Preferences消費者偏好(3)

1、Chapter ThreePreferences 消費者偏好消費者偏好Where Are We in the Course?u We are studying the 1st of the three blocks of microeconomics: Consumer behavior, production theory, and market equilibriumuWithin the 1st block, we are working on the 2nd of the three components: choice set, preference, and consumer de

2、mandWhat Do We Mean by Preference? (偏好)u It refers to the ordered relationship among alternative choices given by an economic agent.u In most economic literature, consumer preference is treated as the ultimate exogenous element.Preference RelationsuComparing two different consumption bundles, x and

3、y: strict preference: x is more preferred than is y.weak preference: x is as at least as preferred as is y.Indifference: x is exactly as preferred as is y.Notationsu denotes strict preference; u denotes indifference; u denotes weak preference;p pf fPreference Relationsux y and y x imply x y.ux y and

4、 (not y x) imply x y.f ff ff ff fp pAssumptions about Preference RelationsuCompleteness: For any two bundles x and y it is always possible to make the statement that either x y or y x.f ff fAssumptions about Preference RelationsuReflexivity: Any bundle x is always at least as preferred as itself; i.

5、e. x x.f fAssumptions about Preference RelationsuTransitivity: 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.f ff ff fIndifference Curves無差異曲線無差異曲線 (或或,無差異集無差異集)uTake a reference bundle x. The set of all bundles equal

6、ly preferred to x is the indifference curve containing x; the set of all bundles y x.uSince an indifference “curve” is not always a curve a better name might be an indifference “set”.Indifference CurvesxIndifference Curves p pp pxyzIndifference Curvesx2x1xAll bundles in I1 arestrictly preferred to a

7、ll in I2.yzAll bundles in I2 are strictly preferred to all in I3.I1I2I3Indifference Curvesx2x1WP(x), the set of bundles weakly preferred to x. WP(x) includes I(x).xI(x)Indifference Curvesx2x1SP(x), the set of bundles strictly preferred to x, does not include I(x).xI(x)Indifference Curves Cannot Inte

8、rsect ! (不相交!)I2Indifference Curves Cannot IntersectI2p pSlopes of Indifference CurvesuWhen more of a commodity is always preferred, the commodity is a good.uIf every commodity is a good then indifference curves are negatively sloped.Slopes of Indifference CurvesSlopes of Indifference CurvesuIf less

9、 of a commodity is always preferred then the commodity is a bad.Slopes of Indifference CurvesExtreme Cases of Indifference Curves; Perfect SubstitutesuIf a consumer always regards units of commodities 1 and 2 as equivalent, then the commodities are perfect substitutes and only the sum of the two com

10、modities in bundles determines their preference rank-order. Extreme Cases of Indifference Curves; Perfect SubstitutesI2I1Extreme Cases of Indifference Curves; Perfect ComplementsuIf a consumer always consumes commodities 1 and 2 in fixed proportion (e.g. one-to-one), then the commodities are perfect

11、 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 ComplementsI2I1Since each of (5,5), (5,9) and (9,5) contains 5 pairs, each is less preferred than the bundle (9,9) which contains 9

12、 pairs. Preferences Exhibiting SatiationuA bundle strictly preferred to any other is a satiation point or a bliss point.uWhat do indifference curves look like for preferences exhibiting satiation?Indifference Curves Exhibiting SatiationIndifference Curves for Discrete CommoditiesuA commodity is infi

13、nitely divisible if it can be acquired in any quantity; e.g. water or cheese.uA 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 Discrete Commodities (study this yourself)uSuppose commodity 2 is an infinitely divisi

14、ble good (gasoline) while commodity 1 is a discrete good (aircraft). What do indifference “curves” look like?Indifference Curves With a Discrete Good (study this yourself)3Well-Behaved PreferencesuA preference relation is “well-behaved” if it ismonotonic and convex.uMonotonicity: More of any commodi

15、ty is always preferred (i.e. no satiation and every commodity is a good).Well-Behaved PreferencesuConvexity (凸性凸性): 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 + (0.5)y.z is at least as preferred as x or

16、y. Well-Behaved Preferences - Convexity.xyz =(tx1+(1-t)y1, tx2+(1-t)y2)is preferred to x and y for all 0 t 1.Well-Behaved Preferences - Convexity.xyPreferences are strictly convex when all mixtures z are strictly preferred to their component bundles x and y.zWell-Behaved Preferences - Weak Convexity

17、.xyzPreferences are weakly convex if at least one mixture z is equally preferred to a component bundle.xzyNon-Convex PreferencesBetterMore Non-Convex PreferencesBetterMarginal Rate-of-Substitution(邊際替代率)uThe slope of an indifference curve is its marginal rate-of-substitution (MRS) (邊際替代率邊際替代率)uHow c

18、an a MRS be calculated?Marginal Rate of SubstitutionMarginal Rate of Substitution D DD DD DD DD DMarginal Rate of Substitutionx1 MRS & Ind. Curve PropertiesMRS & Ind. Curve PropertiesMRS & Ind. Curve PropertiesMRS & Ind. Curve PropertiesMRS = - 0.5MRS = - 5 MRS & Ind. Curve PropertiesMRS= - 0.5MRS = - 1MRS = - 2Summary: The Key Concept of this ChapterIt is the indifference curve