The only way to increase output in a demand-constrained economy is to do something that changes that relationship between output demanded and output, so that more output is demanded for any given level of output.
Emphasis in the original. And no, I don't understand it, either. Maybe there is something confusing about aggregate demand. Or maybe Nick was in a hurry to grade papers.
Bryan was trying to make a relatively simple point. In a world that thinks at the margin, lower wages should increase employment. First, there is the substitution margin, where you decide whether to use labor or other inputs. More energy or more labor? If wages are low, you pick labor. (Green jobs!) More capital or more labor? If wages are low, you pick labor.
Then, there is the expansion margin. With lower wages, your marginal cost goes down, enabling you to cut your price, sell more, and produce more. With more labor input.
One version of macroeconomics, which I call textbook macro, preserves this marginal analysis. In textbook macro, nominal wages are sticky, so that a drop in nominal demand raises real marginal cost and lowers output. Textbook macro is not terribly plausible in theory (it leans really hard on money illusion that even affects potential new employment relationships, not just existing ones), nor is it well supported empirically. We don't observe the strong countercyclical relationship between real wages and employment that is implied by textbook macro.
As an aside, I am not sure I accept the claim that a declining nominal wage is contractionary because of the damage it does to borrowers. Yes, deflation transfers wealth away from borrowers. But by the same token it transfers wealth to lenders. Why is that necessarily contractionary? In fact, if you think about government debt, the effect should go the other way. As you get deflation, the real value of government bonds goes up. If people are not Ricardian-equivalencers and view government bonds as net wealth, then deflation should be expansionary. It works like an increase in real government spending.
Once you leave textbook macro behind, I think you have to come up with a reason to deny that marginal analysis is operative. What Nick may be trying to say is that in the aggregate, demand is inelastic with respect to the nominal price level. Reduce all wages and prices by 10 percent, and nothing real should change (ignoring an increase in the ratio of outstanding money to the price level). I don't like thinking about macro that way, because we pretend that a whole bunch of things happen instantly, and I find that so unrealistic that I cannot get my head around it. I prefer to think about very slow adjustment processes.
The PSST story would be that labor is heterogeneous. The demand for labor with skill set x may be quite inelastic with respect to wages. Maybe skill set x does not even directly produce output (instead, it is Garett Jones labor, building organizational capital), so that lower wages for skill set x do not reduce your marginal cost. Maybe the industry that employed workers with skill set x has been so radically disrupted by new technology that firms are in the process of substituting away from workers with skill set x at almost any wage rate. No wage is low enough to bring back door-to-door encylopedia salesmen.
With the PSST story, unemployment exists because the economy is in the process of adjustment. Entrepreneurs have not figured out a good use for unemployed workers. They won't figure it out faster just because wages are reduced by a little bit. Short-run elasticities are low, so that workers with specific skill sets do not find much in the way of marginal responses to small wage cuts.
If wages are reduced dramatically, then entrepreneurs are likely to create jobs, but those could be the wrong jobs. Jobs that only make sense at ridiculously low wages are not really part of *sustainable* patterns of specialization and trade. In the long run, the economy might find jobs at better wages for those workers.