1. L08
Buying and Selling

2. 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

3. 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

4. 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)?

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

6. Budget Constraints Revisitedx2 x1

7. More generally x2 w2 w1 x1

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

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

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

11. 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

12. Magic Formulas
Cobb Douglass
Perfect Complements

13. Optimal Choice x2
|MRS( )| =1 x1

14. Optimal Choice x2
|MRS( )| =1 x1

15. Optimal Choice x2
MRS( ) =1 x1

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

17. Price Offer Curve x2 x1

18. 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

19. Cobb-Douglass