Preferences and Utility Outline

consumer theory preferences model of consumer theory premises a consumer faces a budget constraint prices of the goods services he buys i PILE's YinL'm 98 4 L Is s based on his income and the Fine IT the amount from of pleasure consuming budget constraint preterenies consumption decision economists assume people have preferences for goods servites their consumption goods are ranked according to how much pleasure graphi and mathmatic that guide consumers recieve strict preference relation given two bundles for an individual a prettered to b indifference relation giventwo bundles for an individual indifferent to b danab define a strict preferente relation b it and only if a is better than b a is as follow strictly as follows a and b define an inditterente relation b itand only if a is just as good as b ca is a propertiesof preferences completeness Yin in The Ides ofgoods a consumer transitivity can a b and b a c then as consumers rankings are logically consistent a rational preferentes preferences are rational if they are complete and transitive more isbetter nonsatiation monotonicity all else the same move of a commodity is better than less good vs bad indifference curves the graphical set of all bundles of goods that an individual equally desirable tire's y ex Stan views as aneriness ya 5 y 4 A of 3 IT L III C D downward sloping in IE an B a's late ii ii complete tot indisierence curves that summarize preserved icy 103 if preferenies are rational complete and transitive and monotonic then these hold every bundle lies on an indifferenie curve bundles on indifference curves farther from the origin are proffered to those on indifference surves closer to the origin in differente curves cannot cross cannot slope upward a b b by def a f Ic by nonsatiation the curvature of the curve tells us about the rate at which an individual is willing to tradeoff bit two goods as we move down a convex curve individual is willing to trade decreasing amounts of onegood for one more unit of the other utility functions utility set of numerital values that reflect relative rankings of 49 9 4945 in m relationship between everypossible bundle of goods given a utility you tan calculate how main from specific consumption choires ex U IX g 2 pizza y bundles of utility measures and utility is derived burritos bundle a contains 16 pizzas and a burritos U a 12 bundle b luntains 13 and 13 burritos V b prias 13 bs a U a Ucb 8 a V a asb b 8 U b utility tells us the relative ranking of two bundles but not how much more one rank is valued than another doesnt matter if U a 12 3 just matters that by V2b a any utilityfunction that generates be these preferences ex U a Ucb b z U b a would be consistent w 12,000 Vial a monotonic transformations utility tunition can be turned to another utility function as long maintained monotonic transformation smiatnin u then text tius where all as preferences are 7999 81 examples Is YET.to adding a constant multiplying by a positive constant assuming rain good ispositive raising to a positive power natural log U x y U b b exponential 2 U a a U b U a bra common utilityfunctions perfect substitutes utility function represents the preferences for 2 goods that a consumer views as perfect substitutes for one another ins to subsiture one good for In L us x y mux ax 1 muy L by a b perfect complements utility function represents the preferences for 2 goods that must be consumed in a fixed proportion a consumer is unwilling to substitute one good for another move of one good without more of another does not change min lax.by u ix 4 Cobb Douglas UtilityFunction one of most commonly used utility functions represents complete transitive monotonic convex preferences U ix 4 a yb a b c so utility Quasilinear Utility function describes preferences for a consumer who purchases the same of a good regardless of hevincome MRS is a function of only one of the goods amt indifference curve graphital representation of utility function level curve of a utility tunition V19 192 shows all the combinations of goods that give the same level of K T IX 4 ex ay a Skye y utility 22 w̅ d's 0 2 ax 70 marginal rate of substitution absolute value of the slope of an indifference curve to mn m 1 MRS ifeng.inunat.ie 9fonsumeriswiningtotrade 1C MRS II y In.ataIiiretation guys I f MRT m 4 s good terente curvesdisplay a diminishing marginal rate of dependson how much extra each good marginal utility extra utility a consumer gets from a little more of utility that a consumer gets from the last unit of a good holding the consumption of other constant marginal utility of marginal utility of 4 144 du d MRS t utility feinition If dy y 19 1 1 1 I to derive the MRS EYE mux'b A B If NY ex May DY mum.BY Mux at MRS goods 1 Max take the total differential of the consuming 3 May 3 MRS If 1 4 8 graphing an IC sign of Mux and Muy determine direction ex My sign of ex 0 and days d Mrs co May20 and and means to slopes downward days determine diers so curvature means is is convex as t.it MRS ax y dy EE indifference lurves different utilityfunctions generate different indifference curves perfect substitutes a ax by É 3 4 1 2 pepsi cans per week w̅ 14 338 3 ex 4 2 Is 9 MRS 213 40 diers 9 ax amesia Ya Peru p 13 n 2 3 pie sliceper week I Eva 0 a rant pie sheeper wee ex U min 2x 34 i ie i no n 4 3 It U min 2 t.su ITI 3 3 iy'obbDoualas ex 12 U 2 a III y 13 solvefor y y 3 a x sh y 4 pizzasper semester d 9 9 29 may 12 95 2 3 a 0 113 12 y co 1 0 0 y MRS Mm d y co 712 w̅ 2 mu 7 512 31 53 dy d so yrs gg 34 I Quasilinear 12 ex u sy y 2 1 112 fx d y d 312 z 2 mux muy 0 If 0 0 genward 0 3 MRS mm in d 31 did 0 as y 0 as MRS ii MRS x̅ in class problems y perfectcomplements 7 Dani 3 Ic 3 I 3 Emily perfectsubstitutes 2 1 s a x y concave power ic.li ie y 43 s 103 112 1 Uz S U ÉÉ 15 applesauce so CO diminishing MU o 78 4 0 1 monotonic 0 diminishing MU IEIw If dfffiIsfotoa.iorma U 12 C 12 F MRS 12 C 12 12 F 112 0 144 F fromA to B as F as Ct Mest d MRS co 2s o 9 1441 d c g 288 F 3 220 0 MRSdiminishes MUF it 1 1 contuming of unit of food I more total utility in treases by 43 u nutanic MUF 1 0 co F MRS 1 2 F 112621 213 F 12 c is for 1 more F trade 312 c i move trade 21s C If