【正文】 Ind. Curve Properties Good 2 Good 1 Two goods a negatively sloped indifference curve MRS 0. 168 MRS amp。 the set of all bundles y ~ x‘. 136 Indifference Curves x2 x1 x‖ x‖‘ x‘ ~ x‖ ~ x‖‘ x‘ 137 Indifference Curves x2 x1 z x y p p x y z 138 Indifference Curves x2 x1 x All bundles in I1 are strictly preferred to all in I2. y z All bundles in I2 are strictly preferred to all in I3. I1 I2 I3 139 Weakly Preferred Set (弱偏好集 ) x2 x1 WP(x), the set of bundles weakly preferred to x. WP(x) includes I(x). x I(x) 140 Strictly Preferred Set (嚴格偏好集 ) x2 x1 SP(x), the set of bundles strictly preferred to x, does not include I(x). x I(x) 141 Indifference Curves Cannot Intersect x2 x1 x y z I1 I2 From I1, x ~ y. From I2, x ~ z. Therefore y ~ z. But from I1 and I2 we see y z, a contradiction. p 142 Indifference Curves 形狀 ?When more of a modity is always preferred, the modity is a good. ?If every modity is a good then indifference curves are negatively sloped. 143 Slopes of Indifference Curves Good 2 Good 1 Two goods a negatively sloped indifference curve. 144 Slopes of Indifference Curves ?If less of a modity is always preferred then the modity is a bad. 145 Slopes of Indifference Curves Good 2 Bad 1 One good and one bad a positively sloped indifference curve. 146 Examples ?Perfect substitutes (完全替代 ) ?Perfect plements (完全互補 ) ?Satiation (饜足 ) ?Discrete goods (離散商品 ) 147 Extreme Cases of Indifference Curves。 –因此它還表示兩種商品之間的 市場替代比率 或者說是相互之間的 機會成本。 ? 《 西方經(jīng)濟學學習精要與習題集（微觀部分） 》 張軍主編，上海財經(jīng)大學出版社。 Jack does not. ?Jill values the apartment at $200。 . they state only the order in which bundles are preferred. 132 Assumptions about Preference Relations ?Completeness (完備性 ): For any two bundles x and y it is always possible to make the statement that either x y or y x. ~ f ~ f 133 Assumptions about Preference Relations ?Reflexivity (反身性 ): Any bundle x is always at least as preferred as itself。 . water or cheese. ?A modity is discrete if it es in unit lumps of 1, 2, 3, … and so on。 that is, (2,3) (4,1) ~ (2,2). p 178 Utility Functions ?U(x1,x2) = x1x2 (2,3) (4,1) ~ (2,2). ?Define V = U2. p 179 Utility Functions ?U(x1,x2) = x1x2 (2,3) (4,1) ~ (2,2). ?Define V = U2. ?Then V(x1,x2) = x12x22 and V(2,3) = 36 V(4,1) = V(2,2) = 16 so again (2,3) (4,1) ~?(2,2). ?V preserves the same order as U and so represents the same preferences. p p 180 Utility Functions ?U(x1,x2) = x1x2 (2,3) (4,1) ~ (2,2). ?Define W = 2U + 10. p 181 Utility Functions ?U(x1,x2) = x1x2 (2,3) (4,1) ~ (2,2). ?Define W = 2U + 10. ?Then W(x1,x2) = 2x1x2+10 so W(2,3) = 22 W(4,1) = W(2,2) = 18. Again, (2,3) (4,1) ~ (2,2). ?W preserves the same order as U and V and so represents the same preferences. p p 182 Utility Functions: Monotonic Transformation ?If –U is a utility function that represents a preference relation and – f is a strictly increasing function, ? then V = f(U) is also a utility function representing . ~ f ~ f 183 Goods, Bads and Neutrals ?A good is a modity unit which increases utility (gives a more preferred bundle). ?A bad is a modity unit which decreases utility (gives a less preferred bundle). ?A neutral is a modity unit which does not change utility (gives an equally preferred bundle). 184 Some Other Utility Functions and Their Indifference Curves 185 Perfect Substi。 Perfect Complements ? consumes modities 1 and 2 in fixed proportion (. onetoone), ? the modities are perfect plements ?only the number of pairs of units of the two modities determines the preference rankorder of bundles. 150 Extreme Cases of Indifference Curves。 before stamps. 109 The Food Stamp Program G F 100 100 F + G = 100: before stamps. 110 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 40 111 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 The family‘s budget set is enlarged. 40 112 The Food Stamp Program ?What if food stamps can be traded on a black market for $ each? 113 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget constraint after 40 food stamps issued. 140 120 Budget constraint with black market trading. 40 114 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget constraint after 40 food stamps issued. 140 120 Black market trading makes the budget set larger again. 40 115 Shapes of Budget Constraints ?Q: What makes a budget constraint a straight line? 116 ?A: A straight line has a constant slope and the constraint is p1x1 + … + p nxn = m ?so if prices are constants then a constraint is a straight line. 117 Shapes of Budget Constraints ?But what if prices are not constants? ?. bulk buying discounts, or price penalties for buying ―too much‖. 118 Shapes of Budget Constraints Quantity Discounts ?Suppose p2 is constant at $1 ? but that p1=$2 for 0 ? x1 ? 20 ?and p1=$1 for x120. 119 Shapes of Budget Constraints Quantity Discounts ?Then the constraint‘s slope is 2, for 0 ? x1 ? 20 p1/p2 = 1, for x1 20 {120 Shapes of Budget Constraints with