ch3现代经济学偏好

1、Chapter ThreePreferences偏好Rationality in Economics Behavioral Postulate:A decisionmaker always chooses its most preferred alternative from its set of available alternatives. So to model choice we must model decision-makers preferences.Preference Relations Preference relations are ordinal relations;

2、i.e. they state only the order in which bundles are preferred.Structure Describe preferences Indifference curves (无差异曲线) Well-behaved preferences Marginal rate of substitution (边际替代率)Preference Relations Comparing two different consumption bundles x and y: strict preference (严格偏好): x is y). Indiffer

3、ence (无差异): x is exactly as preferred as is y (xy). weak preference (弱偏好): x is as at least as preferred as is y (x y).morepreferredthanisy(xPreference Relations x y and y x imply x y.1Preference Relations x y and y x imply x y. x y and (not x y) imply xy.Assumptions about PreferenceRelations Reflex

4、ivity (反身性): Any bundle x is always at least as preferred as itself; i.e.x x.Indifference Curves Take a reference bundle x. The set of all bundles equally preferred to x is the indifference curve containing x; the set of all bundles y x. Since an indifference “curve” is not always a curve a better n

5、ame might be an indifference “set”.Assumptions about PreferenceRelations Completeness (完备性): For any two bundles x and y it is always possible to make the statement that eitherorx yy x.Assumptions about PreferenceRelations Transitivity (传递性): Ifx is at least as preferred as y andy is at least as pre

6、ferred as z thenx is at least as preferred as z; i.e.x y and y z x z.Indifference Curvesx2xx x” x”x”x” x12Indifference Curvesx2xzxyzy x1Indifference CurvesI1All bundles in Iarex21xstrictly preferred toall in I2.zI2All bundles in I2 areyI3strictly preferred toall in I3.x1Weakly Preferred Set (弱偏好集)x2

7、 WP(x) the set ofx bundles weakly preferred to x.I(x)I(x) x1Strictly Preferred Set (严格偏好集)x2 SP(x), the set ofx bundles strictlypreferred to x,does notincludeI(x) I(x). x1Weakly Preferred Set (弱偏好集)x2 xWP(x), the set ofbundles weaklypreferred to x.WP(x)includesI(x)I(x). x1Indifference Curves CannotI

8、ntersectxIFrom I1, x y.From I2, x z.2I12Therefore y z. But from I1and I2 we see yz, acontradiction. xyzx13Slopes of Indifference CurvesSlopes of Indifference Curves When more of a commodity is always preferred, the commodity is a good. If every commodity is a good then indifference curves are negati

9、vely sloped.Good 2 BetterWorseTwo goods a negatively sloped indifference curve.Good 1Slopes of Indifference CurvesSlopes of Indifference Curves If less of a commodity is always preferred then the commodity is a bad.Good 2BetterOne good and onebad a positively slopedindifference curve.WorseBad 1Examp

10、les Perfect substitutes (完全替代) Perfect complements (完全互补) Satiation (餍足) Discrete goods (离散商品)Extreme Cases of IndifferenceCurves; Perfect Substitutes If a consumer always regards units of commodities 1 and 2 as equivalent, then the commodities are perfect substitutes and only the total amount of th

11、e two commodities in bundles determines their preference rank-order.4Extreme Cases of IndifferenceCurves; Perfect Substitutesx2Slopes are constant at - 1.15I2Bundles in I2 all have a total8of 15 units and are strictlypreferred to all bundles inI1I1, which have a total ofonly 8 units in them.815x1Ext

12、reme Cases of Indifference Curves; Perfect Complements If a consumer always consumes commodities 1 and 2 in fixed proportion (e.g. one-to-one), then the commodities are perfect complements and only the number of pairs of units of the two commodities determines the preference rank-order of bundles.Ex

13、treme Cases of Indifference Curves; Perfect ComplementsExtreme Cases of Indifference Curves; Perfect Complementsx245o95I159Each of (5,5), (5,9) and (9,5) contains 5 pairs so each is equally preferred.x1x245o95I159Since each of (5,5), (5,9) and (9,5) contains 5 pairs, each is lessI2 preferred than th

14、e bundle (9,9) whichcontains 9 pairs.x1Preferences Exhibiting Satiation A bundle strictly preferred to any other is a satiation point or a bliss point. What do indifference curves look like for preferences exhibiting satiation?Indifference Curves ExhibitingSatiationx2 Satiation(bliss)pointx15Indiffe

15、rence Curves ExhibitingSatiationx2BetterBetterSatiation(bliss)Betterpointx1Indifference Curves ExhibitingSatiationx2BetterBetterSatiation(bliss)Betterpointx1Indifference Curves for DiscreteCommodities A commodity is infinitely divisible if it can be acquired in any quantity; e.g. water or cheese. A

16、commodity is discrete if it comes in unit lumps of 1, 2, 3, and so on; e.g. aircraft, ships and refrigerators.Indifference Curves for DiscreteCommodities Suppose commodity 2 is an infinitely divisible good (gasoline) while commodity 1 is a discrete good (aircraft). What do indifference “curves” look

17、 like?Indifference Curves With aDiscrete GoodGas-olineIndifference “curves”are collections ofdiscrete points.01234CarWell-Behaved Preferences A preference relation is “well-behaved” if it is Monotonic (单调) and convex (凸状). Monotonicity: More of any commodity is always preferred (i.e. no satiation an

18、d every commodity is a good).6Well-Behaved Preferences Convexity: Mixtures of bundles are(at least weakly) preferred to thebundles themselves. E.g., the 50-50mixture of the bundles x and y isz = (0.5)x + (0.5)y.z is at least as preferred as x or y.Well-Behaved Preferences -Convexity.x2xx2+y2z = x+yi

19、s strictly preferred22to both x and y.y2yx1x1+y1y12Well-Behaved Preferences -Convexity.x2 x z =(tx1+(1-t)y1, tx2+(1-t)y2)is preferred to x and yfor all 0 t 1.yy2x1y1Well-Behaved Preferences -Convexity.Preferences are strictly convexxwhen all mixtures zx2zare strictlypreferred to theircomponenty2y bu

20、ndles x and y.x1y1Well-Behaved Preferences -Weak Convexity.Non-Convex PreferencesxPreferences areweakly convex if atzleast one mixture zxis equally preferredz yto a componentbundle.yx2z y2 x1 y1The mixture z is less preferred than x or y.7More Non-Convex PreferencesSlopes of Indifference Curvesx2y2

21、Betterz x1y1The mixture z is less preferred than x or y. The slope of an indifference curve is its marginal rate-of-substitution (MRS). How can a MRS be calculated? MRS at x is the slope of the indifference curve at xMarginal Rate of SubstitutionMarginal Rate of Substitutionx2 MRS at x islim x2/ x1x2 dx2 = MRS*dx1 so at x MRS i