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L02

L02. Preferences. Rationality in Economics. Behavioral Postulate : A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. Budget set = affordable alternatives To model choice we must have decisionmaker’s preferences. Last Week. oranges. x=(2,3).

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L02

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  1. L02 Preferences

  2. Rationality in Economics • Behavioral Postulate:A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. • Budget set = affordable alternatives • To model choice we must have decisionmaker’s preferences.

  3. Last Week oranges x=(2,3) p1=2 p2=1 M=6 apples

  4. f ~ f ~ Today: Preferences • Rational agents: can rank any two consumption bundles • We call such ranking preferences • weak preference: x is at least as good as is y. (x y) • strict preference: x is strictly better than is y. (x y) • indifference: x is exactly as preferred as is y. (x y)

  5. Completeness: • either or or both x y y x f ~ II) Transitivity: x y and y z x z. f f f f f f f f f z ~ ~ ~ ~ ~ ~ ~ ~ ~ Rational Decisionmaker • Rationality Axioms (Assumptions) x2 y x x1

  6. f ~ Indifference Curves • Convenient representation of Indifference Curve Map • The set of all bundles equally preferred to x is the indifference curve containing x; • The collection of all bundles y ~ x.

  7. Representation: Indifference Curves • Indifference curve = a collection of all indifferent bundles. x2 x’ ~ x” ~ x”’ x’ x” x”’ x1

  8. Indifference Curve Map x2 zxy p p x z y x1

  9. Can Two Indifference Curves Intersect? x2 x y z x1

  10. Example: Perfect Complements • Two goods always consumed in the same proportion • Example: Right and Left Shoes • We like to have more of them but always in pairs

  11. Example 1: Perfect complements Left 1:1 Right

  12. Example: Perfect complements Coffee 1:2 Sugar (teaspoons)

  13. Example: Perfect substitutes • Two goods that are substituted at the constant rate • Example: French and Dutch Cheese (I like cheese but I cannot distinguish between the two kinds)

  14. Example: Perfect substitutes Dutch French

  15. Slopes of Indifference Curves (MRS) • The slope of an indifference curve is its marginal rate-of-substitution (MRS). • Why rate-of-substitution? • Why marginal?

  16. Slope: Marginal Rate of Substitution x2 MRS(x) is a slope of the indifference curve at x x x1

  17. Slope of Indifference Curves • When more of a commodity is always preferred, the commodity is a good. • Two goods. Sign of MRS? Good 2 Good 1

  18. Slope of Indifference Curves • If less of a commodity is prefered the commodity is a bad. (Spinach) • Two goods. Sign of MRS? Bad 2 Good 1

  19. Preferences Exhibiting Satiation • Many commodities become bads after some threshold of consumption (salt and pepper) • Bundle consisting of threshold quantities is called a satiation point or a bliss point. • A satiation point is strictly preferred to any other bundle.

  20. Preferences Exhibiting Satiation (pepper) x2 Satiation point x*2 x*1 x1 (salt)

  21. Well-Behaved Preferences • We will typically assume that preferences are well-behaved: • monotonic (all goods) • weakly convex

  22. Convexity. Preferences are convex if mixtures “z” are (weakly) preferred to extremes x and y. x=(1,3) x2 z =(2,2) y=(3,1) y2 x1 y1

  23. Convex preferences? x2 x2 x1 x1

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