On Partial Equilibrium Models of Demand and Supply

My last post on the aggregate demand effects of changes in nominal wages has attracted some attention, so I'd like to clarify a couple of things.

It was not the point of the post to claim that declines in nominal wages would lower or increase aggregate demand. The point was to argue that the simple partial equilibrium models of demand and supply that were being used by some to address the question were simply not up to the task of answering it. It was a reaction against the view -- expressed by Bryan Caplan and endorsed by Tyler Cowen -- that such effects could easily be deduced from textbook microeconomic theory. And it was a plea to move beyond partial equilibrium analysis in addressing such questions.

Tyler Cowan responded to this with yet another partial equilibrium model of supply and demand:

Graph a monopolist and shift the marginal cost curve down. Watch what happens. The first main paragraph of Sethi simply doesn't consider this mechanism but rather it assumes that changes at the margin don't matter.

That was in the comments section of Mark Thoma's blog. A similar claim now appears on his own page:

There is a simple story here.  Lower the minimum wage and firms with market power will in general hire more labor.  (Sethi's critique refuses to consider that mechanism but simply shift the MC curve and watch it happen.)

By all means, shift the MC curve and watch what happens. But please keep in mind not a single firm but a population of firms, some of which do not pay minimum wage at all. And be sure to shift the demand functions for all firms producing goods and services that minimum wage workers currently purchase. And now tell me whether it is self-evident that aggregate demand will rise in response to a decline in nominal wages.

It is not self-evident. In order to address the question it is necessary at a minimum to work with a model with multiple firms, in which the expenditure patterns from wage and capital income are properly specified, and some alternatives to immediate consumption (such as financial assets) exist. Simulate this model on a computer if you like, and watch what happens. I would be interested to know. But please don't make definitive claims about aggregate demand effects of changes in nominal wages based on an introductory textbook model that is simply incapable of carrying the weight.

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Update (12/17). Andrew Gelman is (understandably) puzzled by the fact that there is a debate going on about a policy that has no chance of being implemented. Mark Thoma provides some explanation, and I hope to post my own thoughts on this soon. Paul Krugman has more. 

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Update (12/19). Some possible signs of progress in this debate.