3. Preferences and Utility FunctionsModel of Consumer BehaviorSlide Number 3Slide Number 4PreferencesPreferencesIndifference CurvesSlide Number 8Indifference CurvesSlide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Preference MapsUtilitySlide Number 17Slide Number 18Slide Number 19UtilitySlide Number 21Utility and Indifference CurvesSlide Number 23Willingness to Substitute Between GoodsSlide Number 25Slide Number 26Slide Number 27Marginal Utility and MRSSlide Number 29Curvature of Indifference CurvesSlide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 423. Preferences and Utility Functions • Preferences • Preference properties • Utility functions • Indifference curves • Marginal utility and marginal rate of substitution • Common utility functions 1Model of Consumer Behavior • Premises of the model:  Individual tastes or preferences determine the amount of pleasure people derive from the goods and services they consume.  Consumers face constraints, or limits, on their choices.  Consumers maximize their well-being or pleasure from consumption subject to the budget and other constraints they face. 2Consumer Preferences tell us how the consumer would rank any two combinations of goods or services, assuming these combinations were available to the consumer at no cost. These combinations of goods are referred to as bundles. These bundles are assumed to be available for consumption at a particular time, place and under particular physical circumstances. Consumer Preferences 3Example: Bundles of Food and Clothing 4Preferences • To explain consumer behavior, economists assume that consumers have a set of tastes or preferences that they use to guide them in choosing between goods. • Goods are ranked according to how much pleasure a consumer gets from consuming each.  Preference relations summarize a consumer’s ranking  is used to convey strict preference (e.g. a b)  is used to convey weak preference (e.g. a b)  is used to convey indifference (e.g. a b) 5Preferences • Properties of preferences: 1. Completeness • When facing a choice between two bundles of goods (e.g. a and b), a consumer can rank them so that either a b, b a, or a ~ b. 2. Transitivity • Consumers’ rankings are logically consistent in the sense that if a b and b c, then a c. 3. Monotonicity (More is Better) • All else the same, more of a commodity is better than less. • In this regard, a “good” is different than a “bad.” 6Indifference Curves • The set of all bundles of goods that a consumer views as being equally desirable can be traced out as an indifference curve. • Five important properties of indifference curves: – Bundles of goods on indifference curves further from the origin are preferred to those on indifference curves closer to the origin. – There is an indifference curve through every possible bundle. – Indifference curves cannot cross. – Indifference curves slope downward. – Indifference curves cannot be thick. 7Completeness ⇒ each bundle lies on only one indifference curve Transitivity ⇒ indifference curves do not cross (Strict) Monotonicity ⇒ indifference curves have negative slope …and… indifference curves are not “thick” Properties of indifference curves 8Indifference Curves • Impossible indifference curves: 9One more assumption usually is made: - Convexity of preferences such that . The reference ( ) is convex if for all . The preference ( ) is strictly convex if for all ,AB∀~AB(1 )C A BAλλ=⋅+− ⋅[0,1]λ∈(1 )C A BAλλ=⋅+− ⋅(0,1).λ∈Indifference curves 10IC2 x y • A • B • (.5A + .5B) IC1 0.5λ=11IC1 IC2 x y Preference direction 12OSU Stadium IC1 IC2 IC3 North East • • • C B A Non-monotonic preferences with a bliss point. 13Example: For the indifference curves graphed below, are the underlying preferences: - Complete? - Transitive? - Monotonic? - Are averages preferred to extremes? x y IC1 IC2 IC3 IC4 Preference direction 0 14Preference Maps • Collection of all the indifference curves • Graphical interpretation of consumer preferences over two goods: 15Utility • Utility refers to a set of numerical values that reflect the relative rankings of various bundles of goods. • The utility function is the relationship between utility measures and every possible bundle of goods. • A utility function preserves the preference ranking. • Example: q1 = pizza and q2 = burritos • Bundle x contains 16 pizzas and 9 burritos: U(x) = 12 • Bundle y contains 13 pizzas and 13 burritos: U(y) = 13 • Thus, y x 16Ordinal ranking: Ranking that indicates whether one bundle is preferred to another, but does not contain quantitative information about the intensity of that preference. Cardinal ranking: Ranking with a quantitative measure of the intensity of a preference for one bundle over another. 17Examples: 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. 18Difference in magnitudes of utility has no interpretation per se; 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 = xy vs. U = xy + 2 represent the same references. Any positive monotone transformation preserves the preference ordering. So utility function is unique only up to a positive monotone transformation. 19Utility • Utility is an ordinal measure rather than a cardinal one. • Utility tells us the relative ranking of two things but not how much more one rank is valued than another. • We don’t really care that U(x) = 12 and U(y) = 13 in the previous example; we