Nick Rowe has a post entitled "AS/AD: A Suggested Interpretation". I'm going to offer a very different interpretation, which (interestingly) has almost identical implications. I'm not quite sure why.
In my view, the "classical dichotomy" lies at the very heart of macroeconomics. It's the central organizing principle:
This is the view that one set of factors determines nominal variables, and a completely different set of factors determines real variables. Both Nick and I agree that monetary factors are what determine nominal variables.
If that's all one had to say about the classical dichotomy, then the AS/AD model might look something like this:
Monetary factors would determine the position of the AD curve, and hence the price level, but would leave real output unchanged. BTW, this view of things makes no assumptions about how the money supply or velocity change over time. It simply looks at the economy in terms of factors that determine nominal variables (AD) and factors that determine real magnitudes (position of long run aggregate supply.)
After teaching the classical dichotomy, textbooks usually explain that wages and prices are sticky, and hence that the classical dichotomy does not hold in the short run. That's the overlap in the Venn Diagram above. But there's no follow up; the textbooks don't explain what any of that means. The chapter with MV=PY and the classical dichotomy and money neutrality just sort of drifts off into nowhere, like a Chinese river than ends up in the Taklamakan desert.
Instead, about 5 chapters later the textbook will start discussing a mysterious AS/AD model, which seems sort of like a S&D model, but is actually completely unrelated to supply and demand. Instead, the AS/AD model is finally explaining to students what we meant 5 chapters earlier when we talked about the classical dichotomy and money neutrality and sticky prices and MV=PY, but of course no student would see the connection---and why should they?
There's a slightly better chance that students would understand what's actually going on here if you called the AD curve the "nominal spending" (NS) curve, or even the MV line. Movements in the line (caused by M or V, it makes no difference) would be called "nominal shocks" not demand shocks. They have nothing to do with "demand" as the concept is taught in microeconomics, but the unfortunate terminology explains why so many people (wrongly) think that "if consumers sit on their wallets then aggregate demand will decline". In fact, sitting on your wallet means saving, and saving equals investment, and attempts to save will reduce interest rates which might reduce velocity, which could reduce AD, except it won't because the central bank targets inflation . . . or something like that.
Then the Short Run Aggregate Supply curve would be introduced. Students would be told that the purpose of the SRAS curve is to show how (because of sticky wages) nominal shocks are partitioned into a change in both output and prices, in the short run. (Long run money neutrality is still assumed.)
I don't have quite as strong an objection to calling the SRAS curve a "supply curve" as I prefer the sticky wage version of AS/AD, which is the version where the term 'supply' fits best. But as a favor to those that don't like the sticky wage version, it might be better to give it a different name, such as the "real output" (RO) line. If you believe in sticky prices, or money illusion, or misperceptions, then it's not really a supply curve.
Thus the AS/AD model is simply a way of showing how nominal shocks have real effects in the short run, but the classical dichotomy holds in the long run. (David Glasner would quibble about the last point, so perhaps we could say monetary neutrality "almost" holds true in the long run.)
Even better would be if you introduced AS/AD immediately after discussing why the classical dichotomy holds in the short run but not the long run. All in one chapter. You dispense with the "three reasons the AD curve slopes downwards", which almost no undergraduate understands.
If you read Nick's post, his AS/AD explanation will seem totally different. And yet we both believe (AFAIK) almost the same things about real world monetary policy, optimal monetary policy, the way that interest rates confuse the issue, the subtle problems with new Keynesian and NeoFisherian theory, the not so subtle problems with MMT, and a dozen other practical monetary questions. One question for further study is how can we end up in almost the exact same place, after taking such different paths?
If you are having trouble contrasting our two views, keep in mind that Nick and I don't disagree as to what the AD curve "really looks like", we are describing totally different concepts. Thus to me, the curve Nick talks about isn't what I think of AD at all, as it could theoretically slope upwards, which can never be true of a "nominal spending line" (which must be a downwards sloping hyperbola). His AD curve depends on the monetary regime, mine does not. In his model the economy can be temporarily "off the line". In mine the economy is always at equilibrium, every single nanosecond, because the "RO" line is derived by looking at where the economy actually is, and the NS line is actual nominal spending.
In a strange way, however, the radically different nature of the two ways that we visualize AS/AD might help to answer the question I posed above. If we had the same conception of AD curves, but different versions, then our two models would surely have different real world implications. But they don't seem to. Again, it seems like two radically different roads, leading to the same destination. Odd.
PS. In my version, it's just as correct to call the NS line 'aggregate supply' as aggregate demand. In fact, it's an equilibrium quantity, both "the quantity of nominal aggregate demand", and "the quantity of nominal aggregate supply". It's merely NGDP.