1. L05
Choice

2. Problem: We know preferences (utility function) and
We want to know optimal choice

3. Choice $ $ $ $ $ $ $ $ $ $

4. Choice: geometric solutionx2 x1

5. Abstract approach In the example we were given
we found demands - two numbers
Now we use abstract parameters
we find demand functionsNow we
4 types of preferences

6. Abstract Cobb Douglass Function
Cobb Douglass utility functions
and
are equivalent in terms of preferences

7. Abstract Cobb Douglass Function

8. Magic (Cobb-Douglass) formula
Parameters:

9. Cobb-Douglas: Summary
Utility function: or
Solution:
Shares of income

10. Quiz!
A) Let and
B) Let and

11. Interiority
Cobb – Douglass (always interior solution)

12. Cobb- Douglass preferencesx2 x1

13. Is solution always interior?
Not necessarily
Even with well behaved preferences
we might have a corner solution
Example: quasilinear preferences

14. Choice $ $ $ $ $ $ $ $ $ $

15. Is solution interior? Hence demand and Geometric interpretation
How to solve for corner solution?
Find a buddle using standard conditions
If some then in optimum

16. Choice: Calculation

17. Quasilinear preferencesx2 x1

18. Perfect substitutes $ $ $ $ $ $ $ $ $ $

19. Perfect Substitutes x2 x1

20. Magic (Substitutes) Formula

21. Magic (Complements) formula

22. In Practice Cobb-Douglass, Perfect Complements? Quasilinear ?
Perfect Substitutes?