How does inflation in income go 'hand in hand with inflation in prices'?
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.