L02

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L02

• Preferences

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Rationality in Economics

• Behavioral PostulateA decisionmaker chooses
  its most preferred alternative from the set of
  affordable alternatives.
• Budget set affordable alternatives
• To model choice we must have decisionmakers
  preferences.

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Last Week
oranges
x(2,3)
p12 p21 M6
apples
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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)

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Rational Decisionmaker

• Rationality Axioms (Assumptions)

x2
y
x
x1
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Indifference Curves

• Convenient representation of Indifference Curves
• The set of all bundles equally preferred to x is
  the indifference curve containing x
  
• The collection of all bundles y x.

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Representation Indifference Curves

• Indifference curve a collection of all
  indifferent bundles.

x2
x x x
x
x
x
x1
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Indifference Curves
x2
z x y
p
p
x
z
y
x1
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Can Two Indifference Curves Intersect?
x2
x
y
z
x1
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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

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Example 1 Perfect complements
Left
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Right
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Example Perfect complements
Coffee
12
Sugar (teaspoons)
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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)

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Example Perfect substitutes
Dutch
French
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Slopes of Indifference Curves (MRS)

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

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

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Preferences Exhibiting Satiation
(pepper)
x2
Satiation point
x2
x1
x1 (salt)
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Well-Behaved Preferences

• We will typically assume that preferences are
  well-behaved
• monotonic (all goods)
• convex

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Convexity.
Preferences are convex if mixtures z are
preferred to extremes x and y.
x(1,3)
x2
z (2,2)
y(3,1)
y2
x1
y1
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Convex preferences?
x2
x2
x1
x1