lecture 2: demand advanced micro theory msc.envinatres 1/2005 charit tingsabadh
Post on 20-Dec-2015
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TRANSCRIPT
Determinants of demand
• Price of own good
• Price of other goods
• Income
• Other things-taste, socio-economic characteristics, etc.
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
Studying effects of changes
• Income elasticity:• By definition: % change in good/%change in income
Q/Q)/(M/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
xi/pj = (xi/pj)Uconstant – xj (xi/dm)
Write as elasticity Multiply by pj/xi and for last term, multiply by m/m
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
Effects (continued)
xi/pj .(pj/xi)= (xi/pj)Uconstant (pj/xi)– xj (xi/dm)( pj/xi.)(m/m)
E = E* -
Where E = total elasticity
E* = compensated effect
= share of expenditure of good I
= income elasticity of good i
• This is the Slutzky equation
Functional forms of Demand functions
• Should have standard properties of demand
• Easy to manipulate mathematically
• Standard forms: AIDS, LES, Direct and indirect Addilog
Almost Ideal Demand System
• AIDS (Deaton and Muellbauer 1980)
• wi = i + ij ln pj + ln (y/P), i ,j=1…n
• wi = share of good I in total expenditure
• pj = price of good j
• P = price index defined by
• lnP = 0 + jln pj + (1/2)ij ln pipj
Linear Expenditure System
• Stone-Geary Utility function (q) = i ln (qj-i) i= 1,…nThis gives the demand function
qj = j +j (y -pii)/pj
Multiply by pj
pj qj = pj j + j (y -pii)
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