Definition:

Income elasticity of demand (Ey, here y stands for income) tells us the relationship a product's quantity demanded and income. It measures the sensitivity of quantity demand change of product X to a change in income.

Price elasticity formula: Ey = percentage change in Quantity demanded / percentage change in Income

If the percentage change is not given in a problem, it can be computed using the following formula:

Percentage change in Qx = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 =  new Qd.

Percentage change in Y = (Y1-Y2) / [1/2 (Y1 + Y2)] where Y1 = initial Income, and Y2 = New income.

Putting the two above equations together:

Ey = {(Q1-Q2) / [1/2 (Q1+Q2)] } / (Y1-Y2) / [1/2 (Y1 + Y2)]

Characteristics:

Ey > 1,  Qd and income are directly related. This is a normal good and it is income elastic.

0< Ey<1,  Qd and income are directly related. This is a normal good and it is income inelastic.

Ey < 0, Qd and income are inversely related. This is an inferior good.

Example:

If income  increased by 10%,  the quantity demanded of a product increases by 5 %. Then the coefficient for the income  elasticity of demand for this product is::

Ey = percentage change in Qx / percentage change in Y = (5%) / (10%) = 0.5 > 0, indicating this is a normal good and it is income inelastic.