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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 consumer’s endowment will be denoted by the vector (omega). Example
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Budget constraint Suppose p1=2 and p2=3 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 constraint is The sum of the values of a consumer’s net demands is zero. Buying, selling?
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Buying, Selling? x2 w2=5 w1=5 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
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