1) A fall in wages
increases the incentive to hire (call this the substitution effect) but it
decreases the income of people who already have jobs and this in turn
decreases their spending and other people’s income (call this the macro income effect). In essence, Krugman and others are arguing that the macro
income effect can dominate under certain situations. See Tyler (here and here) and Scott Sumner (Whom I cannot resist quoting–"no respected macroeconomic theory has ever been so decisively refuted
by the data as the theory that high wage policies can actually help the
economy during a Depression") on this point. I, however, will ignore this debate and take it as given that this is possible.
Now one reason that people are talking about
a cut in the minimum wage in this context is that it follows exactly the two-part logic given above. But bear in mind that the real policy choice
we have is to cut the payroll tax and cutting the payroll tax increases the
incentive to hire and increases the income of people who already have jobs.
2) The idea of the
liquidity trap with its notion of lack of movement, inactivity and firms which "just aren't hiring" is hard to reconcile
with the fact that millions of new jobs are being created every month. I have said this before but I should have shouted it from the rooftops because this error is very common.