Lecture 2: Demand

Advanced Micro TheoryMSc.EnviNatRes

1/2005Charit Tingsabadh

Topics

• Demand

• Demand function

• Demand curve

• Empirical demand functions

Demand

Y

X

Determinants of demand

• 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

Income or total expenditure

Expenditure on good i

Engel Curve

Effect of price change

Y

X

Income effect

Substitution effect

Demand Curveprice

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

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

Further readings

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