mwR p cc Labor Supply C R R endowment C w p R mwR p cc mwR pc slope the real wage rate w pc m pc Labor Supply C R R endowment C w p R mwR p cc mwR pc C R leisure demanded labor supplied m pc Slutsky s Equation Revisited We used to assume that income y did not change as prices changed But so there will be an additional income effect called the endowment income effect ypp 1122 Slutsky s Equation Revisited x1 2 1 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 Slutsky s Equation Revisited x1 2 1 x2 Pure substitution effect Slutsky s Equation Revisited x1 2 1 x2 Pure substitution effect Ordinary income effect Slutsky s Equation Revisited x1 2 1 x2 Pure substitution effect Ordinary income effect Endowment income effect Slutsky s Equation Revisited Overall change in demand caused by a change in price is the sum of i a pure substitution effect ii an ordinary income effect iii an endowment income effect 35 Slutsky Equation with Endowments 111111111 11 11 s xp m pxpxp mxp m x ppmm 1111111 11 11 s xp m pxpxp m x ppm Or 36 Net buyer of normal good Net seller of normal good such as leisure 1111111 11 11 s xp m pxpxp m x ppm Slutsky Equation with Endowments 37