1. L04
Choice

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

3. MRS and Utility Function
MRS is a slope of the indifference curve at x x2
Q: Can we recover MRS from knowledge of U(x)? x x1

4. Utility and Marginal Utility

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

6. Example
U(x1,x2) = x1 x2

7. Example
V(x1,x2) = ln(x1)+ln(x2)

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

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

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

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

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

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

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

15. Choice: Calculation

16. Choice: geometric solutionx2 x1

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

18. Perfect Complements (Shoes)

19. More generally R L

20. Choice: Calculation

21. Perfect Substitutes (F & D cheese)

22. More generally X2 X1

23. Perfect Substitutes