Demand functions and their dependence on income

Summary

Demand functions

• If the optimal choice of $x_1$ and $x_2$ given $p_1,p_2$ and $m$ are unique then the functions

$$x_1=x_1\left( p_1,p_2,m \right)$$

• and

$$x_2=x_2\left( p_1,p_2,m \right)$$

• are called demand functions .

Demand functions and their dependence on income

• Good 1 is said to be normal if $x_1\left( p_1,p_2,m \right)$ is increasing in $m$
• Good 1 is said to be inferior if $x_1\left( p_1,p_2,m \right)$ is strictly decreasing in $m$

• Example:
• $x_1\left( p_1,p_2,m \right)=m/p_1$
• $∂x_1/∂m=1/p_1>0$
• Good 1 is normal.
• Example:
• $x_1\left( p_1,p_2,m \right)=\left( 8m-m^2 \right)/10p_1$ for $0≤m≤8$ .
• $∂x_1/∂m=\left( 8-2m \right)/10p_1$
• Good 1 is normal if $m≤4$ and inferior if $m>4$