(I'm disagreeing with Roger Farmer on the interpretation of the 45 degree line. I say the 45 degree line is not a supply curve. This post explains what I think it is.)
Here's the Keynesian Cross diagram:
How should we interpret the green 45 degree line?
To keep it simple, imagine an economy where all goods are services, so we can forget all that nonsense about desired vs undesired inventory accumulation. It's a haircut economy. You can't cut your own hair. People cut each others' hair, for money. Haircuts get produced-and-bought-and-sold all at the same time.
On the horizontal axis we have the quantity of haircuts actually produced-and-bought-and-sold, Y.
On the vertical axis we have the quantity of haircuts demanded Yd, which means the quantity of haircuts people want to buy, which may or may not be the same as the quantity they actually buy.
On the vertical axis we also have the quantity of haircuts supplied Ys, which means the quantity of haircuts people want to sell, which may or may not be the same as the quantity they actually sell.
The green 45 degree line tells us that the actual quantity of haircuts produced-and-bought-and-sold will equal whichever is less: quantity demanded; or quantity supplied. You don't get a haircut produced unless there is both a willing buyer and a willing seller. So the economy will be where the demand curve cuts the 45 degree line, or where the supply curve cuts the 45 degree line, whichever is less.
If some sellers of haircuts, or some buyers of haircuts, could make you an offer you can't refuse, the economy would not be on the 45 degree line. If some sellers felt an obligation to sell more than they wanted to sell, or if some buyers felt an obligation to buy more than they wanted to buy, the economy would not be on the 45 degree line. If people had false beliefs about how much they were able to sell, or about how much they were able to buy, the economy would not be on the 45 degree line. The 45 degree line tells us something substantive about the economy.
The red demand curve tells us that the quantity of haircuts demanded will be an increasing function of the quantity of haircuts people are able to sell, if they cannot sell all they want to sell.
The blue supply curve tells us that the quantity of haircuts supplied will be an increasing function of the quantity of haircuts people are able to buy, if they cannot buy all they want to buy.
This economy is in semi-equilibrium at Y'. At Y', the quantity of haircuts bought-and-sold is equal to the quantity demanded, but is less than the quantity supplied. Yd=Y<Ys. People can buy as many haircuts as they want to buy, but want to sell more haircuts than they are able to sell. If they could sell 10 more haircuts per year, they would want to buy (say) 6 more haircuts per year. They would increase their expenditure if they were able to increase their income, but they can't, so they won't. There's a demand-side multiplier from shifts in the demand curve.
Now suppose something causes the red demand curve to shift up, so it intersects the 45 degree line at Y*. The economy would now be in full equilibrium at Y*, where Yd=Y=Ys. People are buying the quantity they want to buy, and selling the quantity they want to sell. This is what the economy looks like in full equilibrium:
Now suppose something causes the red demand curve to shift up even further. Or something causes the blue supply curve to shift down. The economy will now be in semi-equilibrium where the supply curve cuts the 45 degree line, so Yd>Y=Ys. There is an excess demand for haircuts. People are selling as many haircuts as they want to sell, but unable to buy as many haircuts as they want to buy. If they could buy 10 more haircuts per year, they would want to sell (say) 6 more haircuts per year. They would increase their income if they were able to increase their expenditure, but they can't, so they won't. There's a supply-side multiplier from shifts in the supply curve.
When Yd=Y<Ys, people can't sell as much as they want, so the demand curve slopes up, but can buy as much as they want, so the supply curve is horizontal.
When Yd>Y=Ys, people can sell as much as they want, so the demand curve is horizontal, but can't buy as much as they want, so the supply curve slopes up.
This is all just old Barro-Grossman/Malinvaud etc. stuff. Roger and I both learned it at the same time in Peter Howitt's advanced macro class. But should we be teaching it in first year?
Worthwhile Canadian Initiative 
Nick Rowe: “The English language doesn’t work for “supply”. We should do like the French, and talk about how much sellers offer to sell.”
In English does it make sense to apply the phrase, “willing and able” to both supply and demand? As in, how much one is willing and able to sell or willing and able to buy?
maybe WW2 rationing in the UK?
At first I thought, no, that doesn’t work. The signature of this kind of supply constraint is the combination of rationing with unemployment, and that doesn’t fit WWII Britain.
But then I thought, what if it’s a two-stage process? First, we have a big fall in supply, or big increase in demand, for some basket of goods. Small shifts of course are dealt with by the price mechanism, but for really big shifts that may not work so well — because of inflation, distributional effects, whatever — so rationing has to be introduced. Initially, there’s no adverse effect on labor supply — in effect, people are being forced to save more than they would choose, but that should have only second-order effects on the perceived value of the wage. But now suppose rationing continues long enough that people doubt whether there will ever be sufficient goods available for sale. Now income in excess of available consumption goods no longer appears to be a form of saving. So now you do get a fall in labor supply, — which reduces current output so that rationing must be even stricter. This is a kind of secondary shortage on top of the original shortage, and this secondary shortage might even persist after the original supply or demand shift is reversed. A simple solution, in that case, would be to expropriate the excess savings — but better not do that if you want to be able to use rationing again in the near future. More interestingly, if the government can somehow procure a short-term increase in the supply of consumption goods, that may increase the perceived value of the wage enough to bring labor supply back up to its old level — a kind of supply-side pump priming.
In this case, we could say that there is a “corridor of stability” on the supply side as well as the demand side, and we just happen to have remained within the corridor. We’ve never had a large enough and persistent enough excess of desired purchases over desired sales for the process to become self-sustaining. But you could.
I wonder if there’s episodes in the history of the Soviet economy we could interpret this way?
Min: “In English does it make sense to apply the phrase, “willing and able” to both supply and demand? As in, how much one is willing and able to sell or willing and able to buy?”
No. Greg Mankiw defined supply/demand as the quantity people are willing and able to sell/buy. When I was Canadian co-author, I crossed out all the “and able” bits. Otherwise he contradicted himself when he talked about price controls; “with a binding price floor, sellers are unable to sell as much as they are willing and able to sell” doesn’t make sense.
JW: what you describe there is exactly the idea. It’s not so much unemployment, as people working less than they normally would otherwise want to. My guess is that it would apply in the old Soviet Union.
JW: Aha! Read this! The supply-side multiplier at work!
Nick, thanks for letting us know what Laidler and Howitt say: semantics or not I feel better that at least one thing was “resolved” here … to some small extent anyway. 😀 It’ll be interesting to see if anything more substantial gets resolved.
Nick Rowe: “Greg Mankiw defined supply/demand as the quantity people are willing and able to sell/buy. When I was Canadian co-author, I crossed out all the “and able” bits. Otherwise he contradicted himself when he talked about price controls; “with a binding price floor, sellers are unable to sell as much as they are willing and able to sell” doesn’t make sense.”
Many thanks, Nick. 🙂 Although I expect that a general semanticist could rescue Mankiw with able1 and able2. 😉