Notation and assumptions Graphing preferences Properties/Assumptions MRS. Preferences. Intermediate Micro. Lecture 3. Chapter 3 of Varian

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1 Preferences Intermediate Micro Lecture 3 Chapter 3 of Varian

2 The central question of economics Microeconomics: study of decision-making under scarcity Scarcity: last topic Decision-making: next 3 topics 1. Ranking of options 2. Putting numbers to the rankings 3. Modeling the decision Applications and interpretations follow

3 Context Usually use 2-good examples and exercises Very restrictive ( Strong assumption ) Fine for specific contexts Methods apply for 2 to goods Real-world: infinitely many goods Context matters, not just item

4 Ranking consumption bundles Consumption bundles (x 1, x 2 ) and (y 1, y 2 ) Strict preference (x 1, x 2 ) (y 1, y 2 ) (x 1, x 2 ) is preferred to (y 1, y 2 ) Indifferent (x 1, x 2 ) (y 1, y 2 ) (x 1, x 2 ) is just as good as (y 1, y 2 ) Weak preference (x 1, x 2 ) (y 1, y 2 ) (x 1, x 2 ) is at least as good as (y 1, y 2 )

5 Properties of preferences Axioms of an individual s preferences 1. Completeness: Either A B or B A 2. Reflexivity: A A 3. Transitivity: If A B and B C, then A C If A B and B C, then A C If A B and B C, then A C If A B and B C, then A C Axioms means we will always assume these properties **Preferences deal with bundles, not goods!**

6 Properties of preferences 3 options: Roosevelt (R), Taft (T ), Wilson (W ) Does each voter follow 3 axioms? Hershel (H): Josiah (J): R T R W T W R T R W T W Kent (K): R T R W T W

7 Properties of preferences within a group H :R T W J :T W R K :W R T Election between R&T 2 for R, 1 for T Election between R&W 2 for W, 1 for R Election between T &W 2 for T, 1 for W Transitive? Election between R, T, W 1 for R, 1 for T, 1 for W Who wins? Primary between R&T, then election against W Who wins?

8 Properties of preferences within a group H :R T W J :T W R K :W R T Election between R&T 2 for R, 1 for T Election between R&W 2 for W, 1 for R Election between T &W 2 for T, 1 for W Transitive? Election between R, T, W 1 for R, 1 for T, 1 for W Who wins? Primary between R&T, then election against W Who wins?

9 Graphing preferences How to illustrate preference relations Pick bundle X = (x 1, x 2 ) Find all Y X Weakly preferred set: Graph of all such Y bundles Indifference curve: Border of weakly preferred set

10 Indifference Curves Different indifference curves can t cross! Suppose X Y Draw indifference curve through X Draw indifference curve through Y Implication if they cross at Z? Hint: axioms

11 Perfect substitutes Indifference curves are straight Constant slope At any (x 1, x 2 ), same willingness to trade between good 1 and 2 Gallon gas from Exxon vs gallon gas from 7-11 Small bag of chips vs large bag of chips

12 Perfect complements Indifference curves are right angles Indifferent between kink point and increase of a single good Left shoes and right shoes Bicycles and handlebar tape

13 In-between

14 Bads x 1 good, x 2 bad Willing to decrease 1 for decrease in 2 Pollution, traffic, coconut,... Neutrals neither good nor bad

15 Satiation Some best point ( x 1, x 2 ) Satiation point, or bliss point True of most specific goods What about $?

16 Discrete goods Discrete good: a good only available in indivisible units Examples: cars, housing, pets Indifference sets are collections of points Preferred sets are collections of rays

17 Properties/Assumptions Assume properties of preferences Not true of all situations Monotonicity Convex preferences Well-behaved indifference curves: Monotonicity, convexity, and 3 axioms make for well-behaved preferences Handy for studying decisions

18 Monotonicity ( y1 x 1 and y 2 x 2, at least one strictly (y 1, y 2 ) (x 1, x 2 ) ) More is always better Moving up and/or right goes to higher indifference curve Indifference curves have negative slope

19 (Strictly) convex preferences (x 1, x 2 ) (y 1, y 2 ) ( (αx1 + (1 α)y 1, αx 2 + (1 α)y 2 ) (x 1, x 2 ) αs.t0 < α < 1 ) Take any 2 consumption bundles from same indifference curve Find a (weighted) average The average is preferred to either extreme

20 Weakly convex preferences (x 1, x 2 ) (y 1, y 2 ) ( (αx1 + (1 α)y 1, αx 2 + (1 α)y 2 ) (x 1, x 2 ) αs.t0 < α < 1 ) Take any 2 consumption bundles from same indifference curve Find a (weighted) average The average is weakly preferred (at least as good) to either extreme

21 Convex preferences Strictly convex preferences Weakly convex preferences

22 Marginal rate of substitution Preferences Rank bundles Show willingness to exchange Given bundle (x 1, x 2 ), indifferent with Gain small x 2 Lose small x 1 x 2 x 1 Value of good 1 relative to good 2 ( 1 )Slope of indifference curve

23 Marginal rate of substitution If offered trade: From (x1, x 2 ) To anywhere on red line Will choose to change Higher indifference curve

24 Marginal rate of substitution lim x1 0 x 2 x 1 dx 2 dx 1 Marginal rate of substitution: Slope of indifference curve at (x 1, x 2 ) No benefit to trading on these terms: (x 1, x 2 ) price of good 2 in terms of good 1 = MRS

25 Marginal rate of substitution With monotone, convex preferences MRS is slope of line tangent to indifference curve at (x 1, x 2 ) Unwilling to trade from (x 1, x 2 ) along MRS line

26 Diminishing marginal rate of substitution Monotone, convex preferences Diminishing marginal rate of substitution: MRS goes towards zero as x 1 Intuition?

27 Perfect substitutes

28 Perfect complements