In ECON 1000 we teach that a monopolist picks a point on his demand curve that maximises his profits. We can think of the monopolist as setting a price to hit that point, or we can think of the monopolist as setting a quantity to hit that point; and we teach that it doesn't make any difference which way we think of it. Economists normally think of the monopolist as setting a quantity, simply because it's easier for us economists to think that way, but if we set the problem up in math, and maximise with respect to price, or maximise with respect to quantity, we end up with the same answer either way.
Here's an example where it does matter whether the monopolist picks a price or picks a quantity:
Suppose the monopolist is selling a new communications gizmo. Some people are rich, or really like new communications gizmos, and are willing to pay a lot to buy one. Other people are poor, or don't care much for new communications gizmos, and aren't willing to pay very much to buy one. And there's a whole distribution of people between those two extremes.
But communications gizmos are different from other goods: the more people who own one, and the more people you can communicate with if you buy one, the more you would be willing to pay to buy one. There's a network externality. That's what creates the weird-looking demand curve I've drawn above.
The height of the demand curve at any given quantity shows the willingness to pay of the marginal buyer. That's standard. What's non-standard about the demand curve I've drawn is that the willingness to pay of every buyer depends positively on the number of other people who own a gizmo.
Start where nobody owns a gizmo, where Q=0. The very richest person, or the one who wants a gizmo more than anyone, and who has the highest willingness to pay, still wouldn't be willing to pay very much. Because there would be nobody he could talk to on his new gizmo. So the height of the demand curve for the first gizmo is very low. It might even be zero.
As the quantity increases, and the number of people you can talk to increases, the willingness to pay of the marginal buyer will increase. Sure, you are going down the list of potential customers, from the richest towards the poorest, and from the keenest towards the least keen, both of which would reduce the willingness to pay of the next buyer in line. But at the same time the number of people you can talk to increases, which raises the willingness to pay of everybody.
So as quantity increases, the height of the demand curve first increases, then eventually falls, as the market gets saturated. It's probably going to look roughly the way I've drawn it.
Suppose the monopolist sets a price of $100. There are three equilibria: Q=0, where nobody buys a gizmo so nobody is willing to pay $100 because there's nobody to talk to; Q=150, where lots of people buy a gizmo because there are lots of people to talk to; and Q=50, where only the richest and keenest buy a gizmo because there aren't many people to talk to.
Suppose instead the monopolist sets a quantity of 150. There is only one equilibrium: P=$100.
In this example, it does matter whether we think of the monopolist as setting a quantity or setting a price. We might get the same answer either way; but there again, we might not.
When I say it does matter whether we think of the monopolist as setting a price or setting a quantity, who's the "we" that does the thinking? It's not just the economist. It's the customers buying gizmos. If they think that the monopolist is setting a price of $100, they don't know whether to buy one or not. Each potential customer watches to see how many other people will buy a gizmo before deciding whether to buy one himself. But if they think the monopolist is setting a quantity of 150, exactly 150 customers will be willing to pay a price of $100 or more, just like in the normal case.
In this example, the monopolist will want his potential customers to think of him as setting a quantity, not a price. That way he can sell 150 gizmos at a price of $100 each. Even if he knows the exact shape and position of the demand curve, he can't be sure how many he will sell if he sets a price of $100. It could be 150, it could be 50, or it could be 0.
In 1970 William Poole wrote a classic paper on the theory of monetary policy under uncertainty (pdf). He set up an ISLM model, with unforecastable shocks to the IS curve and to money demand, and asked whether it would be better for macroeconomic stabilisation if the central bank set an interest rate or a quantity of money. His answer was that the optimal monetary policy instrument depends on the size of the shocks, and on the elasticities underlying the IS and LM curves.
In Poole's model, if there are no shocks, so the central bank knows the position of the IS and LM curves, it doesn't matter which instrument the central bank chooses. We can think of the central bank setting an interest rate, or setting the money supply (or base money), and we get exactly the same answer either way. We could even think of the central bank as setting NGDP, and we get exactly the same result that way too. It's exactly like the theory of monopoly we teach in ECON1000, where it doesn't matter whether the monopolist sets a price or sets a quantity.
That's because in Poole's ISLM model, and in the ECON 1000 monopoly model, there is a unique equilibrium whichever instrument the central bank/monoplist sets. If you know Q you know P, and if you know P you know Q. But, as I have shown above, it does matter whether the monopolist sets P or Q if you know P given Q but don't know Q given P.
Suppose we had an ISLM model in which equilibrium is not unique for some instruments. Suppose, for example, the IS curve wasn't always and everywhere downward-sloping. Suppose the IS curve looked something like the demand curve I have drawn above.
Why might an IS curve look like that?
The answer should be obvious. In my microeconomic example, each person's willingess to buy a gizmo depends positively on how many other people he expects to buy a gizmo. Hmmm. Maybe in macroeconomics each person's willingness to buy all goods and services depends positively on how many goods and services he expects other people to buy? Hmmm, that idea does sound familiar. Of course that idea sounds familiar! It's the Old Keynesian multiplier!
If the Old Keynesian multiplier effect is strong enough, the IS curve will slope up; just as if the network externality effect is strong enough, the demand curve for gizmos will slope up.
And there is nothing in theory to prevent the Old Keynesian multiplier effect being strong enough to make the IS curve slope up. All you need is for the marginal propensity to consume plus the marginal propensity to invest to exceed one. There is nothing to say that cannot happen.
The same price of gizmos may be too high if nobody expects anybody else to buy one, and too low if everybody expects everybody else to buy one.
The same rate of interest may be too high if nobody expects anybody else to spend, and too low if everybody expects everybody else to spend.
It does matter what we think of central banks as setting. But again, we need to ask: who's "we"? And the answer is: people, not economists, or central banks. But where do people get their ideas from, when it comes to how to think about monetary policy? From economists, and central banks.
Should we economists think about central banks setting a nominal rate of interest or a target for NGDP? Should central banks think of themselves as setting a nominal rate of interest or a target for NGDP? How should we best communicate to the public what it is that central banks do? It matters.
It's just like when the monopolist sets a price of gizmos, and each person can't decide whether to buy one or not, and waits to see whether other people are buying before buying one himself. When the central bank sets a nominal rate of interest, each person can't decide whether to buy or not, and waits to see whether other people are buying before buying himself.
[Addendum: Off-topic ECON 1000 test: Draw the Marginal Revenue curve associated with that demand curve.]