The income elasticity of demand for inferior goods is :

Income elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in consumer income. For inferior goods, there is an inverse relationship between income and demand; as consumers' income rises, they tend to switch to superior substitutes, causing the quantity demanded of the inferior good to fall [1]. Mathematically, this results in a negative income elasticity of demand, which is expressed as being less than zero (YED < 0). In contrast, normal goods have a positive income elasticity (greater than zero), where demand increases as income rises [1]. Within normal goods, necessities typically have an elasticity between 0 and 1, while luxury goods have an elasticity greater than 1 [1]. Therefore, the defining characteristic of an inferior good is an income elasticity that is less than zero.

Sources

1. [1] https://en.wikipedia.org/wiki/Income_elasticity_of_demand