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 2(p1,p2,y) change as prices p,, p 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. p1" 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. p1" 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 p, 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 a X1(p1,p2,y)= y a+b p1 and x2(p1,p,v-b y a+b p2 Notice that x, *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 X (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 X (a+b)p1
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 * ( ) = +
