L08

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L08

• Buying and Selling

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Review

• Model of choice
• We know preferences and
• we find demands
• Q Where does the mysterious income come from?
  
• From selling goods (e.g. labor)!
• Today Model of choice with endowments

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Endowments

• Instead of nominal income goods
• The list of commodities with which a consumer
  starts is his endowment.
• A consumers endowment will be denoted by the
  vector (omega).
• Example

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Budget constraint

• Suppose p12 and p23 and
• what is the value of endowment?
• What is a collection of all affordable bundles
  (budget set)?

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Budget Constraints Revisited

• Given p1 and p2, the budget constraint for a
  consumer with an endowment
• is
• Example

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Budget Constraints Revisited
x2
x1
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More generally

x2
w2
w1
x1
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Net Demands

• Net demands actual trades of a consumer
• Example
• Net demands (buying, selling)?

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Budget Constraints Revisited

• The constraintis
• The sum of the values of a consumers net demands
  is zero.
• Buying, selling?

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Buying, Selling?
x2
w25
w15
x1
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Optimal Choice

• Almost the same as before
• We only need to find m first
• When are we net buyers of good 1?
• We first answer it graphically
• Price offer curve

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Magic Formulas

• Cobb Douglass
• Perfect Complements

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Optimal Choice
x2
MRS( ) 1
x1
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Optimal Choice
x2
MRS( ) 1
x1
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Optimal Choice
x2
MRS( ) 1
x1
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Gains-to-Trade

• Consumer engages in trade if
• In particular

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Price Offer Curve
x2
x1
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Price offer curve

• With initial endowments price offer curve is
  enveloped by the indifference curve that
  passes though endowment
• Intuition Agents engage in trade only trade
  gives higher utility

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Cobb-Douglass