Chapter 3 Preferences

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• Chapter 3 Preferences
• Choose the best thing one can afford
• Start with consumption bundles (a complete list
  of the goods that are involved in consumers
  choice problem)
• A binary relation w
• (x1, x2) w (y1, y2) is read as (x1, x2) is at
  least as good as (y1, y2)
• This binary relation w is complete, reflexive and
  transitive

2

• Complete for any (x1, x2), (y1, y2), either (x1,
  x2) w (y1, y2), (y1, y2) w (x1, x2) or both
  (every two bundles can be compared)
• Reflexive for any (x1, x2), (x1, x2) w (x1, x2)
  (any bundle is at least as good as itself)
• Transitive for any (x1, x2), (y1, y2), (z1, z2),
  if (x1, x2) w (y1, y2) and (y1, y2) w (z1, z2),
  then (x1, x2) w (z1, z2)
• Rational preference
• One can experimentally test whether these three
  axioms are satisfied. (kids, social preference)

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• From this binary relation w, one can derive two
  other binary relations s and i.
• (x1, x2) s (y1, y2) if and only if (x1, x2) w
  (y1, y2) and it is not the case that (y1, y2) w
  (x1, x2). Read this as the consumer strictly
  prefers (x1, x2) to (y1, y2).
• (x1, x2) i (y1, y2) if and only if (x1, x2) w
  (y1, y2) and (y1, y2) w (x1, x2). Read this as
  the consumer is indifferent between (x1, x2) and
  (y1, y2).

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• Given a binary relation w and for (x1, x2),
• can list all the bundles that are at least as
  good as it the weakly preferred set
• Similarly, can list all the bundles for which
  the consumer is indifferent to it the
  indifference curve
• We dont need to use the idea of utility.
  Preferences are enough.

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Fig. 3.1
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• Two distinct indifference curves cannot cross.
• Perfect substitutes ten dollar coins and five
  dollar coins
• Perfect complements left shoe and right shoe
• Bads, neutrals
• Satiation
• Discrete goods

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Fig. 3.2
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Fig. 3.3
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Fig. 3.4
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Fig. 3.5
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Fig. 3.6
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Fig. 3.7
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Fig. 3.8
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• Some useful assumption
• Monotonicity if x1 y1, x2 y2 and (x1, x2) ?
  (y1, y2), then (x1, x2) s (y1, y2) (the more, the
  better) (indifference curves have negative
  slopes) (Examine)
• Convexity if (y1, y2) w (x1, x2) and (z1, z2) w
  (x1, x2), then for any weight t between 0 and 1,
  (ty1(1-t)z1, ty2(1-t)z2) w (x1, x2) (averages
  are preferred to extremes) (Examine) (interior
  solution, non convex ref to circle)

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Fig. 3.9
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Fig. 3.10
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• Strict convexity if (y1, y2) w (x1, x2), (z1,
  z2) w (x1, x2), and (y1, y2) ? (z1, z2), then for
  any weight t strictly in between 0 and 1,
  (ty1(1-t)z1, ty2(1-t)z2) s (x1, x2)
• The marginal rate of substitution (the MRS one
  thing for another thing, evaluated where)
  measures the rate at which the consumer is just
  willing to substitute one thing for the other

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• MRS1, 2 for a little of good 1, the amount of
  good 2 that the consumer is willing to give up to
  stay indifferent about this change, ?x2/ ?x1
• The MRS1, 2 at a point is the slope of the
  indifference curve at that point (to stay put)
  and measures the marginal willingness to pay for
  good 1 in terms of good 2. If good 2 is money,
  then it is often called the marginal willingness
  to pay.

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Fig. 3.11
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• Useful assumption diminishing MRS (when you have
  more of x1, it can substitute for x2 less)