L08 Buying and Selling

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

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

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)?

Budget Constraints Revisited Given p1 and p2, the budget constraint for a consumer with an endowment is Example:

Budget Constraints Revisited x2 x1

More generally x2 w2 w1 x1

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

Budget Constraints Revisited The constraint is The sum of the values of a consumer’s net demands is zero. Buying, selling?

Buying, Selling? x2 w2=5 w1=5 x1

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

Magic Formulas Cobb Douglass Perfect Complements

Optimal Choice x2 |MRS( )| =1 x1

Optimal Choice x2 |MRS( )| =1 x1

Optimal Choice x2 MRS( ) =1 x1

Gains-to-Trade Consumer engages in trade if: In particular:

Price Offer Curve x2 x1

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

Cobb-Douglass