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Lecture 2: Demand

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

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Lecture 2: Demand

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  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 Expenditure on good i Engel Curve Income or total expenditure

  7. Effect of price change Y Income effect X 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 • dxi/dpj = (dxi/dpj)Uconstant – xj (dxi/dm) • Write as elasticity • Multiply by pj/xi 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) • 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

  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) • wi = ai + Sgij 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 + Sajln pj + (1/2)SSgij ln pipj

  15. Linear Expenditure System • Stone-Geary Utility function • f(q) = Sbi 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)

  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

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