Income and substitution effect
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1 Income and substitution effect O93 (pring 0) 6 & (Tutorial 4) X Initial equilibrium: with, and Y uppose to, and Y remains unchanged. ew equilibrium: with, and Y The price effect is composed of two effects: substitution effect () and income effect (I). I ubstitution effect: change in consumption of a good associated with a change in its price, with the level of utility held constant. is always negative, i.e. when and vice versa. Income effect: change in consumption of a good resulting from an increase in purchasing power, with relative prices held constant. I can be positive or negative ormal goods: positive I, i.e. Y Inferior goods: negative I, i.e. Y Derivation of demand curve (Uncompensated Demand) Y (I) Y X (I) X Z (I) Z (I) I ormal good (+I) I + (oint ) Downward sloping DD Inferior good (I) (a) > I ( > ) I + (oint Z) Downward sloping DD (b) = I ( = ) I + (oint X) Vertical DD (c) < I ( < ) I + (oint Y) Upward sloping DD (Giffen goods)
2 ompensated and Uncompensated demand curve ompensated (Hicksian)demand curve: x = h(p x, p y, U) It shows the quantity demanded for a good at each price, holding utility constant. (ubstitution effect only, real income remains constant) Uncompensated (arshallian, Ordinary) demand curve: x =l(p x, p y, I) It shows the quantity demand for a good at each price, holding nominal income constant. (ubstitution effect and Real income effect) Y (I) Y X (I) X Z (I) Z (I) ompensated DD ( only) Uncompensated DD ( + I) Good is a normal good When drops, real income is higher and is higher Real income effect is positive ormal good ore elastic uncompensated DD Uncompensated DD ( + I) Z ompensated DD ( only) Good is an inferior good When drops, real income is higher and is lower Real income effect is negative Inferior good ore inelastic uncompensated DD
3 Demand relationships among goods and lasticities () Own price effect ormal good if (downward sloping demand) Giffen good if (upward sloping demand) rice elasticity of demand () Income effect ormal good if (downward sloping demand) Inferior good if (downward/ upward sloping demand) Income elasticity of demand Luxury/ superior good if ecessity if (3) ross price effect Gross substitutes if Gross complement if Does imply? ross-price elasticity of demand lasticities and Demand functions Does the own price/ income/ cross price elasticity of demand depends on p x, I and p y? () Linear demand function: rice elasticity of demand Income elasticity of demand ross-price elasticity of demand () on-linear demand function: ( and rice elasticity of demand Income elasticity of demand ross-price elasticity of demand 3
4 (3) Other demand functions: logarithmic regression models Logarithms convert changes in variables into percentage changes (a) Linear demand function: What are a, b, c and d? What are, and? (b) Linear-log demand function: % change in p x is associated with a change of x by 0.0b If, then % change in p y is associated with a change of x by 0.0c % change in I is associated with a change of x by 0.0d (c) Log-linear demand function: change in p x by unit is associated with a (00)b% change in x change in p y by unit is associated with a (00)c% change in x change in I by unit is associated with a (00)d % change in I (d) Log-log demand function: (constant elasticity model) % change in p x is associated with a b% change in x (price elasticity of demand) = price elasticity of demand % change in p y is associated with a c% change in x (cross price elasticity) = cross price elasticity of demand % change in I is associated with a d% change in x (income elasticity) = income elasticity of demand 4
5 asic mathematical tools roperties of linear functions: Intercept = a lope = b marginal effect of x on y is constant and is equal to b atural Logarithm (when is small) Differential alculus Let artial derivative : Let, holding constant xample: 5
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