Demand Functions
Professor Jay Bhattacharya Spring 2001 Demand Part I Demand Functions • Recap: The Consumer’s Optimization Problem • The budget constraint and the tangency condition •AMarshalliandemand function relates the determine the amount of each good the consumer quantity demanded of a good to prices and income will purchase. • Demand depends on all prices X2 • Preferences and constraints together determine the The consumer’s choice of (X ,X ) 1 2 shape of demand (i.e. demand for X1 and X2) depends upon: •prices(p , p ) = 1 2 X1 f ( p1, p2 , I) •income(I) • preferences—U(X1,X2) = X 2 g( p1, p2 , I) X1 Spring 2001 Econ 11--Lecture 5 1 Spring 2001 Econ 11--Lecture 5 2 Comparative Statics Zero Degree Homogeneity of • What happens to demand when prices or income Demand changes? • A function f(x1,x2,…xn) is homogenous of –e.g., if prices f ()()tx ,tx ,...tx = t k f x , x ,...x I double and degree k if 1 n n 1 n n p 2 income doubles, • Marshallian demand functions are what happens to homogenous of degree zero. This fact is demand? I consistent with the absence of “money 2 p 2 illusion.” = Ι X 1 ( p1, p2 , I ) X 1 (2 p1,2 p2 ,2 ) I I 2 p1 p1 Spring 2001 Econ 11--Lecture 5 3 Spring 2001 Econ 11--Lecture 5 4 What happens to demand when income Income Expansion Path changes? (Income-Offer Curve) x • Budget constraint shifts in/out. Slope of budget 2 constraint does not change. I Prices are fixed 2 along the income x p2 2 expansion path I1 Increasing income p2 I0 p2 I0 I1 I2 x p1 p1 p1 1 Spring 2001 Econ 11--Lecture 5x1 5 Spring 2001 Econ 11--Lecture 5 6 Econ 11--Lecture 5 1 Professor Jay Bhattacharya Spring 2001 Engel Curves • But what if the IEP or Engel curve looks like this? An increase in income leads to • Engel curve relates income to quantity more x but less x .
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