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 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
w25
w15
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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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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Optimal Choice
x2
x1
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Cobb-Douglass
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Labor Supply

• Two goods leisure time, R,
• and consumption, C
• A worker is endowed with time 24h
• Consumption goods price is pc.
• w is the wage rate in .

¾
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Labor Supply
C
24
R
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Labor Supply

• The workers budget constraint iswhere C, R
  denote gross demands for the consumption good and
  for leisure.
• This can be rewritten as

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Labor Supply
C
24
R
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Cobb Douglass
C
24
R