ECON6021 Microeconomic Analysis Consumption Theory II

Topics covered Price Change Price Elasticities Income Elasticities Market Demand

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

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

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

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.

Price Elasticities

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

Price Elasticity of Expenditure

>1 Elastic <1 Inelastic =1 Unitary No change

An Example: Linear demand

An Example: Linear Demand

Review: Linear Demand Q P TR

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

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

Income Elasticities

Income Elasticity

if exI>1 if exI=1 If exI<1

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

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

Cobb-Douglas Utility: U=xy

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.

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

Corollary of Euler Theorem

Lump Sum Principle AOG A B S x

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.

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.

Market Demand

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

Market Demand 100 12.5 50 112.5

The End