Unformatted text preview: Microeconomics, 2nd Edition David Besanko and Ronald Braeutigam Chapter 3: Consumer Preferences and the Concept of Utility 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. 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. 2 Complete: 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) Transitive: 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 C A B; B C 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 original basket.
3 Age Number of Subjects Intransitive Choices (%) 4 39 83 5 33 82 6 23 82 7 35 78 8 40 68 9 52 57 10 45 52 11 65 37 12 81 23 13 81 41 Adults 99 13 Source: See Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998.
4 An Indifference Curve or Indifference Set: is the set of all baskets for which the consumer is indifferent An Indifference Map : illustrates a set of indifference curves for a consumer 5 1). Monotonicity => indifference curves have negative slope ...and... indifference curves are not "thick" 2). Transitivity => indifference curves do not cross 3). Completeness => each basket lies on only one indifference curve 6 Averages preferred to extremes => indifference curves are bowed toward the origin (convex to the origin). One more assumption usually is made: 7 Families Who Had Another Child (by Number and Sex of Children) Number of Children Number of Boys Number of Families that Families had another Child 56 51 56 47 44 45 48 40 40 38 40 41 2 2 35,674 1 64,585 0 31,607 3 3 10,431 2 26,497 1 24,897 0 8,948 4 4 2,619 3 8,260 2 11,489 1 7,527 0 2,241 Source: See Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998.
8 boys Preference direction (locally) 2 1 0 1 2 Indifference curves girls
9 y IC1 x
10 y Preference direction IC2 IC1 x
11 y A IC1 x
12 y Preferred to A A IC1 x
13 y Preferred to A Less preferred A IC1 x
14 y IC1 Suppose that B preferred to A. but..by definition of IC, B indifferent to C A indifferent to C => B indifferent to A by transitivity. Contradiction. A x 15 y IC1 IC2 A B Suppose that B preferred to A. but..by definition of IC, B indifferent to C A indifferent to C => B indifferent to C by transitivity. Contradiction. C x
16 y A B IC1 x
17 y A (.5A, .5B) IC2 B IC1 x
18 y A (.5A, .5B) IC2 B IC1 x
19 North Nonmonotonic preferences with a bliss point. C University Of Essex A B IC3 IC2 IC1 (complete and transitive only) East 20 Example: For the indifference curves graphed below, are the underlying preferences:
IC1 IC2 y IC3 IC4
Complete? Transitive? Monotonic? Are averages preferred to extremes? Preference direction 0 "Neutrals" x 21 The 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...or... 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...or... 22 It is the rate of exchange between goods x and y that does not affect the consumer's welfare...or... It is the negative of the slope of the indifference curve: MRSx,y = y/x (for a constant level of preference) 23 An indifference curve exhibits a diminishing rate of substitution: if 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 axis. Example: The Diminishing Marginal Rate of Substitution 24 Example: For the following indifference curves, the marginal rate of substitution between x and y is: 1, .5, 2, 5 diminishing? y 1 2 3 Example: Marginal Rate of Substitution 0 IC1 1 IC2 2 IC3 3 x 25 Example: For the following indifference curves, the marginal rate of substitution between x and y is: 0? Infinite? undefined ? Diminishing? all of the above? 26 y IC2 IC1 0 x
27 The utility function: assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets. Utility is an ordinal concept: the precise magnitude of the number that the function assigns has no significance. 28 Utility, elevation Example: Utility and elevation Alps UK 0 Pyrenees location
29 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 marks would be an ordinal ranking. 30 difference in magnitudes of utility have 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 preferences. 31 Example: U = xy Check that underlying preferences are complete, transitive, monotonic and averages are preferred to extremes... 32 y Example: Utility and a single indifference curve 5 2 0 2 5 10 = xy x
33 y Example: Utility and a single indifference curve 5 Preference direction 20 = xy 2 0 2 5 10 = xy x
34 The 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 held constant) = MUx U/y (x held constant) = MUy ...or...the marginal utility of x is the slope of the utility function with respect to x. The principle of diminishing marginal utility: states that the marginal utility falls as the consumer consumes more of a good 35 Relative Income and Life Satisfaction (within nations) Relative Income Percent > "Satisfied" Lowest quartile 70 Second quartile 78 Third quartile 82 Highest quartile 85
Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998. 36 Absolute Income and Life Satisfaction (across nations)
GNP per number of median "satisfaction" capita nations score < $2,000 1 5.5 $2,000$4,000 3 6.6 $4,000$8,000 6 7.0 $8,000$16,000 14 7.4 Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: U Saddle River, New Jersey. 1998. 37 MUx(x) + MUy(y) = 0 ...along an IC... MUx/MUy = y/x = 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)
38 2 2 Example: U = Ax +By ; MU =2Ax; MU =2By x y (where: A and B positive) 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 39 Implications of this... Indifference curves are negativelysloped, bowed out from the origin, preference direction is up and right Indifference curves intersect the axes 40 y
Example: Graphing Indifference Curves IC1 0 x
41 y
Example: Graphing Indifference Curves Preference direction IC1 0 IC2 x
42 .5 .5 .5 .5 .5 Example: U= (xy) ;MU =y /2x ; MU =x /2y x y 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/x 43 Do the indifference curves intersect the axes? A value of x = 0 or y = 0 is inconsistent with any positive level of utility. 44 y Example: Graphing Indifference Curves IC1 x
45 y Example: Graphing Indifference Curves Preference direction IC2 IC1 x
46 1. CobbDouglas: U = Axy where: + = 1; A, , positive constants MUX = Ax1y Ax 1 MUY = y MRSx,y = (y)/(x) "Standard" case
47 y Example: CobbDouglas (speed vs. maneuverability) IC1 x
48 y Example: CobbDouglas (speed vs. maneuverability) Preference direction IC2 IC1 x
49 Perfect 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). 50 y Example: Perfect Substitutes (Tylenol, ExtraStrength Tylenol) Slope = A/B 0 IC1 IC2 IC3 x
51 3. Perfect 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) 52 y Example: Perfect Complements (nuts and bolts) IC1 0 x
53 y Example: Perfect Complements (nuts and bolts) IC2 IC1 0 x
54 U = 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 tradeoff between x and y is how much x you already have." *can be used to "add up" utilities across individuals* 55 y Example: Quasilinear Preferences (consumption of beverages) IC1 0 x
56 y Example: Quasilinear Preferences (consumption of beverages) IC2 IC1 IC's have same slopes on any vertical line 0 x 57 1. Described consumer preferences without any restrictions imposed by budget 2. Minimal assumptions on preferences to get interesting conclusions on demand...seem to be satisfied for most people. (ordinal utility function) 58 ...
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 Spring '08
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 Utility, indifference curves, Upper Saddle River, D. Hirshleifer

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