1. L06
Demand

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

3. Perfect Complements

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

5. Own-Price Changes We focus on good 1 We hold p2 and m constant.
We change p1
The change represented by:
Price offer curve
Demand curve

6. Own-Price Change p1 Vary p1=1, p1’=3, p1’’=4 Fix p2=1 and m=12. x2
Demand curve for commodity 1
p1 price offer
curve p1
(5,7)
(2.5,3)
(3,3)
x1* x1

7. Own-Price Changes
The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and m constant, is the p1- price offer curve.
The plot of optimal choice of x1 against p1 is the demand curve for commodity 1.

8. Own-Price Changes
The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and m constant, is the p1- price offer curve.
The plot of optimal choice of x1 against p1 is the demand curve for commodity 1.

9. Ordinary and Giffen goodsp1
x1*

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

11. Cobb-Douglass example
Data , variable

12. Perfect Complements
Data , variable

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

14. Giffen Good Demand curve has a positively sloped part p1 price offerx2
p1 price offer
curve p1 Û
Good 1 is Giffen x1
x1*

15. Income Changes We still focus on good 1 We hold p1 and p2 constant.
We change m
The change represented by:
Income offer curve
Engel curve

16. Income Changes Fix p1=1, p2=1 Vary m=12, m’=6, m’’=4 x2
Engel curve for commodity 1
income offer
curve m
(5,7)
(3,3)
(2,2)
x1* x1

17. Goods
A good for which quantity demanded rises with income is called normal.
(positive slope of Engel curve)
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
Cobb-Douglas preferences
Perfect complements
In both cases we assume

19. Cobb-Douglass example
Data , variable

20. Perfect Complements
Data , variable

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

22. Cross-Price Effects If an increase in p2
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