1. Lecture 2: Demand Advanced Micro Theory MSc.EnviNatRes 1/2005 Charit Tingsabadh

2. Topics Demand Demand function Demand curve Empirical demand functions

3. Demand Y X

4. Determinants of demand Price of own good Price of other goods Income Other things-taste, socio-economic characteristics, etc.

5. Effects of changes: income change Y X Outward Shift in budget line, more of each good

6. Income-consumption curve Income or total expenditure Expen diture on good i Engel Curve

7. Effect of price change Y X Income effect Substitution effect

8. Demand Curve price quantity

9. Representations Utility function: U = U(X), –Consumer problem: Max U, s.t. PX l.e. M –Solution: X = f(P,M) Indirect utility function: U=U(P,M) Consumer cost (Expenditure) function: C=C(P,U) –CP: C(P,U) = Min PX s.t. u(X) m.e. U, solution: Compensated demand function: demand curve obtained holding utility level constant (compensated income for price change)=> Hicksian demand curve

10. Studying effects of changes Income elasticity: By definition: % change in good/%change in income  Em =(DQ/Q)/(DM/M) Price elasticity: By definition: % change in good/%change in price From graph, there are two parts to change in quantity when price changes: substitution effect (U constant) and income effect · d x i / d p j = ( d x i / d p j ) Uconstant – x j ( d x i /dm) ·Write as elasticity ·Multiply by p j /x i and for last term, multiply by m/m

11. A note on income effect of price change Suppose price change by small amount dp, From px = m Price changes to p+dp This is equivalent to a fall in income –dm So, (p+dp)x = m-dm Expanding to px+dp.x = m-dm So, dm=-dp.x or dm/dp = -x

12. Effects (continued) · d x i / d p j.(p j /x i )= ( d x i / d p j ) Uconstant (p j /x i )– x j ( d x i /dm)( p j /x i. )(m/m) ·E = E* - Q m Where E = total elasticity E* = compensated effect Q = share of expenditure of good I m = income elasticity of good i This is the Slutzky equation

13. Functional forms of Demand functions Should have standard properties of demand Easy to manipulate mathematically Standard forms: AIDS, LES, Direct and indirect Addilog

14. Almost Ideal Demand System AIDS (Deaton and Muellbauer 1980) w i = a i + S g ij ln p j + b ln (y/P), i,j=1…n w i = share of good I in total expenditure p j = price of good j P = price index defined by lnP = a 0 + S a j ln p j + (1/2) SSg ij ln p i p j

15. Linear Expenditure System Stone-Geary Utility function  f (q) = S b i ln (q j - a i ) i= 1,…n This gives the demand function  q j = a j + b j (y - S p i a i )/p j ·Multiply by p j  p j q j = p j a j + b j (y - S p i a i )

16. Addilog functions See in paper by Lester Taylor: Estimation of Theoretically Plausible Demand Functions from US Consumer Expenditure Survey Data, 2004. http://ag.arizona.edu/arec/pubs/workingpapers.html

17. Further readings