1. Reminder: Assessed Test on this coming Monday Test based on Problem Sheet 1 for Monday night exercise classes All you really need … but should know what Adding-up and Cournot conditions are..and be able to identify an income and substitution effect. Examples on J:\Files\Econ|Tests and Sols Note TFU Class Questions for Final Exam in last week

2. WORK Towards End of Term Econ 201 Week 9 Mon Test on Problem Sheet 2 Week 11 Mon Test on Problem Sheet 3 Week 11 Thur TFU Exam on Course Econ 203 Week 11 Exam on my last part of course and Prof. Backhouse’s section Econ 204 Multiple Choice in January Econ 206 Computer Assessment Week 9 & 10 Econ 212 Week 11 Last week for Essay Econ 211 Essay deferred to January

3. Revealed Preference Approach Chapter 7 Varian Previous process asked what properties must utility functions have to yield the demand functions we usually fit to observed data Some people worry about this.

4. ‘The Austrians’ The Austrians were a group of economists who rejected the use of utility and marginal utility as they saw it as relying on something unmeasurable –Utility They pioneered a process called Revealed preference where they tried to use the ‘known’ – the demands we actually observe - to discover something about the nature of peoples preferences

5. What we will show is that the ‘reveled preference approach’ yields essentially the same outcomes. However, the approach is useful in its own right as it allows to develop a variety of welfare measures commonly used by governments and other policy makers.

6. Revealed Preference All affordable bundles must satisfy the budget constraints (x 1, y 1 ) x y  Optimal bundle will exactly satisfy budget constrains

7. Revealed Preference (x 1, y 1 ) x y  If we observe that (x 1, y 1 ) is chosen then it is directly revealed preferred to (x 2,y 2 ), for all (x 2,y 2 ) that satisfy All affordable bundles must satisfy the budget constraints Optimal bundle will exactly satisfy budget constrains

8. Revealed Preference Thus, we know that (x 1, y 1 ) x y  If we observe that (x 1, y 1 ) is chosen then it is directly revealed preferred to (x 2,y 2 ), for all (x 2,y 2 ) that satisfy

9. So (x 1,y 1 ) is indirectly revealed preferred to (x 3,y 3 ) x y If at another set of prices we observe that the bundle (x 2,y 2 ) is chosen, then for all (x 3,y 3 ) that satisfies It follows that

10. So (x 1,y 1 ) is indirectly revealed preferred to (x 4,y 4 ) x y We can now extend this idea, suppose that (x 3,y 3 ) is chosen at another set of prices. Then that bundle is preferred to everything we could have bought and didn’t

11. It is forming an indifference curve x y But what have we got now? Look at the edge of this revealed preference set. So revealed preference theory is essentially the same as indifference theory

12. If (x 1, y 1 ) is directly revealed preferred to (x 2,y 2 ), and the two bundles are not the same, then it cannot happen that (x 2,y 2 ) is directly revealed preferred to (x 1, y 1 ). This is the weak axiom of revealed preference (WARP) If this occurs then WARP is violated

13. That is:If (x 1,y 1 ) is revealed preferred when (x 2,y 2 ) was affordable then (x 1,y 1 ) is preferred always (or at all prices). Formally: If we observed two bundles of purchases, (x 1,, y 1 ) at p x 1,p y 1 and (x 2,, y 2 ) at p x 2,p y 2 Then if we observe (x 1,, y 1 ) is purchased when Optimising consumers must satisfy WARP then we cannot observe

14. If (x 1,y 1 ) is revealed preferred to (x 3,y 3 ) either directly or indirectly) then (x 3,y 3 ) cannot be directly or indirectly revealed preferred to (x 1,y 1 ) Strong Axiom of Revealed Preference (SARP) SARP is a necessary and sufficient condition for observed behaviour to be consistent with the underlying model of consumer choice

15. Revealed Preference and the Substitution effect: Given revealed preference it MUST be the case that (Slutsky) (x s,y s)