Sunday, 6 April 2014

Low price but high cost: The economics of queues

How do you know that the price of a good is too low? This happens. Or this. Or this (which maybe goes against my earlier post on the high cost of weddings). If the price of a good is 'too low', what economists often mean is that the price is below the market clearing or equilibrium price. At this low price, the quantity demanded (the amount of the good that the consumers want to buy) exceeds the quantity supplied (the amount of the good that is available at that price), leading to a shortage, or excess demand. One of the ways that excess demand is manifest is in the form of waiting lists, or queues.

Now, you might think that low prices are a great thing for consumers. I'm going to argue that they aren't necessarily a great thing for consumers at all, because there are hidden costs that go along with the low prices.

First, let's look at a market with a price that is set below the equilibrium price (let's assume for the moment that we are talking about a competitive market, i.e. one that we can represent easily with supply and demand. This would be the case if there was a government-mandated maximum (ceiling) price that is below the equilibrium price). At the low price (P1 in the diagram below), there is excess demand (quantity demanded is Q2, and quantity supplied is much lower at Q1). So, there are a number of consumers who would be willing to purchase at the price P1, but are unable to find a supplier.

Consumers know that the price is really low, and they worry about missing out. So, to ensure that they get the product before it runs out, they show up at the store early, i.e. before it opens, and queue for the product. This increases the total cost to the consumer, because they face opportunity costs (foregone sleep perhaps, if they are getting up early to go and wait in line at the store). The total cost to the consumer is the price they pay plus the opportunity cost of waiting in line.

How long should the customers wait? That depends on their willingness to pay. If they are willing to pay a high price for the good, they will be willing to wait in line for longer (i.e. they will get to the store earlier). At the extreme, they will be willing to go early enough so that the total cost (price of the good plus the opportunity cost of waiting) is exactly equal to their willingness to pay.

What does that do to the graph above? The price remains P1, but the total cost to the consumers is actually P2. In fact, the queueing makes consumers worse off because they end up paying a much higher cost (including opportunity costs) than without queueing. In economic welfare terms, the consumer surplus (the difference between what the consumers are willing to pay and what they actually pay, shown by the area between the demand curve and the price) is actually lower with the low price (it is the area ABP2), than it would have been with the higher equilibrium price (there it is AEP0). And the deadweight loss is way bigger than expected (with queueing it is the large area P2BECP1, but if there was not queueing it would only be the area BEC).

The irony is that the government often implements maximum (or ceiling) prices in order to help consumers. If the shortage is managed by queues, it actually makes consumers worse off both in welfare terms (consumer surplus of ABP2 instead of AEP0) and intuitively (now they pay a lower price, but including the opportunity costs of time spent queueing the total cost is higher).

Of course, there could be a better way. Instead of queueing, the firms could adopt some other way of managing the shortage, like using a lottery to allocate the good. That way there is no additional opportunity cost.

Or, maybe the market will adapt, which is what we have seen recently. Some firms have set themselves up as professional line sitters, such as those described in this article from Racked last week. These guys can be hired to sit and wait in line for you, so that you avoid the opportunity costs of waiting (of course, instead you now face the added monetary cost of paying some guy to sit in line for you). Provided the amoung the line sitters charge (according to the article, US$25 for the first hour and US$10 for each additional half hour) is less than the difference between the consumer's willingness-to-pay and the price, the consumer should be happy to pay for the line sitter. And guess what? In welfare terms this is way better, since at least part of the large deadweight loss of queueing is converted into back into economic welfare gains (for the line sitter).

The above analysis relates to a competitive market, but what about firms with market power, i.e. those firms that can set their own price? As we discuss in ECON100, these firms want to set the price that will maximise their profits, but setting a profit-maximising price is very difficult in practice. Firms may not know exactly what demand is going to be, so there is a chance that they set the price too low (as above, this leads to a shortage which can be settled through queueing).

Also, firms are playing a complex long-run strategic game with their customers. If you set the price low and encourage queueing for your product, that attracts publicity. Also, consumers might see queues as a signal of high product quality (after all, why would so many people be willing to wait in line to get the product?). So, the next time that firm releases a new product, demand may well be higher. So, even though encouraging shortages and queueing might not be profit maximising in the immediate future, over the longer term it might be an optimal strategy for a profit-maximising firm with market power.

In either case (competitive or less competitive markets), queueing inevitably makes the consumer face a low price but a high cost for whatever good they are waiting for.

[HT: Marginal Revolution]


  1. I like the point that large firms will intentionally restrict supply for publicity purposes. But, what if supply is restricted because the firm is unable to get enough supply, and the supply curve (MC) becomes perfectly inelastic at Q1?
    Apple often runs out of product and blames the supply chain (they can't make enough). If we took that at face value, then the short run marginal cost for the first good after Q1 would be extraordinarily high (hence the inelasticity). Would this mean that the short run economically efficient price is P2?

  2. You're right Ed. If there was a supply constraint at Q1, then P2 would be an efficient price (in terms of maximising welfare). But, actually so would P1 since total welfare would be the same in both cases - the difference is the distribution of welfare. At P1, the consumer surplus is larger and producer surplus lower. And at P1 there is the excess demand that we observe (but not at P2).

    The problem with this example of course is that Apple isn't operating in a perfectly competitive market - they have market power, so rather than the diagram above, we should be drawing a monopolist (but the principles are similar - price too high, shortage which can be managed by queueing).