1. L06 Demand

2. u Model of choice u parameters u Example 1: Cobb Douglass Review

3. Perfect Complements

4. Perfect complements u We know u Focus on one good (x1) u How the demand is affected by a change a) in “own” price b) in income c) in price of other commodity u One variable at the time!

5. Own-Price Changes u We focus on good 1 u We hold p 2 and m constant. u We change p 1 u The change represented by: - Price offer curve - Demand curve

6. Own-Price Change p 1 x1x1 x2x2 Fix p 2 =1 and m=12. Vary p 1 =1, p 1 ’=3, p 1 ’’=4 (5,7) (3,3) (2.5,3) p 1 price offer curve x1*x1* p1p1 Demand curve for commodity 1

7. Own-Price Changes u The curve containing all the utility- maximizing bundles traced out as p 1 changes, with p 2 and m constant, is the p 1 - price offer curve. u The plot of optimal choice of x 1 against p 1 is the demand curve for commodity 1.

8. Ordinary and Giffen goods x1*x1* p1p1

9. Ordinary and Giffen Goods u A good is called ordinary if the quantity always increases as the price decreases. u If, for some values of the price, the quantity demanded rises as the price increases, then the good is called Giffen.

10. Two examples We find price offer and demand curve for u Cobb-Douglas preferences u Perfect complements u In both cases we keep fixed

11. Cobb-Douglass example Data, variable

12. Perfect Complements Data, variable

13. Summary: u Price offer curve - Cobb-Douglas – flat line - Perfect Complements – optimal proportion line u Demand curve - Cobb-Douglas – downward slopping - Perfect Complements – downward slopping Conclusion: both ordinary goods u Preferences generating Giffen good?

14. Giffen Good x1x1 x2x2 p 1 price offer curve x1*x1* Demand curve has a positively sloped part Good 1 is Giffen  p1p1

15. Income Changes u We still focus on good 1 u We hold p 1 and p 2 constant. u We change m u The change represented by: - Income offer curve - Engel curve

16. x1x1 x2x2 Fix p 1 =1, p 2 =1 Vary m=12, m’=6, m’’=4 (5,7) (3,3) (2,2) income offer curve x1*x1* m Engel curve for commodity 1 Income Changes

17. Goods u A good for which quantity demanded rises with income is called normal. (positive slope of Engel curve) u A good for which quantity demanded falls as income increases is called income inferior. (negative slope of Engel curve)

18. Two examples We find income offer and Engel curve for u Cobb-Douglas preferences u Perfect complements u In both cases we assume

19. Cobb-Douglass example Data, variable

20. Perfect Complements Data, variable

21. Summary: u Income offer curve - Cobb-Douglas – ray from origin - Perfect Complements – optimal proportion line u Engel curve - Cobb-Douglas – upward slopping - Perfect Complements – upward slopping Conclusion: both normal goods u Preferences generating inferior good: textbook.

22. Cross-Price Effects u If an increase in p 2 –increases demand for commodity 1 then commodity 1 is a gross substitute for commodity 2. – reduces demand for commodity 1 then commodity 1 is a gross complement for commodity 2.

23. Cobb Douglas example Gross complements of substitutes?

24. Perfect Complements example Gross complements