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. Ordinary and Giffen goodsp1
x1*

9. Ordinary and Giffen Goods
A good is called ordinary if the quantity always increases as the price decreases.
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
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 of substitutes?