I think Donald‘s demonstration is pedagogically interesting, although it suffers from the same problems as any demonstration of a general-equilibrium effect with a partial equilibrium model. And I would argue that the sort of general equilibrium model needed, contrary to what Germain perhaps suggests, is not a Keynesian aggregate-demand model. Why not a standard Pareto model where individuals converge to the contract curve?
Pierre’s comment (as does Germain’s) gives me the opportunity to attempt to summarize differently the ultimate point that I sought, futilely, to make in that post. That point is this one: An increase in nominal demand (MV) will not raise aggregate real income – it will not improve average living standards – unless that increase in demand sparks an increase in real output. In an economy with full-employment, however, such spending, even on naive Keynesian assumptions, will not increase real output. An increase in such spending in an economy with full employment will only raise nominal wages and prices. Further, if this fully employed economy is also reasonably competitive, then even if (as, for example, Robert Reich assumes) the higher nominal incomes earned by low-skilled workers from the minimum wage are indeed spent by these workers overwhelmingly on outputs that these minimum-wage workers produce, there is no obvious source of the additional real inputs that are necessary to produce the additional, real goods and services that must be produced and bought by minimum-wage workers if the minimum wage is to increase the real incomes of all low-skilled workers without causing any of these workers to lose jobs (or to endure jobs that are excessively demanding).
In short, among other errors, those who assert that the increased spending that is imagined to arise from the imposition of a minimum wage raises the real incomes of all low-skilled workers, without causing any of these workers to lose employment, at best mistake changes in nominal prices and wages for changes in real incomes. For the real incomes of all low-skilled workers to rise, these workers must gain access to more real output – more real output that is either produced, or that is transferred from people who are not low-skilled workers. Nothing in the assertion that ‘minimum wages increase consumer demands for the outputs produced by low-skilled workers’ even begins to explain how minimum wages cause low-skilled workers to gain access to a larger flow of real goods and services.