How does inflation in income go 'hand in hand with inflation in prices'? Source: p 594, Economics, 3 Ed, 2014, by N G Mankiw, M P Taylor


  Yet further thought reveals a fallacy in this answer. When prices rise, buyers of goods and services pay
  more for what they buy. At the same time, however, sellers of goods and services get more for what they sell.
  Because most people earn their incomes by selling their services, such as their labour, inflation in incomes goes
  hand in hand with inflation in prices. Thus, inflation does not in itself reduce people‘s real purchasing power.


Is the bolded (independent) clause too presumptuous? I doubt its truth. Even if hand in hand means any positive correlation weaker than 100%, the bolded can be false. For example, despite being in view of inflation in prices, a greedy employer can simply refuse to increase wages. Then no inflation in incomes exists, and so inflation DOES reduce people‘s real purchasing power?
In the situation you describe people's real purchasing power would indeed be reduced. However such a situation is not likely. If the employer was a monopolist, how come employees could afford more than the bare necessities in the first place? (See the works of Carl Marx.)

In real life it is more likely that if an employer does not raise wages when businesses are doing well another employer will make a competitive wage offer. Thus inflation will result in the rise of wages.

Mind that Mankiw's book is not a mathematical treatise, his statements are not precise. The book is merely a collection of stories aimed at students who are just familiarizing themselves with economic phenomena.