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 \(p_2\)