8 Chapter Highlights Preferences A. Preferences are relationships between bundles 1. if a consumer would choose bundle(r1, r2)when(y1, y2)is available, then it is natural to say that bundle (a1, r2)is preferred to(y1, y2) by thi consumer 2. preferences have to do with the entire bundle of goods, not with individual B. Notation 1.(1, r2)>(y1, y2) means the x-bundle is strictly preferred to the y- bundle 2.(1, T2)N(y1, y2) means that the x-bundle is regarded as indifferent to 3.(31, 122(91, y2) means the x-bundle is at least as good as(preferred to or indifferent to) the y-bundle C. Assumptions about preferences 1. complete- any two bundles can be compared 2. reflexive any bundle is at least as good as itself 3. transitive-if X >Y and Y>Z, then X>Z a)transitivity necessary for theory of optimal choice D. Indifference curves 1. graph the set of bundles that are indifferent to some bundle. See Figure 2. indifference curves are like contour lines on a map 3. note that indifference curves describing two distinct levels of preference cannot cross. See Figure 3.2. a)proof- use transitivity E. Examples of preferences 1. perfect substitutes. Figure 3.3 a)red pencils and blue pencils; pints and quarts b) constant rate of trade-off between the two goods b)right shoes and left shoes; coffee and crean 3. bads. Figure 3.5. 4. neutrals. Figure 3.6 5. satiation or bliss point Figure 3.7. F. Well-behaved preference monotonicity more of either good is better a)implies indifference curves have negative slope. Figure 3.9 2. convexity -averages are preferred to extremes. Figure 3.10 a)slope gets Hatter as you move further to righ b) example of non-convex preferences G. Marginal rate of substitution l. slope of the indifference curve 2. MRS=A r2/ AT1 along an indifference curve. Figure 3.11 3. sign problem - natural sign is negative, since indifference curves will generally have negative sloy for consumption of good 2. Figure 3. 12 trade off consumption of good 1 4. measures how the consumer is willing to8 Chapter Highlights Preferences A. Preferences are relationships between bundles. 1. if a consumer would choose bundle (x1, x2) when (y1, y2) is available, then it is natural to say that bundle (x1, x2) is preferred to (y1, y2) by this consumer. 2. preferences have to do with the entire bundle of goods, not with individual goods. B. Notation 1. (x1, x2)  (y1, y2) means the x-bundle is strictly preferred to the y￾bundle 2. (x1, x2) ∼ (y1, y2) means that the x-bundle is regarded as indifferent to the y-bundle 3. (x1, x2)  (y1, y2) means the x-bundle is at least as good as (preferred to or indifferent to) the y-bundle C. Assumptions about preferences 1. complete — any two bundles can be compared 2. reflexive — any bundle is at least as good as itself 3. transitive — if X  Y and Y  Z, then X  Z a) transitivity necessary for theory of optimal choice D. Indifference curves 1. graph the set of bundles that are indifferent to some bundle. See Figure 3.1. 2. indifference curves are like contour lines on a map 3. note that indifference curves describing two distinct levels of preference cannot cross. See Figure 3.2. a) proof — use transitivity E. Examples of preferences 1. perfect substitutes. Figure 3.3. a) red pencils and blue pencils; pints and quarts b) constant rate of trade-off between the two goods 2. perfect complements. Figure 3.4. a) always consumed together b) right shoes and left shoes; coffee and cream 3. bads. Figure 3.5. 4. neutrals. Figure 3.6. 5. satiation or bliss point Figure 3.7. F. Well-behaved preferences 1. monotonicity — more of either good is better a) implies indifference curves have negative slope. Figure 3.9. 2. convexity — averages are preferred to extremes. Figure 3.10. a) slope gets flatter as you move further to right b) example of non-convex preferences G. Marginal rate of substitution 1. slope of the indifference curve 2. MRS = ∆x2/∆x1 along an indifference curve. Figure 3.11. 3. sign problem — natural sign is negative, since indifference curves will generally have negative slope 4. measures how the consumer is willing to trade off consumption of good 1 for consumption of good 2. Figure 3.12