Quản trị kinh doanh - Chapter 3: Consumer preferences and the concept of utility

1Consumer Preferences and the Concept of UtilityChapter 3Copyright (c)2014 John Wiley & Sons, Inc.2Chapter Three Overview1. Motivation2. Consumer Preferences and the Concept of Utility3. The Utility FunctionMarginal Utility and Diminishing Marginal Utility4. Indifference Curves5. The Marginal Rate of SubstitutionSome Special Functional FormsChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.3Motivation• 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 goods and servicesChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.4Consumer PreferencesConsumer 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.These allotments of goods are referred to as baskets or bundles. These baskets are assumed to be available for consumption at a particular time, place and under particular physical circumstances. Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.5Consumer PreferencesAssumptionsPreferences are complete if the consumer can rank any two baskets of goods (A preferred to B; B preferred to A; or indifferent between A and B)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 CComplete and TransitiveA  B; B  C = > A  CChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.6Consumer PreferencesAssumptionsPreferences are monotonic if a basket with more of at least one good and no less of any good is preferred to the original basket.Monotonic / Free DisposalChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.7Types of RankingExample: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 marks would be an ordinal ranking.Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.8The Utility FunctionChapter ThreeThe 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.– assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets.– U = u(y)Copyright (c)2014 John Wiley & Sons, Inc.9The Utility FunctionImplications: 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 representation of preferences. e.g. U = vs. U = + 2 represent the same preferences.Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.10Marginal UtilityMarginal Utility of a good y additional utility that the consumer gets from consuming a little more of y i.e. the rate at which total utility changes as the level of consumption of good y rises MUy = U/y slope of the utility function with respect to yChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.11Diminishing Marginal UtilityThe principle of diminishing marginal utility states that the marginal utility falls as the consumer consumes more of a good.Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.Diminishing Marginal Utility12Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.13Marginal UtilityThe marginal utility of a good, x, is the additional utility that the consumer gets from consuming a little more of x when the consumption of all the other goods in the consumer’s basket remain constant.U(x, y) = x + y U/x (y held constant) = MUx U/y (x held constant) = MUy Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.14Marginal UtilityExample of U(H) and MUHU(H) = 10H – H2MUH = 10 – 2HChapter ThreeHH2U(H)MUH2416641624263624-286416-6101000-10Copyright (c)2014 John Wiley & Sons, Inc.15Marginal UtilityChapter ThreeU(H) = 10H – H2MUH = 10 – 2HCopyright (c)2014 John Wiley & Sons, Inc.16Marginal UtilityExample of U(H) and MUHChapter ThreeThe point at which he should stop consuming hotdogs is the point at which MUH = 0This gives H = 5. That is the point where Total Utility is flat.You can see that the utility is diminishing.Copyright (c)2014 John Wiley & Sons, Inc.17Marginal Utility – multiple goodsU = xy2MUx = y2MUy = 2xyChapter Three More is better? More y more and more x indicates more U so yes it is monotonic Diminishing marginal utility? MU of x is not dependent of x. So the marginal utility of x (movies) does not decrease as the number of movies increases. MU of y increases with increase in number of operas (y) so neither exhibits diminishing returns.Copyright (c)2014 John Wiley & Sons, Inc.18Indifference CurvesAn Indifference Curve or Indifference Set: is the set of all baskets for which the consumer is indifferentAn Indifference Map : Illustrates a set of indifference curves for a consumerChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.19Indifference Curves1) Monotonicity => indifference curves have negative slope – and indifference curves are not “thick”2) Transitivity => indifference curves do not cross3) Completeness => each basket lies on only one indifference curveKey PropertiesChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.20Indifference CurvesMonotonicityChapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.21Indifference CurvesCannot CrossSuppose that B preferred to A.but..by definition of IC,B indifferent to CA indifferent to C => B indifferentto C by transitivity. And thus a contradiction.Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.22Indifference CurvesExampleU = xy2Check that underlying preferences are complete, transitive, and monotonic.Chapter Threexyxy^284.24143.84614436.93144.07112144Copyright (c)2014 John Wiley & Sons, Inc.23Indifference CurvesExample: Utility and the single indifference curve. Chapter ThreeU = 144Copyright (c)2014 John Wiley & Sons, Inc.24Marginal Rate of SubstitutionThe marginal rate of substitution: is the maximum rate at which the consumer would be willing to substitute a little more of good x for a little less of good y;It is the increase in good x that the consumer would require in exchange for a small decrease in good y in order to leave the consumer just indifferent between consuming the old basket or the new basket;It is the rate of exchange between goods x and y that does not affect the consumer’s welfare;It is the negative of the slope of the indifference curve:MRSx,y = -y/x (for a constant level of preference)Chapter ThreeCopyright (c)2014 John Wiley & Sons, Inc.25The Diminishing MarginalRate of SubstitutionIf the more of good x you have, the more you are willing to give up to get a little of good y or  the indifference curves get flatter as we move out along the horizontal axis and steeper as we move up along the vertical axisChapter ThreeMarginal Rate of SubstitutionCopyright (c)2014 John Wiley & Sons, Inc.26-y/x = MUx(x) + MUy(y) = 0 along an IC MUx/MUy = MRSx,y Positive marginal utility implies the indifference curve has a negative slope (implies monotonicity)Diminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes)Chapter ThreeMarginal Rate of SubstitutionCopyright (c)2014 John Wiley & Sons, Inc.27Implications of this substitution: Indifference curves are negatively-sloped, bowed out from the origin, preference direction is up and right  Indifference curves do not intersect the axesChapter ThreeThe Marginal Rate of SubstitutionMarginal Rate of SubstitutionCopyright (c)2014 John Wiley & Sons, Inc.28Indifference CurvesChapter ThreeAverages preferred to extremes => indifference curves are bowed toward the origin (convex to the origin).Key PropertyCopyright (c)2014 John Wiley & Sons, Inc.29Chapter ThreeIndifference CurvesDo the indifference curves intersect the axes? A value of x = 0 or y = 0 is inconsistent with any positive level of utility. Copyright (c)2014 John Wiley & Sons, Inc.30Marginal utilities are positive (for positive x and y)Example: U = Ax2+By2; MUx=2Ax; MUy=2By(where: A and B positive)MRSx,y= MUx/MUy= 2Ax/2By= Ax/ByMarginal utility of x increases in x;Marginal utility of y increases in yChapter ThreeThe Marginal Rate of SubstitutionMarginal Rate of SubstitutionCopyright (c)2014 John Wiley & Sons, Inc.31 Example: U= (xy).5;MUx=y.5/2x.5; MUy=x.5/2y.5A. Is more better for both goods? Yes, since marginal utilities are positive for both. B. Are the marginal utility for x and y diminishing? Yes. (For example, as x increases,for y constant, MUx falls.)C. What is the marginal rate of substitution of x for y? MRSx,y = MUx/MUy = y/xChapter ThreeIndifference CurvesCopyright (c)2014 John Wiley & Sons, Inc.32Example: Graphing Indifference Curves IC1IC2xyPreference directionChapter ThreeIndifference CurvesCopyright (c)2014 John Wiley & Sons, Inc.33Cobb-Douglas: U = Axy where:  +  = 1; A, , positive constants MUX =Ax-1y MUY = Ax y-1MRSx,y =(y)/(x)“Standard” caseChapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.34Example: Cobb-Douglas (speed vs. maneuverability) IC1IC2xyPreference DirectionChapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.35Perfect Substitutes: U = Ax + By Where: A, B positive constants  MUx = A MUy = B  MRSx,y = A/B so that 1 unit of x is equal to B/A units of y everywhere (constant MRS).Chapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.36Example: Perfect Substitutes (Tylenol, Extra-Strength Tylenol) x0yIC1IC2IC3Slope = -A/BChapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.37Perfect Complements: U = Amin(x,y) where: A is a positive constant.  MUx = 0 or A MUy = 0 or A  MRSx,y is 0 or infinite or undefined (corner)Chapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.38Example: Perfect Complements (nuts and bolts)x0yIC1IC2Chapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.39U = v(x) + Ay Where: A is a positive constant.MUx = v’(x) = V(x)/x, where  small MUy = A"The only thing that determines your personal trade-off between x and y is how much x you already have." *can be used to "add up" utilities across individuals*Quasi-Linear Preferences: Chapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.40Example: Quasi-linear Preferences (consumption of beverages)••IC’s have same slopes on anyvertical linexy0IC2IC1Chapter ThreeSpecial Functional FormsCopyright (c)2014 John Wiley & Sons, Inc.