Rational Consumer Behavior and Social Efficiency

1
Rational Consumer Behavior and Social Efficiency

• ECO61 Microeconomic Analysis
• Udayan Roy
• Fall 2008

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Economic efficiency

• What does the tangency condition for rational
  consumer choice tell us about the overall
  efficiency of the economy?
• Or, what can we say about the overall efficiency
  of the economy if the tangency condition is not
  satisfied?

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Economic efficiency

• As all consumers pay the same prices, PX/PY is
  the same for all
• Therefore, the tangency condition for rational
  consumer behavior implies that MRSXY must be the
  same for all
• Why is this significant?
• To see why, imagine two consumers, Blue and Red,
  such that Reds MRSXY exceeds Blues

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Economic efficiency

• Blues (Reds) goods bundle is B (R)
• The shaded areas denote superior bundles
• The (negatives of the) slopes of the tangent
  lines at B and R denote MRSXY.
• Blues MRS
• Reds MRS 3
• Blues MRS 0.5

R
3
-1
0.5
-1
B
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Economic efficiency

• Shift Blues indifference curve till B coincides
  with R
• It is now possible to find a blue arrow and a red
  arrow, of equal length and pointing in
  diametrically opposed directions, from R such
  that the red arrow is pointing to an improved
  bundle for Red and the blue arrow, when moved to
  B, points to an improved bundle for Blue.
• In this way, it can be shown that when MRSXY is
  not equal for two or more consumers, it is
  possible to make everybody better off by simply
  redistributing X and Y among the consumersno
  additional X or Y is necessary!
• This proves that an economy in which not all
  consumers have the same MRSXY is inefficient

R
B
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Economic efficiency

• In this example, Blue and Red have the same MRSXY
• Recall that this is what prevails under rational
  consumer behavior
• Now it is impossible to redistribute goods among
  them in a way that would benefit both
• This satisfies one condition of Pareto efficiency

R
B
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Economic efficiency

• Under the tangency condition of rational consumer
  behavior, Blue and Red have the same MRSXY
• As a result, it is impossible redistribute X and
  Y between Blue and Red so as to make both of them
  better off
• This is one condition that an efficientformally,
  Pareto efficienteconomy must satisfy
• A competitive, free-market economy does satisfy
  this requirement of Pareto efficiency

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Economic efficiency

• Heres another way to look at the issue
• Suppose
• Red is willing to pay 3 units of Y for 1 unit of
  X. (That is, Reds MRSXY 3.)
• Blue is willing to pay 0.5 units of Y for 1 unit
  of X
• Then it is easy to make both Red and Blue better
  off by
• taking 1 unit of X from Blue (who does not like X
  very much) and giving it to Red (who likes X a
  lot)
• and compensating Blue by taking, say, 2 units of
  Y from Red and giving it to Blue

2Y
Blue
Red
MRSXY 3
MRSXY 0.5
1X
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Economic efficiency

• Under rational consumer behavior both Blue and
  Red will have the same MRSXY
• Suppose both individuals are willing to pay 2
  units of Y for 1 unit of X
• If you take 1 unit of X from Red to give to Blue,
  you will have to compensate Red by taking 2 units
  of Y from Blue and giving it to Red
• But in that case neither Red nor Blue would be
  better off and the redistribution would be
  pointless
• This shows that under rational consumer behavior,
  it is impossible to improve upon the market
  outcome
• If the market outcome is unimprovable (in
  Paretos sense) it must be efficient to begin with