Price setting in the labor market is done by firms.
They will try and stick at their same nominal wage for as long as possible. So obviously peoples real income is taking a hit. Eventually, firms will need more employees, so they will choose to raise the nominal wage to account for inflation.
When prices go up and this brings real wages(W/P) go down. The effect of this is that unemployment tends to rise as firms aren’t keeping up with wage demands. Eventually firms adjust wages when they need people.
Firms as the price setters will tend to be stubborn at first in regards to changing wages.
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