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. A) Let and
B) Let and

11. Interiority
Cobb – Douglass (always interior solution)

12. Cobb- Douglass preferencesx2 x1

13. SOH (Perfect Complements)

14. SOH (Perfect Complements)

15. Perfect Complements (SOH)
Interior or corner solution?

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

17. Perfect substitutes $ $ $ $ $ $ $ $ $ $

18. Perfect Substitutes x2 x1

19. Magic (Substitutes) Formula

20. Choice $ $ $ $ $ $ $ $ $ $

21. 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

22. Choice: Calculation

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