1. L04 Choice

2. Big picture u Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. u Budget set = affordable alternatives u To model choice we must have decisionmaker’s preferences.

3. MRS and Utility Function x2x2x2x2 x1x1x1x1 RS is a slope of the indifference curve at x MRS is a slope of the indifference curve at x x Q: Can we recover MRS from knowledge of U(x)?

4. Utility and Marginal Utility

5. MRS and Marginal Utility u Yes, but we have to find marginal utilities for both goods first (MU) u MU: How much utility we gain by adding an extra unit of good i

6. Example u U(x 1,x 2 ) = x 1 x 2

7. Example u V(x 1,x 2 ) = ln(x 1 )+ln(x 2 )

8. u Cobb Douglass utility function u Log function Cobb-Douglass utility u Conclusion: preferences are Cobb-Douglass

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

10. MRS of Monotonic transformations u V=f(U) and f strictly increasing u Can we say something about MRS?

11. Choice $ $ $$$ $ $$ $$

12. u How can we modify our argument if u Marginal utility of a dollar Different prices u We should equalize MU of a $!

13. Choice $ $ $$$ $ $$ $$

14. Problem (thinking on the margin!) Two secrets of happiness: 1. Spend your total income 2. Equalize marginal utility of a $ Rearranging:

15. Choice: Calculation

16. Choice: geometric solution x1x1 x2x2

17. u SOH for Well-behaved preferences But: u Perfect Complements (Right and Left shoe) u Perfect Substitutes (Example: French and Dutch Cheese) SOH for other preferences

18. Perfect Complements (Shoes) L R

19. More generally L R

20. Choice: Calculation

21. Perfect Substitutes (F & D cheese) F D

22. More generally X1X1 X2X2

23. Perfect Substitutes