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1、Chapter ThreePreferences 偏好偏好StructureuDescribe preferencesuIndifference curves(无差异曲线无差异曲线)uWell-behaved preferencesuMarginal rate of substitution(边际替边际替代率代率)Rationality in Economicsu Behavioral Postulate:A decision-maker always chooses its most preferred alternative from its set of available altern
2、atives.uSo to model choice we must model decision-makers preferences.Preference RelationsuComparing two different consumption bundles,x and y:strict preference(严格偏好严格偏好):x is more preferred than is y(x y).Indifference(无差异无差异):x is exactly as preferred as is y(xy).weak preference(弱偏好弱偏好):x is as at l
3、east as preferred as is y(x y).ppffPreference RelationsuPreference relations are ordinal relations;i.e.they state only the order in which bundles are preferred.Preference Relationsux y and y x imply x y.ffffPreference Relationsux y and y x imply x y.ux y and(not y x)imply x y.ffffffffppAssumptions a
4、bout Preference RelationsuCompleteness(完备性完备性):For any two bundles x and y it is always possible to make the statement that either x y or y x.ffffAssumptions about Preference RelationsuReflexivity(反身性反身性):Any bundle x is always at least as preferred as itself;i.e.x x.ffAssumptions about Preference R
5、elationsuTransitivity(传递性传递性):Ifx is at least as preferred as y,andy is at least as preferred as z,thenx is at least as preferred as z;i.e.x y and y z x z.ffffffIndifference CurvesuTake a reference bundle x.The set of all bundles equally preferred to x is the indifference curve containing x;the set
6、of all bundles y x.uSince an indifference“curve”is not always a curve a better name might be an indifference“set”.Indifference Curvesx2x1x”x”x x”x”xIndifference Curvesx2x1z x yppppxyzIndifference Curvesx2x1xAll bundles in I1 arestrictly preferred to all in I2.yzAll bundles in I2 are strictly preferr
7、ed to all in I3.I1I2I3x2x1I(x)xI(x)WP(x),the set of bundles weakly preferred to x.Weakly Preferred Set(弱偏好集)Weakly Preferred Set(弱偏好集)x2x1WP(x),the set of bundles weakly preferred to x.WP(x)includes I(x).xI(x)Strictly Preferred Set(严格偏好集)x2x1SP(x),the set of bundles strictly preferred to x,does not
8、include I(x).xI(x)Indifference Curves Cannot Intersectx2x1xyzI1I2From I1,x y.From I2,x z.Therefore y z.But from I1 and I2 we see y z,a contradiction.ppSlopes of Indifference CurvesuWhen more of a commodity is always preferred,the commodity is a good.uIf every commodity is a good then indifference cu
9、rves are negatively sloped.Slopes of Indifference CurvesBetterWorseGood 2Good 1Two goodsa negatively sloped indifference curve.Slopes of Indifference CurvesuIf less of a commodity is always preferred then the commodity is a bad.Slopes of Indifference CurvesBetterWorseGood 2Bad 1One good and onebad a
10、 positively sloped indifference curve.ExamplesuPerfect substitutes(完全替代完全替代)uPerfect complements(完全互补完全互补)uSatiation(餍足餍足)uDiscrete goods(离散商品离散商品)Extreme Cases of Indifference Curves;Perfect SubstitutesuIf a consumer always regards units of commodities 1 and 2 as equivalent,then the commodities are
11、 perfect substitutes and only the total amount of the two commodities in bundles determines their preference rank-order.Extreme Cases of Indifference Curves;Perfect Substitutesx2x1881515Slopes are constant at-1.I2I1Bundles in I2 all have a totalof 15 units and are strictlypreferred to all bundles in
12、 I1,which have a total of only 8 units in them.ExamplesuCoke and PepsiuRed bus and white busuGood sold by a white salesperson and by a black salespersonExtreme Cases of Indifference Curves;Perfect ComplementsuIf a consumer always consumes commodities 1 and 2 in fixed proportion(e.g.one-to-one),then
13、the commodities are perfect complements and only the number of pairs of units of the two commodities determines the preference rank-order of bundles.Extreme Cases of Indifference Curves;Perfect Complementsx2x1I145o5959Each of(5,5),(5,9)and(9,5)contains5 pairs so each is equally preferred.Extreme Cas
14、es of Indifference Curves;Perfect Complementsx2x1I2I145o5959Since each of(5,5),(5,9)and(9,5)contains 5 pairs,each is less preferred than the bundle(9,9)which contains 9 pairs.Preferences Exhibiting SatiationuA bundle strictly preferred to any other is a satiation point or a bliss point.uWhat do indi
15、fference curves look like for preferences exhibiting satiation?Indifference Curves Exhibiting Satiationx2x1Satiation(bliss)pointIndifference Curves Exhibiting Satiationx2x1BetterBetterBetterSatiation(bliss)pointIndifference Curves Exhibiting Satiationx2x1BetterBetterBetterSatiation(bliss)pointIndiff
16、erence Curves for Discrete CommoditiesuA commodity is infinitely divisible if it can be acquired in any quantity;e.g.water or sugar.uA commodity is discrete if it comes in unit lumps of 1,2,3,and so on;e.g.cars,ships and refrigerators.Indifference Curves for Discrete CommoditiesuSuppose commodity 2
17、is an infinitely divisible good(sugar)while commodity 1 is a discrete good(car).What do indifference“curves”look like?Indifference Curves With a Discrete GoodSugarCar01234Indifference“curves”are collections ofdiscrete points.Well-Behaved PreferencesuA preference relation is“well-behaved”if it isMono
18、tonic(单调单调)and convex(凸状凸状).uMonotonicity:More of any commodity is always preferred(i.e.no satiation and every commodity is a good).Well-Behaved PreferencesuConvexity:Mixtures of bundles are(at least weakly)preferred to the bundles themselves.E.g.,the 50-50 mixture of the bundles x and y is z=(0.5)x
19、+(0.5)y.z is at least as preferred as x or y.Well-Behaved Preferences-Convexity.x2y2x2+y22x1y1x1+y12xyz=x+y2is strictly preferred to both x and y.Well-Behaved Preferences-Convexity.x2y2x1y1xyz=(tx1+(1-t)y1,tx2+(1-t)y2)is preferred to x and y for all 0 t 1.Well-Behaved Preferences-Convexity.x2y2x1y1x
20、yPreferences are strictly convex when all mixtures z are strictly preferred to their component bundles x and y.zWell-Behaved Preferences-Weak Convexity.xyzPreferences are weakly convex if at least one mixture z is equally preferred to a component bundle.xzyNon-Convex Preferencesx2y2x1y1zBetterThe mi
21、xture zis less preferredthan x or y.More Non-Convex Preferencesx2y2x1y1zBetterThe mixture zis less preferredthan x or y.Slopes of Indifference CurvesuThe slope of an indifference curve is its marginal rate-of-substitution(MRS).uHow can a MRS be calculated?uuMRS at x is the slope of theindifference c
22、urve at xMarginal Rate of Substitutionx2x1 MRS at x is lim D Dx2/D Dx1 D Dx1 0=dx2/dx1 at xD Dx x2 2D Dx x1 1xMarginal Rate of Substitutionx2x1dxdx2 2dxdx1 1dxdx2 2=MRS*dx=MRS*dx1 1 so,at x,MRS is so,at x,MRS is the rate at which the consumer the rate at which the consumer is only is only just willi
23、ngjust willing to exchange to exchange commodity 2 for a small commodity 2 for a small amount of commodity 1.amount of commodity 1.Marginal willingness to pay.Marginal willingness to pay.xMRS&Ind.Curve PropertiesBetterWorseGood 2Good 1Two goodsa negatively sloped indifference curveMRS 0.Diminishing
24、MRSGood 2Good 1MRS=-5MRS=-0.5MRS always increases with x1(becomes less negative)if and only if preferences are strictly convex.MRS&Ind.Curve Propertiesx1x2MRS=-0.5MRS=-5MRS decreases(becomes more negative)as x1 increasesnonconvex preferences MRS&Ind.Curve Propertiesx2x1MRS=-0.5MRS=-1MRS=-2MRS is not always increasing as x1 increases nonconvex preferences.