L08 Buying and Selling

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

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

Budget constraint u Suppose p 1 =2 and p 2 =3 and what is the value of endowment? u What is a collection of all affordable bundles (budget set)?

Budget Constraints Revisited u Given p 1 and p 2, the budget constraint for a consumer with an endowment is u Example:

Budget Constraints Revisited x2x2 x1x1

u Q: shift of the budget line A) Is parallel, outwards B) Is parallel inwards C) Is a rotation around D) Is a rotation around Quiz x2x2 x1x1   

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

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

Buying, Selling? x2x2 x1x1   =5   =5

Quiz x2x2 x1x1 u Q: Consumer is A) Buying, selling B) Buying C) Selling D) Buying, selling

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

Magic Formulas u Cobb Douglass u Perfect Complements

Optimal Choice x2x2 x1x1 |MRS( )| =1

Optimal Choice x2x2 x1x1 |MRS( )| =1

Optimal Choice x2x2 x1x1 MRS( ) =1

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

Price Offer Curve x2x2 x1x1

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

Cobb-Douglass