1. ECON6021 Microeconomic Analysis
Consumption Theory II

2. Topics covered Price Change Price Elasticities Income Elasticities
Market Demand

3. Price effect y B A x Price consumption curve (PCC)
Or Price expansion path (PEP) x
Ordinary (Marshallian)
Demand function Px x

4. Price Effects A B S X Y x0 xs x1 J K M Q Initial consumption: A
Price decreases from Px to Px’
Real income—Hick’s definition: an initial level of utility
x0 to xs (or A to S) is the sub. effect
xs to x1 (or S to B) is the income effect

5. Price Effects Price Effects= substitution effect + Income effect
Substitution Effect a.k.a (also known as) pure price effect: a change in relative price while keeping utility constant

6. For income effects, S is the reference point.
M: no income effect
M-Q: X is normal
J-M: X is inferior
A is the reference point for the analysis
of combined effect of income and
substitution effect.
K-Q:
J-K: Giffen gd.
Giffen gd  inferior gd.

7. Price Elasticities

8. Price and Expenditure Elasticities
Own Price Elasticity
Elastic demand
Unitary demand
Inelastic demand

9. Price Elasticity of Expenditure

10. >1 Elastic
<1 Inelastic =1
Unitary
No change

11. An Example: Linear demand

12. An Example: Linear Demand

13. Review: Linear Demand Q P TR

14. Income Change
IEP X
AOG
AOG X
IEP (Income Expansion
Path)

15. x Px
variable
fixed
Demand
IEP I x
fixed
variable
Engel Curve

16. Income Elasticities

17. Income Elasticity

19. if exI>1
if exI=1
If exI<1

20. Engel Aggregation (Adding-up condition)
Aggregate Income elasticity=1

21. Consider an income change…
A-B B
B-C C
C-D D
D-E
X Y
Inferior superior
No income eff superior
Normal only superior
Normal only normal only
Superior normal only
Superior no income effect
Superior inferior Y X A B C D E C’ I0 I1

22. Cobb-Douglas Utility: U=xy

23. Homogenous function Homogenous function of degree k
If there exists a constant k so that for all m>0 and for all a, b
Then, we say F(.) is homogenous of degree k.

24. Euler Theorem Euler Theorem Proof of Euler Theorem.
If F(a,b) is homogenous of degree k, then we have
Proof of Euler Theorem.
Differentiate equation (1) with respect to m & then set m=1

25. Corollary of Euler Theorem

26. Lump Sum Principle
AOG A B S x

27. Lump Sum Principle Chosen dependent on IC
Note that the new consumption at (S) is in a higher IC. In order to get a fixed amount of taxation, lump-sum tax is less harmless to consumers/citizens.

28. Lump Sum Principle AOG X A
The amount of A is a free gift from government.
A sum of money equivalent to the value of gift is even better.

29. Market Demand

30. Market Demand
Individual demand
Assume 2 agents (1 and 2)

31. Market Demand
100
12.5 50
112.5

32. The End