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Section 2 - Consumer Theory • Consumer theory attempts to explain why consumers choose one good or bundle of goods over another good or bundle of goods. 1 Section 2 - Consumer Theory • In Consumer Theory we will discuss: –Consumer Utility (Chapter 3) –Utility and Constraints (Chapter 4) –Utility and the Demand Curve (Chapter 5) 2 Chapter 3 – Consumer Preferences and the Concept of Utility • Every day, people make choices about what they prefer: –Buy a red car with a sunroof or a green truck with 4 wheel drive –Buy Edo and a chocolate milk or MacDonalds and a Diet Coke –Buy a computer with a 24” LCD screen and windows or a computer with a 21” screen with an apple on it 3 Chapter 3 – Consumer Preferences and the Concept of Utility • In this chapter we will study: 3.1 Preferences and Ranking 3.2 Utility Functions 3.3 Indifference Curves 3.4 Marginal Rates of Substitution 3.5 Special Utility Functions 4 3.1 Preference Definitions • Basket (bundle) – any combination of goods and services –3 hot dogs, 2 pop and 1 ice cream –Haircut, manicure and 20 min massage –2 punches in the gut, 1 kick in the groin • Consumer preferences – any ranking of two baskets –I prefer 2 hot dogs and a coke to a hot dog, coke and ice cream 5 Preference Assumptions 1) Preferences are complete - A consumer can always rank preferences: a) A is preferred to B: A B b) B is prefered to A: B A c) A consumer is indifferent between A and B: A ≈ B 6 Preference Example 1)Preferences are complete - “I would rather go to a movie with Bobby than go skiing with Mark.” (valid) -“I prefer a computer with a good video card and large screen to a computer with a good sound card and good speakers.” (valid) - “I hate everyone equally!” (valid) - “I can’t decide whether Ruth or Victoria is hotter!” (invalid) 7 Preference Assumptions 2) Preferences are transitive - Choices are consistent: If a) A is preferred to B: A B b) B is preferred to C: B C then a) A is preferred to C: A C 8 Preference Example 2) Choices are transitive - “I would rather see the movie Star Wars than Tears and Feelings. I prefer seeing Oceans 13 to Star Wars. Therefore, I prefer Oceans 13 to Tears and Feelings.” (valid) -“Ruth is hotter than Victoria and Susan is cuter than Ruth. Victoria is more attractive than Susan, however.” (invalid) 9 Preference Assumptions 3) More is better - A consumer always prefers having more of a good Examples: -“I prefer seven hot dogs to 3.” -“It’s better to have loved and lost than never to have loved at all!” -“2 heads are better than 1.” 10 Ranking Ordinal Ranking -baskets are ordered or compared to each other without any quantitative information or intensity of preference -ie: “I like dogs more than cats.” Cardinal Ranking -baskets are quantitatively compared -ie: “I like dogs ten times more than cats.” 11 3.2 Utility •util: unit of pleasure. • utility: a number that represents the level of satisfaction that the consumer derives from consuming a specific quantity of a good. 12 Total Utility, Marginal Utility • TU (total utility): –the total amount of satisfaction that you get from consuming a product. • MU (marginal utility): –the increase in TU that comes about as a result of consuming one more unit of the product. –The slope of the total utility function 13 Marginal Utility • If one more unit of a good is consumed, the marginal utility is equal to the increased utility from that extra good • If more than one additional good is consumed: Utility MU Goods 14 Law of Diminishing MU • The MU (marginal utility) of a good or service will decline as more units of that good or service are consumed. •Marginal utility is what counts for rational consumer decisions. • The “More is Better” assumption is violated if MU ever becomes negative (ie: eating 23 pieces of pizza) 15 Total utility is maximized... 34 Marginal Utility (utils per week) Total Utility (utils per week) Maximizing Unconstrained Utility 28 22 0 2 3 4 5 6 7 8 Performances per Week 10 8 6 4 2 0 2 3 4 …where marginal utility equals zero. 5 6 7 Performances per Week 16 Marginal Utility Example • Let Utility (U) depend on how much pizza you eat (P), therefore U(P) 2 P • Therefore the first piece of pizza gives you 2 “utils” of pleasure, but 4 pieces of pizza give you 4 “utils” of pleasure, not 10….marginal utility is diminishing: 1 MU(P) P 17 Utility With 2 or More Goods • Utility and 1 good can be measured on a 2dimensional graph • Utility and 2 goods must be measured on a 3dimensional graph • Here Marginal Utility uses the ceteris paribus assumption: how does utility change when 1 good changes, everything else held constant? U MU x X y held constant 18 Marginal Utility Example • Let Utility (U) depend on how much pizza (P) and hot dogs (H) you eat, therefore U(P) 2 PH • If hot dogs are held constant, each additional pizza yields less utility: MU(P) H P 19 3.3 Indifference Curves • 3 dimensional graphs are difficult to graph and understand • In practice, consumer preference is graphed using 2 goods on the X and Y axis and INDIFFERENCE CURVES • Each INDIFFERENCE CURVE plots all the goods combinations that yield the same utility; that a person is indifferent between 20 y Consider the utility function U=(xy)1/2. Each indifference curve below shows all the baskets of a given utility level. Consumers are indifferent between baskets along the same curve. 2 • • • 1 • U=2 U=√2 0 1 2 4 x 21 y From the indifference curves, we know that: A ≈ B, C ≈ D C A & D A & A 2 • 1 • C • B C B, D B D • U=2 U=√2 0 1 2 4 x 22 1). Completeness => each basket lies on only one indifference curve 2). Transitivity => indifference curves do not cross 3). Negative Slope => when a consumer likes both goods (MUa and MUb are positive), the indifference curve is downward sloping 4). Thin curves => indifference curves are 23 not “thick” y IC1 B A. (different indifference curves) A ≈ C (same indifference curve) B ≈ C (same indifference curve) Therefore: IC2 B ≈ A by transitivity Contradiction! B • A • C • x 24 y More of any good is more preferred and less of a good is less preferred, so an indifference curve cannot extend into areas I or II; it must slope downward I: Preferred to A • A II: Less preferred IC1 x 25 y Since more is better, baskets B and C should be preferred to basket A BUT they all lie on the same indifference curve, implying indifference. C 2 • • • A B 1 2 1 0 4 x 26 Renegade Indifference Curves • Note that some specialized models produce indifference curves that violate one or more of our assumptions • These models may still be useful, but their violations must always be kept in mind 27 North Example of “more is better” violation •B C • • A IC3 University Of Alberta IC2 IC1 28 East Example: Goods people don’t care about Are these curves Complete? Yes Are these curves Transitive? Catfish in the city Yes 0 IC1 IC2 IC3 IC4 Do these curves have Negative Slope? No Preference direction 29 Movies watched 3.4 Marginal Rate of Substitution (MRS) • All along an individual’s indifference curve, an individual consumes different baskets of goods while remaining at the same utility • The individual is willing to SUBSTITUTE one good for another • An individual must be compensated by an increase in one good if the other good decreases – Ie) if Bob is equally happy with 3 hot dogs and 1 soda or 2 hot dogs and 2 soda, he is willing to give up 1 hot dog for 1 soda or 1 soda for 1 hot dog 30 Marginal Rate of Substitution (MRS) • The marginal rate of substitution (MRS) is the change (loss) in one good needed to offset the change (gain) in another good – In this case, MRS is the trade-off (loss) of y for a small increase in x -”The Marginal Rate of Substitution of x for y” -x is gained, so how much y must be given up -alternately, if x is given up, how much y can we get? • The MRS is equal to the SLOPE of the indifference curve (slope of the tangent to the indifference curve) MRS x , y y x utilityconstant 31 Marginal Rate of Substitution (MRS) U MU x x MU y y but since U 0 as one moves along the indifference curve, -MUx xMU y y MUx y MUy x y x utilityconstant MU x MRS utilityconstant x, y MUy 32 MRS Example Let Ut ility x y MUx 1 2 x , MUy 1 2 y 1 MRSx, y MUx 2 x 1 MUy 2 y MRSx, y y x 33 Diminishing MRS • In general, people tend to value more what they have less of: – Ie) If Frank has 30 chicken wings and 1 Pepsi, he is very willing to give up wings for another Pepsi. If Frank has 10 chicken wings and 2 Pepsi’s, he is less willing to give up wings for Pepsi • Therefore MRSx,y diminishes as x increases along the indifference curve 34 Pepsi Diminishing Marginal Utility • Very willing to give up Pepsi for wings (steep slope=high MRS) Less willing to give up Pepsi for wings (flat slope = low MRS) • IC1 Wings 35 Diminishing MRS • Due to Diminishing MRS, most indifference curves are “bowed” towards the origin (0,0) – As seen in the above graph • If Diminishing MRS does not hold (ie: trading quarters for loonies), the graph is not bowed towards the origin Exercise: Let Utility=(Pepsi)(Wings). For a utility level of 16, sketch the graph and see if 36 Diminishing MRS applies. 3.4 Special Utility Functions • In Economics, utility functions dealing with 2 categories of goods create unique indifferent curves: – Perfect Substitutes – Perfect Compliments • Furthermore, 2 utility functions are widely used by Economists for their desirable properties: – Cobb-Douglas Utility Function – Quasi-Linear Utility Function 37 Perfect Substitutes • Goods that are perfect substitutes can always be substituted for each other on a 1-to-1 basis – If a restaurant doesn’t carry Pepsi, you order a Coke instead – Therefore, MRSCoke, Pepsi=1 and MUCoke/MUPepsi =1 – In general, MRS=a constant, and indifference curves are a straight line 38 Perfect Substitutes: U = Ax + By Where: A, B positive constants MUx = A MUy = B MRSx,y = A/B 1 unit of x is equal to B/A units of y everywhere (constant MRS). 39 Example: Perfect Substitutes (Tylenol, Extra-Strength Tylenol) y Slope = -A/B IC1 0 IC2 IC3 x 40 Perfect Compliments • Some goods are only useful in a set ratio to each other; extra of one good is useless without extra of the other: – Shoes: 1 Left shoe for every Right shoe – Cars: 4 full-size tires for every car – Kraft Dinner: 6 cups of water for every packet – Marriage: 1 Bride for Every Groom • Indifference curves are right angles 41 3. Perfect Complements: U = A min(x,y) where: A is a positive constant. MUX = 0 or A MUY = 0 or A MRSX,Y is 0 (horizontal) or infinite (vertical) or undefined (at corner) 42 Example: Perfect Complements (nuts and bolts) y IC2 IC1 0 x 43 Cobb-Douglas Utility Function • The Cobb-Douglas Utility function is the holy grail of economic models for a variety of reasons: – It’s straightforward – It’s easily modified to suit the model – It has desirable mathematical properties • The Cobb-Douglas Utility function also yields “STANDARD” indifference curves 44 1. Cobb-Douglas: U = Axy where: + = 1; A, , positive constants MUX = Ax-1y (Positive) MUY = Axy-1 (Positive) MRSx,y = (y)/(x) “Standard” case: Downward sloping IC, diminishing MRS 45 y Example: Cobb-Douglas (speed vs. maneuverability) Preference direction IC2 IC1 x 46 Quasi-Linear Utility Function • Quasi-Linear Utility Functions often explain consumer behavior without an overly complex model – It’s effective – It’s simple – It has a catchy name – “Quasi” • In a Quasi-Linear Utility Function, MRS is equal for all points above and below each other: 47 U = v(x) + Ay Where: A is a positive constant. MUx = v’(x) = V(x)/x, where small MUy = A Example: U=4(x)1/2+2y MUx=2/(x) ½ MUy=2 -Useful if one good’s consumption changes little (ie:soap) -linear in Y, non-linear in X (hence quasi48 linear) movies Example: Quasi-linear Preferences (movies and toothpaste) IC’s have same slopes on any vertical line • • 0 IC2 IC1 toothpaste 49 Chapter 3 Key Concepts Preferences Preference Assumptions Utility Marginal Utility Diminishing Marginal Utility Indifference Curves Indifference Curve Properties Marginal Rate of Substitution Diminishing MRS 50 Chapter 3 Key Concepts Special Utility Functions Perfect Substitutes Perfect Compliments Cobb-Douglas Quasi-Linear 51