The income elasticity of demand for a public good or service (Einc) by the population is given by the following formula:

• Einc = (the percentage change in demand for the public good or service) / (the percentage change in the average level of income).

Goods and services are generally classified for convenience as follows:

• Einc negative, inferior good
• Einc greater than zero, a normal good
• Einc greater than zero but less than or equal to 1, a necessity or basic good
• Einc greater than 1, a superior of luxury good.

Consider two examples. If the average level of income increases by 10% and demand for a good increases by 15%, the Einc is 1.5 (i.e., 15%/10%) so the good is definitely a normal good and would also commonly be classified as a superior or luxury good. If for another good demand increases by 5% when income increases by 10%, Einc is 0.5 (i.e., 5%/10%) so the good is also a normal good but would commonly be classified as a necessity or basic good.

The question of what the income elasticity of demand is for any particular public good or service is of course an empirical question and can only be determined through appropriate empirical analysis. Moreover, empirical results will obviously differ among locations that have different characteristics such as needs, absolute average levels of income, distributions of income and so on. It is important to bear in mind as well that we are considering only an increase in average income of the population, with all else assumed constant. This includes the cost of inputs used to provide public goods and services and other supply-side factors. With those caveats, it is nevertheless possible to postulate some prior expectations based on knowledge of the nature of particular public goods and services and the circumstances in which they are typically demanded.

(a.) Public goods and services that increase more than proportionately with income are those that have an Einc greater than 1, that is, superior or luxury goods. Examples of these could include education, health care, and arts and culture. As average incomes rise and basic private needs are increasingly covered among the population, the demand for these public services could well be expected to increase more than proportionately with income.

(b.) Public goods and services that increase less than proportionately with income are those that have an Einc less than 1, that is, necessity or basic goods. Examples of these could include law enforcement, fire protection and social support programs. With increasing average incomes, crime rates might be expected to drop, building fire safety standards to increase and the need for social programs to decline.