Chapter Copyright (c)2014 John Wiley & Sons, Inc Consumer Preferences and the Concept of Utility Chapter Three Overview Motivation Motivation Consumer Preferences and the Concept of Utility Consumer Preferences and the Concept of Utility The Utility Function The Utility Function •• Marginal Utility and Diminishing Marginal Utility Marginal Utility and Diminishing Marginal Utility Copyright (c)2014 John Wiley & Sons, Inc Indifference Curves Indifference Curves The Marginal Rate of Substitution The Marginal Rate of Substitution 6.6 Some Special Functional Forms Some Special Functional Forms Chapter Three Motivation • Why study consumer choice? • Study of how consumers with limited resources choose goods and services • Helps derive the demand curve for any good or service • Businesses care about consumer demand curves • Government can use this to determine how to help and whom to help buy certain Copyright (c)2014 John Wiley & Sons, Inc goods and services Chapter Three Consumer Preferences Consumer Preferences tell us how the consumer would rank (that is, compare the desirability of) any two combinations or allotments of goods, assuming these allotments were available to the consumer at no cost available for consumption at a particular time, place and under particular physical circumstances Chapter Three Copyright (c)2014 John Wiley & Sons, Inc These allotments of goods are referred to as baskets or bundles These baskets are assumed to be Consumer Preferences Assumptions Complete and Transitive Preferences are complete if the consumer can rank any two baskets of goods (A preferred to Preferences are transitive if a consumer who prefers basket A to basket B, and basket B to basket C also prefers basket A to basket C A  B; B  C = > A  C A  B; B  C = > A  C Chapter Three Copyright (c)2014 John Wiley & Sons, Inc B; B preferred to A; or indifferent between A and B) Consumer Preferences Assumptions Monotonic / Free Disposal Preferences are monotonic if a basket with more of at least one good and no less of any good is preferred to the Copyright (c)2014 John Wiley & Sons, Inc original basket Chapter Three Types of Ranking Example: Students take an exam After the exam, the students are ranked according to their performance An ordinal ranking lists the students in order of their performance (i.e., Harry did best, Joe did second best, Betty did third best, and so on) A cardinal ranking gives the mark of the exam, based on an absolute marking standard (i.e., Harry got 80, Joe got 75, Betty got 74 and so on) Alternatively, if the exam were graded on a curve, the Copyright (c)2014 John Wiley & Sons, Inc marks would be an ordinal ranking Chapter Three The Utility Function The three assumptions about preferences allow us to represent preferences with a utility function Utility function – a function that measures the level of satisfaction a consumer receives from any basket of goods and services Copyright (c)2014 John Wiley & Sons, Inc – assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets – U = u(y) Chapter Three The Utility Function Implications: • An ordinal concept: the precise magnitude of the number that the function assigns has no significance • Utility not comparable across individuals • Any transformation of a utility function that preserves the original ranking of bundles is an equally good y Copyright (c)2014 John Wiley & Sons, Inc representation of preferences e.g U = vs U = + represent the same preferences y Chapter Three Marginal Utility Marginal MarginalUtility Utilityofofaagood goodyy •• additional additionalutility utilitythat thatthe theconsumer consumergets getsfrom fromconsuming consumingaalittle littlemore moreofofyy •• i.e.i.e.the therate rateatatwhich whichtotal totalutility utilitychanges changesasasthe thelevel levelofofconsumption consumptionofofgood goodyyrises rises Copyright (c)2014 John Wiley & Sons, Inc •• MU MUyy==∆U/∆y ∆U/∆y •• slope slopeofofthe theutility utilityfunction functionwith withrespect respecttotoyy Chapter Three 10 Marginal Rate of Substitution MU (∆x) + MU (∆y) = x y MU /MU = x y -∆y/∆x = …along an IC… MRS x,y Positive marginal utility implies the indifference curve has a negative slope (implies Diminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes) Chapter Three 26 Copyright (c)2014 John Wiley & Sons, Inc monotonicity) Marginal Rate of Substitution The Marginal Rate of Substitution Implications Implicationsofofthis thissubstitution: substitution: •• Indifference Indifferencecurves curvesare arenegatively-sloped, negatively-sloped,bowed bowedout outfrom fromthe theorigin, origin,preference preferencedirection direction Copyright (c)2014 John Wiley & Sons, Inc isisup upand andright right •• Indifference Indifferencecurves curvesdo donot notintersect intersectthe theaxes axes Chapter Three 27 Indifference Curves Key Property Averages preferred to extremes => indifference curves are bowed Copyright (c)2014 John Wiley & Sons, Inc toward the origin (convex to the origin) Chapter Three 28 Indifference Curves Do Dothe theindifference indifferencecurves curvesintersect intersectthe theaxes? axes? AA value value of of xx == 00 or or yy == 00 isis inconsistent inconsistent with with any any Copyright (c)2014 John Wiley & Sons, Inc positive positivelevel levelof ofutility utility Chapter Three 29 Marginal Rate of Substitution The Marginal Rate of Substitution 2 Example: U = Ax +By ; MU =2Ax; MU =2By x y (where: A and B positive) = MU /MU x y = 2Ax/2By = Ax/By Copyright (c)2014 John Wiley & Sons, Inc MRS x,y Marginal utilities are positive (for positive x and y) Marginal utility of x increases in x; Marginal utility of y increases in y Chapter Three 30 Indifference Curves 5 5 Example: U= (xy) ;MU =y /2x ; MU =x /2y x y A Is more better for both goods? Yes, since marginal utilities are positive for both B Are the marginal utility for x and y Copyright (c)2014 John Wiley & Sons, Inc diminishing? Yes (For example, as x increases, for y constant, MU falls.) x C What is the marginal rate of substitution of x for y? MRS = MU /MU = y/x x,y x y Chapter Three 31 Indifference Curves y Example: Graphing Indifference Curves Copyright (c)2014 John Wiley & Sons, Inc Preference direction IC2 IC1 Chapter Three 32 x Special Functional Forms α β Cobb-Douglas: U = Ax y where: α + β = 1; A, α,β positive constants MUY = αAx α-1 β y α β-1 β Ax y MRSx,y = Copyright (c)2014 John Wiley & Sons, Inc MUX = (αy)/(βx) “Standard” case Chapter Three 33 Special Functional Forms y Example: Cobb-Douglas (speed vs maneuverability) Copyright (c)2014 John Wiley & Sons, Inc Preference Direction IC2 IC1 Chapter Three 34 x Special Functional Forms Perfect Substitutes: U = Ax + By Where: Where:A,A,BBpositive positiveconstants constants Copyright (c)2014 John Wiley & Sons, Inc MU MUx ==AA x MU MUy ==BB y MRS MRSx,y ==A/B A/Bsosothat that11unit unitofofxxisisequal equaltoto x,y B/A B/Aunits unitsofofyyeverywhere everywhere (constant (constantMRS) MRS) Chapter Three 35 Special Functional Forms y Example: Perfect Substitutes • (Tylenol, Extra-Strength Tylenol) IC2 IC1 Copyright (c)2014 John Wiley & Sons, Inc Slope = -A/B IC3 x Chapter Three 36 Special Functional Forms Perfect PerfectComplements: Complements: UU==Amin(x,y) Amin(x,y) where: where:AAisisaapositive positiveconstant constant MU MUx ==00ororAA x Copyright (c)2014 John Wiley & Sons, Inc MU MUy ==00ororAA y MRS MRSx,y isis00ororinfinite infiniteororundefined undefined(corner) (corner) x,y Chapter Three 37 Special Functional Forms y Example: Perfect Complements • (nuts and bolts) Copyright (c)2014 John Wiley & Sons, Inc IC2 IC1 x Chapter Three 38 Special Functional Forms Quasi-Linear Preferences: U = v(x) + Ay Where: A is a positive constant "The "Theonly onlything thingthat thatdetermines determinesyour yourpersonal personaltrade-off trade-offbetween betweenxxand andyyisishow howmuch muchxxyou you already alreadyhave." have." *can be used to "add up" utilities across individuals* *can be used to "add up" utilities across individuals* Chapter Three 39 Copyright (c)2014 John Wiley & Sons, Inc MU = v’(x) = ∆V(x)/∆x, where ∆ small MU = A x y Special Functional Forms y Example: Quasi-linear Preferences • (consumption of beverages) IC2 IC’s have same slopes on any IC1 Copyright (c)2014 John Wiley & Sons, Inc vertical line • • x Chapter Three 40 ... utility Chapter Three 29 Marginal Rate of Substitution The Marginal Rate of Substitution 2 Example: U = Ax +By ; MU =2Ax; MU = 2By x y (where: A and B positive) = MU /MU x y = 2Ax/ 2By = Ax /By Copyright... indifferent And thus a contradiction And thus a contradiction Chapter Three 21 Copyright (c)2014 John Wiley & Sons, Inc to C by transitivity to C by transitivity Indifference Curves Example U = xy Check... ononly onlyone oneindifference indifferencecurve curve Chapter Three 19 Indifference Curves Copyright (c)2014 John Wiley & Sons, Inc Monotonicity Chapter Three 20 Indifference Curves Cannot Cross