In a two good society, can both goods be inferior ?

Answer 1

Certainly, yes.

Answer 2

Hmmm...good question.

Inferior goods imply that income elasticity of demand is negative, meaning as income increases, less of the good is consumed, generally to improve consumption of a normal good. This implies a more than 1-to-1 impact on the income effect.

However, if all goods are inferior, then as income increases fewer goods are purchased, and overall consumption decreases. This means that utility DECREASES with increased income, and violates the assumption that there is no waste (all resources are consumed, all income is utilized).

Thus, by the general neo-classical microeconomic model, it is impossible for all goods in a society to be inferior. However, this is possible if you are willing to relax the above assumptions.