Non-classical forms of market rationing
Capitalism isn't supposed to have shortages (at least according to the classical understanding of economics typically taught). If the demand of something outstrips the supply, prices go up. The prices continue going up until a portion of the buyers are no longer able or willing to buy.
However, I've found this is not always really true in reality.
Take housing for example, more specifically shortages of affordable housing in certain high-price areas.
You have a large pool of people who all have about the same income (more or less) and they are all clamoring to rent the limited number of housing situations they can afford.
Now it's true the demand-price interaction comes into play a little bit, but that's not really a good full description of what's happening here.
When you have a group of 10 people, all can only afford about $700 a month, and only 6 housing units, what's going to happen?
Well, a few of those people are really really going to want to get that housing so they might be willing to pay $750. But anything over $700 is going to be a big stretch for them.
So to some extent, the individuals who get the housing out of this low income group is not going to be determined by their incomes but by who is willing to suffer the most, taking a big cut into their personal budget, or those types of things.
But the reality is that a small increase in price is going to be a much bigger strain for the one paying the money than it is for the one renting out the housing. (That is a price increase of $700 to $750 is going to be a much bigger inducement for these people to decide they can't afford housing, whereas that same price increase from $700 to $750 won't be that much of an inducement for the one renting out the housing, comparatively.)
In classical economics, we usually see an intersection of supply and demand which look both like curves, going diagonally up in either direction. So naturally it's easy for quantity to move in either direction depending on price. But here we have a demand curve that suddenly seems to drop off after a certain price, almost at a right angle, and a supply curve that barely changes with change in the price, at least in the particular area we're looking at.
In this situation, it's practically going to be like a game of musical chairs. First come, first serve. Who gets the scarce housing is in large part going to be determined by random chance. Not really all that different from other forms of government rationing in non-market situations.
Adding more low income people looking for housing might not really increase price all that much. What it will do is decrease the chance that any particular low income individual will be able to find housing that they can afford.
Indeed, this is probably going to lead to what are termed "market inefficiencies" because these people are going to try to immediately jump on any housing opening they see (before someone else can get it) without taking into consideration whether that particular housing situation is really going to be the best fit for them as an individual. (This is especially true when it comes to shared living and roommate situations)
This type of phenomena can also lead to housing providers or employers being extremely picky about which candidates they choose, since they have plenty of different candidates to choose from, and whomever they choose the price points will be nearly the same.
Individuals with certain qualities going for them might be much more likely to get the jobs or housing, since price may not be the determining factor in deciding which candidate gets chosen. One could describe these attributes as intangible qualities. Still a form of market rationing but not all of the price is paid in money (if you want to view it that way).
One example might be an employer who is looking to hire a secretary. Two female applicants apply, both requiring the same amount of pay, but one is more attractive than the other.