1PreferencesECON 370: Microeconomic TheorySummer 2004 – Rice UniversityStanley GilbertEcon 370 - Consumer Preferences 2Choices• The theory of consumer preferences is based fundamentally on choices– The steak dinner or the salad bar– Major in Economics or Engineering– Save money for retirement or take that vacation to Maui• We say a consumer Prefers bundle A to bundle B if:– Assuming both are feasible– And all else being equal (¡cēterīs paribus!)– She would choose bundle A instead of bundle BEcon 370 - Consumer Preferences 3Preference Relations• Consumers can compare two different consumption bundles, x and y: – strict preference: x ≻ y• “x is strictly preferred to y”– weak preference: x ≿ y• “x is at least as good as y”– indifference: x ~ y• These are ordinal (not cardinal) relations– Only order alternative bundles– Do not specify magnitude of preference differencesEcon 370 - Consumer Preferences 4Indifference Curves• An indifference curve (level set)– Take a reference bundle x´– Indifference curve: set of all bundles y ∼ x´Good xGood x22Good xGood x11Indifference CurveIndifference Curve(Weakly) Preferred Set(Weakly) Preferred Setxxzzyy2Econ 370 - Consumer Preferences 5Assumptions about PreferencesA1 Completeness: All bundles can be ranked.A2 Transitivity: If x ≿ y and y ≿ z, then x ≿ z.A4 Convexity: The “better-than” set is convex.A3 Non-Satiation: More is always better.We usually assume preferences meet the following assumptions:Econ 370 - Consumer Preferences 6From I1, x ∼ yxx22xx11II11I2xxyyzzIndifference Curves Cannot IntersectFrom I2, x ∼ zImplies: y ∼ z , but y ≻ zEcon 370 - Consumer Preferences 7Non-Satiationxx22xx11xxyyzzStrictlyWorseStrictlyBetterEcon 370 - Consumer Preferences 8Convexityxx22xx11II11aabbccTwo points on the same indifference curveDraw a line drawn between the two pointsAny point on that line will be at least as goodMathematically:αa + (1 – α)b≿ a ~ b3Econ 370 - Consumer Preferences 9Non-Convex Examplesxx22xx11II11II22II33Econ 370 - Consumer Preferences 10Comments about Assumptions• Assumptions A1 & A2 are essential to our concept of rationality• Preferences that also meet Assumptions A3 & A4 are called Well Behaved.– Non-Satiation• This clearly does not apply in the real world• We can usually get away with it because people will generally choose a consumption bundle in the region where more is still better (Why?).• Important exception: ‘Bads’ – Convexity• There is no fundamental reason why preferences should meet this• Again, it is mathematically convenient• It also turns out not to matter much if it is not metEcon 370 - Consumer Preferences 11Examples of Preferences• Examples that meet our assumptions:– Perfect Substitutes– Perfect Complements• Examples that do not meet our assumptions– ‘Bads’• (But, we can turn a bad into a good…)– SatiationEcon 370 - Consumer Preferences 12Perfect Substitutes•Tastes:– If consumer always regards commodities 1 and 2 as equivalent, – then commodities are Perfect Substitutes.– Only total amount of two commodities in bundles determines their preference rank-order.• Indifference Curves:– Straight Lines•Example– Brand-Name v. Generic Flour4Econ 370 - Consumer Preferences 13Perfect Complements•Tastes:– If consumer always consumes commodities 1 and 2 in fixed proportions,– Then, commodities are Perfect Complements.– Only number of pairs of two commodities determines preference rank-order of bundles.• Indifference Curves:– “L-Shaped” Indifference curves•Example– Coffee and sugarEcon 370 - Consumer Preferences 14Discrete Goods• A commodity is infinitely divisible if it can be acquired in any quantity (water, cheese).• A commodity is discrete if it comes in indivisible (cars, refrigerators).• Indifference curves for discrete goods– Suppose commodity 1 is infinitely divisible (gas)– Suppose commodity 2 is discrete (cars)Econ 370 - Consumer Preferences 15Marginal Rate of Substitution (MRS)xx22xx11xx’’MRS at xMRS at x’’is slope of is slope of indifference curve at xindifference curve at x’’12dxdxMRS =Econ 370 - Consumer Preferences 16Marginal Rate of Substitutionxx22x1dxdx22dxdx11MRS = rate at which the MRS = rate at which the consumer is willing to consumer is willing to exchange commodity 2 exchange commodity 2 for a small amount of for a small amount of commodity 1.commodity 1.xx’’5Econ 370 - Consumer Preferences 17MRS and Indifference Curves• Two goods: IC has negative slope– I.e., MRS < 0• If (and only if) prefs. are strictly convex:– MRS always increases with x1(becomes less negative)• MRS decreases (becomes more negative)as x1increases ⇒ nonconvex