Queueing, rationing, and queue-rationing

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Queueing, rationing, and queue-rationing are a family of forms of non-price competition where a seller or regulatory authority deals with a shortfall (excess demand -- more demanded than supplied) by controlling who can buy how much when.

Queueing: Here, potential buyers have to wait in a queue, generally a first-come-first-serve queue. This could be a physical queue; for instance, shoppers waiting in line outside a store in order to enter and claim items, or waiting in line at a checkout counter in order to complete the transaction. If a good is sold out by the time a buyer gets to the front of the queue, the buyer is out of luck. A buyer can have only one position in a queue at a time.

Rationing: Here, potential buyers are limiting in the total quantity of an item they can purchase. The limit may be imposed per unit time (for instance, at most one loaf of bread a day). Unused rations are usually not tradable, though it may be possible to roll them over.

Queue-rationing: A mix of queueing and rationing: buyers have to wait in a queue, generally a first-come-first-serve queue. However, even when it's the buyer's turn, the buyer is constrained by rationing. There are different variants: in one variant, the buyer can immediately go to the back of the queue after completing the purchase, for the next turn. In another version, the ration is over a time period (like a day or month) so the buyer has to wait for the next time period to get in the queue again.

Causes of queueing, rationing, and queue-rationing

Excess demand due to inability of prices to adjust

Queueing typically occurs in a case of excess demand because prices are unable to adjust to market-clearing levels due to sticky prices, price ceilings or other factors.

A deliberate choice by sellers to shape their customers

In some cases, producers/suppliers may deliberately maintain shortages and not raise prices in order to make the good appear more attractive. Some possible advantages of queueing and rationing are:

  • By queueing, sellers may be able to get a profile of customers who may be better for them in the long run.
  • By rationing, sellers increase the number of people who buy the good, which may have long-term value for the sellers.
  • Standing in a long queue itself makes people buy more: There are often a lot of items for impulse purchase at the checkout counters in supermarkets, so the longer people have to stand in queue, the more such purchases they may make. Similarly, people on a waiting list for a good sold through a website may check the website more frequently, and may as a result make many other auxiliary purchases.

More fairness

For queueing: Standing in line may be considered a fairer way of distributing resources among people with varying degrees of wealth, compared to charging a high price. This is particularly true for goods that are highly valued by all, but for which wealth effects make it much easier for the rich to purchase them. This includes, for instance, goods such as education and health care.

For rationing: Rationing distributes a scarce good more equally among people, thereby being more fair.

Tamping down on panic buying

Panic buying is a situation where buyers' "true" demand for a good does not change, but buyers still try to purchase larger quantities because of fear that other buyers will use up the existing stock. This is most common for cases where intertemporal substitution is easy: one can buy now and stock up for the future.

Panic buying can become a self-fulfilling prophecy, causing shortages. Moreover, it can lead to the bullwhip effect, where sellers incorrectly conclude that demand has intrinsically increased, leading to them producing more, but then find reduced demand in the next time period as buyers start using up their existing stocks rather than buying more.

Done correctly, rationing is most helpful for panic buying because it provides a solution to the coordination problem of buyers not trusting each other. By committing all buyers to purchasing a limited quantity of the good, rationing increases the confidence of all buyers that there will be enough for them.

Efficiency of allocation of queueing, rationing, and queue-rationing

In a situation of a shortfall, where the quantity demanded exceeds the quantity supplied, there is some deadweight loss compared to what there would be if prices reached the market price. The inevitable deadweight loss is represented by the area of a Harberger triangle (see effect of price ceiling on economic surplus).

Beyond this inevitable deadweight loss, there is further loss that may happen if the non-price competition between buyers fails in one of these two ways:

  • It does not allocate the good to the buyers who value it most, i.e., it does not generate the most high-value part of the consumer surplus
  • It imposes transaction costs on buyers and sellers

Setting aside transaction costs, we now discuss the question of the efficiency of allocation of queueing, rationing, and queue-rationing.

Pure rationing allocates efficiently when buyers have similar reservation prices and there are sharp diminishing returns to each individual buyer after the ration

If all buyers have sharply diminishing returns after buying the first two units of a good, so much so that any buyer's first two units have a higher reservation price for that buyer than any other buyer's third or later unit, and there is enough for everybody to buy two units, then rationing to two units leads to an efficient allocation.

Even if the above isn't strictly true, if it's generally true that the reservation prices of buyers are similar, and see sharp diminishing returns, setting a ration to before the point of diminishing returns, if feasible, is likely to lead to an efficient or close-to-efficient allocation.

Pure queueing allocates efficiently when reservation prices differ between buyers, don't differ much across the quantity range for each buyer, and the order of buyers in the queue mirrors their reservation price

If some buyers value a good more than others, and this effect is stronger than any diminishing returns within the range that a buyer may buy in, then queueing to give the higher-value buyers priority makes sense. However, without buyers explicitly bidding to indicate how much they value a good, it may be hard for a queue that forms in practice to reflect the relative value placed by buyers.

If it is possible for buyers to pay people to stand in a queue for them, and the transaction costs are negligible, then we might expect queueing to give more priority to higher-value buyers (as they will be willing to bid higher to pay somebody to stand in queue for them and grab an earlier slot) and lead to an efficient allocation.

A suitable queue-rationing strategy can be found for a wide range of intermediate situations

The "queue" part of queue-rationing helps prioritize between different buyers, and the "ration" part helps deal with diminishing marginal returns. By combining these two tools through queue-rationing, it is possible to design strategies for efficient allocation for many situations.

Sellers in general may not have incentives to allocate efficiently

Regardless of how sellers allocate the good, they will sell it all, because quantity demanded exceeds quantity supplied. Therefore, viewed naively, sellers have no incentive to allocate efficiently.

However, sellers do have some incentives. First, they care about perceived fairness, which often relates with efficiency of allocation. Second, a single seller is often selling not just the one good that has a shortfall, but many other goods that don't. The seller is also interested in long-term buyer loyalty. These considerations push the seller in the general direction of allocating efficiently. However, the considerations don't align perfectly with efficient allocation.

For instance, a seller may adopt a rationing strategy even though a queueing strategy would be more efficient, because a rationing strategy gives more of an appearance of full shelves (by slowing down the rate at which a good is sold) thereby giving others looking at the store the perception that it is well-stocked.