Chapter 3 - Consumer preferences and the concept of utility. This chapter presents the following content: Motivation, consumer preferences and the concept of utility, the utility function, indifference curves, the marginal rate of substitution, some special functional forms.
Chapter Copyright (c)2014 John Consumer Preferences and the Concept of Utility Chapter Three Overview Motivation Consumer Preferences and the Concept of Utility Copyright (c)2014 John The Utility Function • Marginal Utility and Diminishing Marginal Utility Indifference Curves The Marginal Rate of Substitution 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 goods and services Chapter Three Copyright (c)2014 John • Consumer Preferences 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 Three Copyright (c)2014 John 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 Consumer Preferences Assumptions Preferences 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 C A B; B C = > A Chapter Three C Copyright (c)2014 John Complete and Transitive Consumer Preferences Assumptions Preferences are monotonic if a basket with more of at least one good and no less of any good is preferred to the original basket Chapter Three Copyright (c)2014 John Monotonic / Free Disposal Types of Ranking 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 Three Copyright (c)2014 John Example: The Utility Function The three assumptions about preferences allow us to represent preferences with a 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) Chapter Three Copyright (c)2014 John Utility function 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 y e.g U = vs U = + representation of preferences represent the same preferences Chapter Three Copyright (c)2014 John • Marginal Utility Marginal 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 y 10 Chapter Three Copyright (c)2014 John • Marginal Rate of Substitution MUx( x) + MUy( y) = 0 …along an IC… 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 Three 26 Copyright (c)2014 John MUx/MUy = - y/ x = MRSx, y Marginal Rate of Substitution The Marginal Rate of Substitution • • Indifference curves are negatively-sloped, bowed out from the origin, preference direction is up and right Indifference curves not intersect the axes Chapter Three 27 Copyright (c)2014 John Implications of this substitution: Indifference Curves Averages preferred to extremes => indifference curves are bowed toward the origin (convex to the origin) Chapter Three 28 Copyright (c)2014 John Key Property Indifference Curves A value of x = or y = is inconsistent with any positive level of utility Chapter Three 29 Copyright (c)2014 John Do the indifference curves intersect the axes? Marginal Rate of Substitution The Marginal Rate of Substitution Example: U = Ax2+By2; MUx=2Ax; MUy=2By MRSx,y = MUx/MUy = 2Ax/2By = Ax/By 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 Copyright (c)2014 John (where: A and B positive) Indifference Curves Example: U= (xy).5;MUx=y.5/2x.5; MUy=x.5/2y.5 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/x Chapter Three 31 Copyright (c)2014 John A Is more better for both goods? Yes, since marginal utilities are positive for both Indifference Curves y Copyright (c)2014 John Example: Graphing Indifference Curves Preference direction IC2 IC1 Chapter Three 32 x Special Functional Forms Cobb-Douglas: U = Ax y where: + = 1; A, , positive MUX = Ax constants Copyright (c)2014 John 1y MUY = Ax y -1 MRSx,y = ( y)/( x) “Standard” case Chapter Three 33 Special Functional Forms y Copyright (c)2014 John Example: Cobb-Douglas (speed vs maneuverability) Preference Direction IC2 IC1 Chapter Three 34 x Special Functional Forms Perfect Substitutes: U = Ax + By MUx = A MUy = B MRSx,y = A/B so that unit of x is equal to B/A units of y everywhere (constant MRS) Chapter Three 35 Copyright (c)2014 John Where: A, B positive constants Special Functional Forms y Slope = -A/B IC1 IC2 IC3 x Chapter Three 36 Copyright (c)2014 John Example: Perfect Substitutes • (Tylenol, Extra-Strength Tylenol) Special Functional Forms Perfect Complements: U = Amin(x,y) MUx = or A MUy = or A MRSx,y is or infinite or undefined (corner) Chapter Three 37 Copyright (c)2014 John where: A is a positive constant Special Functional Forms y Example: Perfect Complements • (nuts and bolts) Copyright (c)2014 John IC2 IC1 Chapter Three 38 x Special Functional Forms QuasiLinear Preferences: U = v(x) + Ay MUx = v’(x) = V(x)/ x, where A small MUy = "The only thing that determines your personal tradeoff between x and y is how much x you already have." *can be used to "add up" utilities across individuals* Chapter Three 39 Copyright (c)2014 John Where: A is a positive constant Special Functional Forms y Example: Quasi-linear Preferences • (consumption of beverages) IC1 • • IC’s have same slopes on any vertical line Chapter Three 40 x Copyright (c)2014 John IC2 ... constant) = MUy Chapter Three 13 Copyright (c)2014 John Marginal Utility Marginal Utility Example of U(H) and MUH U(H) = 10H – H2 MUH = 10 – 2H H2 16 36 64 100 U(H) MUH 16 24 24 -2 16 -6 -1 0 Chapter. .. contradiction Chapter Three 21 Copyright (c)2014 John Cannot Cross Indifference Curves Example U = xy2 MU x MU y y 2 xy for U x Chapter Three 144 y xy^2 4.24 1 43. 8 144 144.0 6. 93 22 Copyright... curves not 3) Completeness => each basket lies on only one indifference curve Chapter Three 19 Copyright (c)2014 John Key Properties Indifference Curves Copyright (c)2014 John Monotonicity Chapter