y A B Price consumption curve (PCC) Or Price expansion path (PEP) x AB Ordinary (Marshallian) Demand function Price effect PxPx x
A B S X Y x0x0 xsxs x1x1 JK M Q Price Effects Initial consumption: A Price decreases from P x to P x Real incomeHicks definition: an initial level of utility x 0 to x s (or A to S) is the sub. effect x s to x 1 (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.
Own Price Elasticity Elastic demand Unitary demand Inelastic demand Price and Expenditure Elasticities
Price Elasticity of Expenditure
if e xI >1 if e xI =1 If e xI
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 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
S A B x AOG 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
The amount of A is a free gift from government. A sum of money equivalent to the value of gift is even better. AOG X A 0 Lump Sum Principle
Individual demand Assume 2 agents (1 and 2) Market Demand