Demand functions and their dependence on price

Summary

Demand functions and their dependence on own price

• Good 1 is said to be ordinary if $x_1\left( p_1,p_2,m \right)$ is de creasing in $p_1$
• Good 1 is said to be Giffen if $x_1\left( p_1,p_2,m \right)$ is strictly increasing in $p_1$

• If we allow $p_1$ to affect preferences (e.g. snobb effect) and $x_1\left( p_1,p_2,m \right)$ is strictly increasing in $p_1$ then good 1 is called a Veblen good

Price offer curve and demand curve

• The price offer curve is the collection of optimal choices $x_1,x_2$ for all possible values of one price (income and other price fixed)
• Example
• $u\left( x_1,x_2 \right)=x_1x_2$ , $m=10,p_2=1$
• Optimal choice: $x_1=5/p_1$ , $x_2=5$
• Price offer curve: horisontal line at $x_2=5$
• A Demand curve show the relationship between optimal choice of a good and its price

Demand functions and their dependence on other price

• Good 1 is said to be a substitute for good 2 if $x_1\left( p_1,p_2,m \right)$ is strictly increasing in $p_2$
• Good 1 is said to be a complement for good 2 if $x_1\left( p_1,p_2,m \right)$ is strictly decreasing in $p_2$