Will inflation reduce unemployment?

Given that I wrote that lower labor costs are a key to reducing unemployment but that nominal wage rigidity prevents this from happening and given that I wrote that inflation reduces real wages, should we then conclude that inflation will reduce unemployment?
Well, it will under some circumstances, but the issue is like the issue of the effects of inflation on debtors not as simple as it seems at first glance.
First we must ask us why lower real wages can increase employment. It's certainly not that employers are encouraged to hire more people just because their workers are worse off.
No, the reason why it can increase employment is that it means that the difference between the net marginal revenue generated for the employer by a worker and the cost of hiring the worker increases, or turns from negative to positive. Inflation doesn't reduce the nominal cost of hiring the worker, but it could perhaps increase the nominal net marginal revenue generated by the worker.
But we should as in the case of the discussion about debtors remind ourselves that monetary inflation doesn't increase all prices equally at the same time. Some prices, particularly commodity prices tend to increase quickly and rapidly, while others increase later and less-or not at all.

For companies that sell products that increase a lot in price because of monetary inflation while seeing only small increases in their costs, it will certainly become more profitable to hire more workers and that's what they'll do.
We can see this in current employment statistics. While overall payroll employment rose slightly less than 1% in the latest year in the United States, employment in the mining sector has risen as much as 13%. This is clearly a result of the high commodity prices.
However, many other companies haven't seen the prices of the products they sell rise as much or anything at all. Meanwhile, the prices of their inputs have risen because of the same commodity price boom that has benefited the mining sector. As a result. the marginal net revenue that their workers generated have increased far less, nothing at all or even declined. Accordingly, in other sectors inflation will generate far less or no jobs at all or could even mean that they will be forced to reduce their workforce.
And because America, despite the recent boom in its mining sector, is still a large net importer of commodities, it is dubious whether the recent increase in inflation has really, outside of the growing but relatively small mining sector (less than 0.6% of workers work in the mining sector), created more jobs than it has destroyed. What is clear is however that any positive net effect is much smaller than you would normally expect with such a big drop in real wages.