Chapter six Demand 需求函数的静态比较分析
Chapter Six Demand 需求函数的静态比较分析
What Do We do in This Chapter? We conduct comparative statics analysis of ordinary demand functions -the study of how ordinary demands x,*(p, p2y)and x2*(p1, p2,y) change as prices p1, p2 and income y change Theoretically, nothing new
What Do We Do in This Chapter? We conduct comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x1 *(p1 ,p2 ,y) and x2 *(p1 ,p2 ,y) change as prices p1 , p2 and income y change. Theoretically, nothing new
Own-Price Changes How does x, *(p,p2 y) change as p changes, holding p2 and y constant? Suppose only p, increases, from p, top” and then to p1
Own-Price Changes How does x1 *(p1 ,p2 ,y) change as p1 changes, holding p2 and y constant? Suppose only p1 increases, from p1 ’ to p1 ’’ and then to p1 ’’’
p Own-Price Changes Ordinary demand curve Fixed p2 and y. p123 for commodity 1 p x1(p1”)x1(p1)X1 x1*(p1”) x1(p1”):X1(p1) x1(p1)
x2 x x1 1 *(p1 ’’’) x1 *(p1 ’) x1 *(p1 ’’) p1 x1 *(p1 x ’) 1 *(p1 ’’’) x1 *(p1 ’’) p1 ’ p1 ’’ p1 ’’’ x1 * Own-Price Changes Ordinary demand curve Fixed p2 and y. for commodity 1
p Own-Price Changes Ordinary demand curve Fixed p2 and y. p y】】 for commodity 1 p p1 price offer p curve x1(p1”)x1(p1)X1 x1*(p1”) x1(p1”):X1(p1) x1(p1)
x2 x x1 1 *(p1 ’’’) x1 *(p1 ’) x1 *(p1 ’’) p1 x1 *(p1 x ’) 1 *(p1 ’’’) x1 *(p1 ’’) p1 ’ p1 ’’ p1 ’’’ x1 * Own-Price Changes Ordinary demand curve for commodity 1 p1 price offer curve Fixed p2 and y
Own-Price Changes The curve containing all the utility- maximizing bundles traced out as p1 changes, with p2 and y constant, is the p, price offer curve The plot of the x,-coordinate of the p1-price offer curve against p, is the ordinary demand curve for commodity 1
Own-Price Changes The curve containing all the utilitymaximizing bundles traced out as p1 changes, with p2 and y constant, is the p1 - price offer curve. The plot of the x1 -coordinate of the p1 - price offer curve against p1 is the ordinary demand curve for commodity 1
The Case of Cobb-Douglas Utility Function Take U(X1, X2)=XiX Then the ordinary demand functions for commodities 1 and 2 are
The Case of Cobb-Douglas Utility Function Take Then the ordinary demand functions for commodities 1 and 2 are U x x x x a b ( , ) . 1 2 = 1 2
Own-Price Changes X1(p1,p2,y) y a+b p1 and X2(p1,p2,y) a +b p Notice that x2 does not vary with p, so the p, price offer curve is flat and the ordinary demand curve for commodity 1 is a rectangular hyperbola
Own-Price Changes x p p y a a b y p 1 1 2 1 * ( , , ) = + x p p y b a b y p 2 1 2 2 * ( , , ) = . + and Notice that x2 * does not vary with p1 so the p1 price offer curve is flat and the ordinary demand curve for commodity 1 is a rectangular hyperbola
Own-Price Changes Fixed p2 and y X2 by (a+ b)p2 ay (a+b)p1
x1 *(p1 ’’’) x1 *(p1 ’) x1 *(p1 ’’) x2 x1 Own-Price Changes Fixed p2 and y. x by a b p 2 2 * ( ) = + x ay a b p 1 1 * ( ) = +
p Own-Price Changes Ordinary demand curve Fixed p2 and y for commodity 1 s ay (a+b)pl X2 by (a+ b)p2 ay (a+bp
x1 *(p1 ’’’) x1 *(p1 ’) x1 *(p1 ’’) x2 x1 p1 x1 * Own-Price Changes Ordinary demand curve for commodity 1 is Fixed p2 and y. x by a b p 2 2 * ( ) = + x ay a b p 1 1 * ( ) = + x ay a b p 1 1 * ( ) = +