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