Question

a)cross price elasticity eij= dxi/dpj. pj/xi

find Cobb couples, perfect substitute and perfect complement b)income elastic of demand ni= dx1/dm . mi/x1 find Cobb Douglas, perfect substitute and perfect complement

b)income elastic of demand ni= dx1/dm . mi/x1

find Cobb Douglas, perfect substitute and perfect complement

Answer 1

a. cross price elasticity eij= dxi/dpj. pj/xi

Cobb-Douglas demand curve:

x1= am/p1

x2= (1-a)m/p2

So, dx1/dp2= 0

So, e12= dx1/dp2. p2/x1= 0 (Similarly find e21)

Perfect Substitutes demand curve:

x1= m/p1

x2= m/p2

So, dx1/dp2= 0

This gives: e12= dx1/dp2. p2/x1= 0 (Similarly find e21)

Perfect complements demand curve:

x1= m/(p1+p2)

x2= m/(p1+p2)

So, dx1/dp2= -m(p1+ p2)^-2= -m/(p1+p2)²

So, e12= dx1/dp2. p2/x1= -m/(p1+p2)². p2/(m/(p1+p2))= -p2/ (p1+p2) (simiarly find for e21)

b. income elastic of demand ni= dx1/dm . mi/x1

for Cobb-douglas

dx1/dm= a/p1

So, e12= a/p1. m/(am/p1)=1

Perfect substitutes:

dx1/dm= 1/p1

So, e12= 1/p1. m/(m/p1)= 1

Perfect complements:

dx1/dm= 1/(p1+p2)

e12= 1/(p1+p2). m/(m/(p1+p2)= 1