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Dive into consumer theory to understand why consumers make choices, explore preferences, utility functions, indifference curves, and more. Learn about total utility, marginal utility, and rational decision-making.
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Section 2 - Consumer Theory • Consumer theory attempts to explain why consumers make choices: one good or bundle of goods over another good or bundle of goods.
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)
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 desktop computer with a 26” LED screen and windows or a laptop with a 14” screen with an apple on it
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
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
Preference Assumptions • Preferences are complete • A consumer can always rank preferences: • A is preferred to B: A B • B is prefered to A: B A • A consumer is indifferent between A and B: A ≈ B
Preference Example • 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 cuter!” (invalid)
Preference Assumptions 2) Preferences are transitive • Choices are consistent: If • A is preferred to B: A B • B is preferred to C: B C then • A is preferred to C: A C
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)
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.”
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.”
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.
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
Marginal Utility • If one more unit of a good is consumed, the marginal utility is equal to the increased utility from that extra good • Mathematically:
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. • The “More is Better” assumption is violated if MU ever becomes negative (ie: eating 23 pieces of pizza) • Marginal utility is what counts for rational consumer decisions.
Total utility is maximized... 34 28 Total Utility (utils per week) 22 0 2 3 4 5 6 7 8 …where marginal utility equals zero. Performances per Week Maximizing Unconstrained Utility 10 8 6 Marginal Utility (utils per week) 4 2 0 7 2 3 4 5 6 Performances per Week
Marginal Utility Example • Let Utility (U) depend on how much pizza you eat (P), therefore • Therefore the first piece of pizza gives you 2 “utils” of pleasure, but 4 pieces of pizza give you 4 “utils” of pleasure, not 8 (2x4)…marginal utility is diminishing:
Utility With 2 or More Goods • Utility and 1 good can be measured on a 2-dimensional graph • Utility and 2 goods must be measured on a 3-dimensional graph • Here Marginal Utility uses the ceteris paribus assumption: how does utility change when 1 good changes, everything else held constant?
Marginal Utility Example • Let Utility (U) depend on how much pizza (P) and hot dogs (H) you eat, therefore • If hot dogs are held constant, each additional pizza yields less utility:
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
Indifference Curves 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 • • U=2 1 U=√2 0 x 1 2 4
Indifference Curves y From the indifference curves, we know that: A ≈ B, C ≈ D C A & C B, D A & D B A C • • 2 D B • • U=2 1 U=√2 0 x 1 2 4
Properties of Indifference Curves: 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 not “thick”
y Indifference Curves Cannot Cross: B A. (different indifference curves) A ≈ C (same indifference curve) B ≈ C (same indifference curve) Therefore: B ≈ A by transitivity Contradiction! IC2 IC1 B • • A C • x
Negative Slope 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
No Thick Curves y Since more is better, baskets B and C should be preferred to basket A BUT they all lie on the same indifferencecurve, implying indifference. C • • • B 2 A 1 0 x 1 2 4
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
North Example: Living distance from University Example of “more is better” violation • C • B • A IC3 University Of Alberta IC2 IC1 East
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
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 more y do we need? • The MRS is equal to the SLOPE of the indifference curve (slope of the tangent to the indifference curve)
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
Diminishing Marginal Utility Pepsi 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
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 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
Perfect Substitutes • Goods that are perfect substitutes can always be substituted for each other using a FIXED RATIO • 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
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).
Example: Perfect Substitutes (Tylenol, Extra-Strength Tylenol) y Slope = -A/B IC2 IC3 IC1 0 x
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
3. Perfect Complements: U = A min(Bx,Cy) where: A, B, and C are positive constants. MUX = 0 or A MUY = 0 or A MRSX,Y is 0 (horizontal) or infinite (vertical) or undefined (at corner)
Example: Perfect Complements (nuts and bolts) U = 5 min(n,b) b 2 U=10 U=5 1 0 n 2 1
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
Cobb-Douglas 1. Cobb-Douglas: U = Axy where: + = 1; A, , positive constants Ax-1y (Positive) MUX = Axy-1 (Positive) MUY = MRSx,y = (y)/(x) “Standard” case: Downward sloping IC, diminishing MRS
y Example: Cobb-Douglas (speed vs. maneuverability) Preference direction IC2 IC1 x
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:
Quasi-Linear Preferences: 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 quasi-linear)
movies Example: Quasi-linear Preferences (movies and toothpaste) IC’s have same slopes on any vertical line • IC2 • IC1 0 toothpaste
Chapter 3 Key Concepts • Preferences • Preference Assumptions • Utility • Marginal Utility • Diminishing Marginal Utility • Indifference Curves • Indifference Curve Properties • Marginal Rate of Substitution • Diminishing MRS
Chapter 3 Key Concepts • Special Utility Functions • Perfect Substitutes • Perfect Compliments • Cobb-Douglas • Quasi-Linear