Just as the quantity demanded can be plotted as a function of the price with all other factors held constant, the quantity demanded can be plotted versus income again with all other factors held constant. One would expect that as consumers have more income to spend they might buy more of a good or service and normally that is the case. However, there are some products that consumers buy less of as there income increases. This may be because consumers are switching to a higher quality product as they get more income. Goods such that the quantity demanded goes down as income goes up are called inferior goods. The name inferior does not necessarily mean that there is anything wrong with such goods. For example, beans may be a more important part of the diet of low income consumers because they are a relatively cheap source of protein. When consumers have more income they may get their protein more from meat and less from beans. Goods such that the quantity demanded increases with income are called in economics normal goods. Thus in the above example beans would be an inferior good and meat a normal good.
An income elasticity of demand can be defined. The ratio of the proportional change in quantity to the proportional change in income I is called the income elasticity of demand; i.e.,
This can also be expressed in terms of the expenditure (E=pq)as
In the latter equation (E/I) represents the proportional of income spent on the good and (ΔE/ΔI) represents the proportion of additional income that is spent on the good. Thus if consumers spend 25 percent of their income on food but spend only 20 percent of additional income on food then the income elasticity of the demand for food would be 20/25=0.8.
The income elasticity of demand can be positive (normal) or negative (inferior) or zero. Often economists just A good such that the income elasticity is greater than one is said to have income elastic demand whereas one with income elasticity less than one is said to have income inelastic demand. One expects the income elasticity of necessities like food to be low perhaps even zero where as the income elasticity of luxuries such as travel to be high.