Transcript Document

Lecture 2: Demand
Advanced Micro Theory
MSc.EnviNatRes
1/2005
Charit Tingsabadh
Topics
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Demand
Demand function
Demand curve
Empirical demand functions
Demand
Y
X
Determinants of demand
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Price of own good
Price of other goods
Income
Other things-taste, socio-economic
characteristics, etc.
Effects of changes: income change
Y
X
Outward Shift in budget line, more of each good
Income-consumption curve
Expen
diture
on
good i
Engel Curve
Income or total
expenditure
Effect of price change
Y
Income effect
Substitution effect
X
Demand Curve
price
quantity
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
 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
 dxi/dpj = (dxi/dpj)Uconstant – xj (dxi/dm)
 Write as elasticity
 Multiply by pj/xi and for last term, multiply by m/m
A note on income effect of price
change
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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)
 dxi/dpj .(pj/xi)= (dxi/dpj)Uconstant (pj/xi)– xj (dxi/dm)( pj/xi.)(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
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 = ai + S gij ln pj +b 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 = a0 + S ajln pj + (1/2)SSgij ln pipj
Linear Expenditure System
• Stone-Geary Utility function
 f(q) = S bi ln (qj-ai) i= 1,…n
This gives the demand function
 qj = aj +bj (y -Spiai)/pj
 Multiply by pj
 pj qj = pj aj + bj (y -Spiai)
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
Further readings