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
w2=5
w1=5 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. Optimal Choice x2
|MRS( )| =1 x1

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

14. Optimal Choice x2
MRS( ) =1 x1

15. Price Offer Curve x2 x1

16. Cobb-Douglass

17. 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 $.

18. 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

19. Labor Supply C 24 R

20. Labor Supply C 24 R

21. Cobb Douglass C 24 R

22. Backward-Bending Supply24 R