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L05

L05. Choice. Problem:. We know preferences (utility function) and We want to know optimal choice. Choice. $. $. $. $. $. $. $. $. $. $. Choice: geometric solution. x 2. x 1. Abstract approach. In the example we were given we found demands - two numbers

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L05

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  1. L05 Choice

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

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

  4. Choice: geometric solution x2 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 preferences x2 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?

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