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 w2=5 w1=5 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
Optimal Choice x2 |MRS( )| =1 x1
Optimal Choice x2 |MRS( )| =1 x1
Optimal Choice x2 MRS( ) =1 x1
Price Offer Curve x2 x1
Cobb-Douglass
Labor Supply Two “goods”: leisure time, R, and consumption, C A worker is endowed with time 24h Consumption good’s price is pc. w is the wage rate in $.
Labor Supply The worker’s budget constraint is where C, R denote gross demands for the consumption good and for leisure. This can be rewritten as
Labor Supply C 24 R
Labor Supply C 24 R
Cobb Douglass C 24 R
Backward-Bending Supply 24 R