1. L06
Demand

2. Review: Cobb-Douglass
Utility (2 forms)
Indifference curve map
SoH: Magic formulas:
Solution always interior

3. Extreme p: Perfect Complements
Utility
Indifference curve map
SoH: Magic formulas:
Solution always interior

4. Extreme p: Perfect Substitutes
Utility
Indifference curve map
Magic formulas:
Bang-Bang Solution (typically corners)

5. Comparative statics 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!

6. 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

7. 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

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. Cobb-Douglas example We find price offer and demand curve for
Cobb-Douglas preferences
We keep fixed

11. Cobb-Douglass example
Data , variable

12. Quiz For Cobb-Douglass Price offer curve flat Demand downward-slopping
Q1: For Cobb-Douglas preferences commodities
are ordinary goods
are Giffen goods
Depends on the parameters
I do not know

13. 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

14. 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

15. 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)

16. Cobb-Douglas example We find income offer and Engel curve for
Cobb-Douglas preferences
In both cases we assume

17. Cobb-Douglass example
Data , variable

18. Quiz For Cobb-Douglass Income offer curve- ray from origin
Engel curve upward-slopping
Q1: For Cobb-Douglas preferences commodities
are normal goods
are inferior goods
Depends on the parameters
I do not know

19. 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.

20. Cobb Douglas example
Gross complements of substitutes?

21. Perfect Complements example
Gross complements