Monday, 18 June 2018

The optimal queue

One of the biggest headaches that shoppers have to deal with is queues. Shoppers don't like having to wait, and if the queue is too long, some may simply give up without completing their purchase. But for store owners to reduce the length of queues (or eliminate them), they would face higher costs (at the least, they would need to hire more staff). So, eliminating queues is unlikely to be a good plan for stores. To see why, consider this recent article in The Conversation by Gary Mortimer (Queensland University of Technology) and Louise Grimmer (University of Tasmania):
Businesses face the challenge of identifying the optimum point where the costs of providing the service equal the costs of waiting. People in queues behave in ways that create direct and indirect costs for businesses. Sometimes customers will baulk and simply refuse to join the queue. Or they join the queue but renege, leaving because wait times are too long.
This behaviour leads to measurable costs. These costs are both direct, like abandoned carts, and indirect, like perceptions of poor service quality, increased dissatisfaction and low levels of customer loyalty.
There's lots of interesting points made in Mortimer and Grimmer's article (and for more on queueing, see my 2014 blog post on the topic). However, I want to highlight this diagram:


The diagram illustrates the optimal level of service. The y-axis shows costs to the store, and the x-axis shows the service level (where a higher service level is associated with shorter queues). The store is trying to minimise their total costs, but there are two marginal costs that they are trying to balance. The first cost is the marginal cost of providing service. This is upward sloping as we move from left to right, because each additional 'unit' of service level costs the store more than the last. To see why, consider your local supermarket. If it only had one checkout, adding another checkout would be fairly low-cost - the store would give up a little shelf space (which would entail an opportunity cost of some lost sales of items that would have been displayed there), and have to pay another worker to man the second checkout. A third checkout would entail more cost, as would a fourth, and so on.

So it is easy to see why the total cost of providing service increases, but why does the marginal cost (the cost of providing one additional checkout) increase? It's because each additional checkout is not as productive as the previous one. If you only have one or two checkouts in your supermarket, the workers on those checkouts are going to be going flat out all day. But if you add a seventeenth checkout, that checkout might stand idle during quiet periods (or days, or weeks), and that added cost is going to be spread over fewer customers, so the cost per customer for that checkout (the marginal cost of that checkout) is higher than the first ones. So, that's why the marginal cost of providing service is upward sloping. It is low when providing a low level of service, but increases as you provide higher levels of service.

The second cost is the marginal cost of waiting time. This cost increases when you provide lower levels of service, because the lower service levels, the more frustrated your customers will be. Perhaps they decide to leave the store without completing their purchase, or perhaps they complete their purchase but don't return in future. Either way, that is a cost for the store (an opportunity cost of foregone sales), and the cost is greater the lower the service level. An alternative way of thinking about this is that it is the marginal benefit of providing better service.

The optimal level of service is the level of service where the marginal benefit exactly meets the marginal cost (or, in this case, where the marginal cost of providing service is equal to the marginal cost of waiting time). That's the optimal service level, because if you moved in either direction, the cost to the store would be greater.

To see why, consider a point just to the left of the optimum on the diagram above. The store is offering a slightly lower level of service than optimal. It saves on the cost of providing a checkout, but that cost saving is less than the extra waiting cost it incurs (this is easy to see on the diagram - notice that the marginal waiting cost is above the marginal cost of providing service). That makes the store worse off.

Now consider a point just to the right of the optimum on the diagram above. The store is offering a slightly higher level of service than optimal. It encourages more customers to stay and purchase, saving on waiting cost, but that is less than the amount it saves on the cost of providing better service (again, this is easy to see on the diagram - notice that the marginal cost of providing service is above the marginal waiting cost). That also makes the store worse off.

The optimal service level is probably not to ensure that no customer ever queues. It is to keep the queues just long enough that it balances the marginal cost of providing better service against the marginal cost of lost custom.

Read more:


Friday, 15 June 2018

The future of education may be more blended learning, but I'm still not convinced it should be

Long-time readers of this blog will recognise that I am a skeptic when it comes to online education, massive open online courses (MOOCs), as well as blended learning (for example see here or here). Back in 2016, I argued that MOOCs were approaching that 'trough of disillusionment' section of the hype cycle. The key issue for me isn't that online learning doesn't work for some students - it is that online learning works well for self-directed and highly engaged students, while actually making less self-directed students feel isolated, leading to disengagement with learning.

So, I was really interested to read this April article in The Atlantic by Jeffrey Selingo on the future of college education:
As online learning extends its reach, though, it is starting to run into a major obstacle: There are undeniable advantages, as traditional colleges have long known, to learning in a shared physical space. Recognizing this, some online programs are gradually incorporating elements of the old-school, brick-and-mortar model—just as online retailers such as Bonobos and Warby Parker use relatively small physical outlets to spark sales on their websites and increase customer loyalty. Perhaps the future of higher education sits somewhere between the physical and the digital.
A recent move by the online-degree provider 2U exemplifies this hybrid strategy. The company partnered with WeWork, the co-working firm, to let 2U students enrolled in its programs at universities, such as Georgetown and USC, to use space at any WeWork location to take tests or meet with study groups. “Many of our students have young families,” said Chip Paucek, the CEO and co-founder of 2U. “They can’t pick up and move to a campus, yet often need the facilities of one.”...
As the economy continues to ask more and more of workers, it is unlikely that most campuses will be able to afford to expand their physical facilities to keep up with demand. At the same time, online degrees haven’t been able to gain the market share, or in some cases the legitimacy, that their proponents expected. Perhaps a blending of the physical and the digital is the way forward for both.
So, it seems that the limits of purely online learning are being reached, and (some) students are wanting something different. But reading Selingo's article, it still seems to me that it's the self-directed students that are arguing for something more than purely online learning. Again, those are the students who thrive in this model, but they are not necessarily the students that we should be focused on as teachers. And it we are trying to extend the reach of higher education to more non-traditional students, then a move to more blended learning is even more unconvincing to me. I'm still yet to see an online approach that incorporates a meaningful (and effective) way of engaging students below the median of the grade distribution, and keeping them engaged through to course completion.

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    Tuesday, 12 June 2018

    Immigrant restrictions and wages for locals

    A simple economic model of demand and supply tells us that, if there are two substitute goods and the supply of one of them decreases, then demand for the other substitute will increase. This leads the price to increase for both goods. If the two 'goods' here are the labour of immigrants and the labour of locals, then a decrease in the supply of immigrant workers should lead to an increase in the demand for local workers, and higher wages for both groups. However, that simple analysis ignores that there is often another substitute for labour - mechanisation (or capital). So, it is by no means certain that restricting the number of immigrant workers will raise the wages of local workers, because employers might substitute from immigrant workers to technology, rather than from immigrant workers to local workers.

    Which brings me to this new paper (ungated earlier version here) by Michael Clemens (Center for Global Development), Ethan Lewis (Dartmouth College), and Hannah Postel (Princeton), published in the journal American Economic Review. In the paper, Clemens et al. look at the effect of the 1964 exclusion of Mexican braceros from the U.S. farm labour market. At the time, the exclusion was argued for because it would lift wages for domestic farm labourers. However, looking at data from 1948 to 1971, Clemens et al. find that it had no effect. That's no effect on wages and no effect on employment of domestic farm workers.

    They argue that the reason for the null effects is that farmers shifted to greater use of mechanisation (which they had not adopted in great numbers up to that point). They provide some empirical support for this. Crops where there was an existing technology that was not in wide use (e.g. tomatoes, where expensive harvesting machines were available that could double worker productivity) didn't suffer a drop in production after the bracero exclusion, because farmers simply adopted the available technology. In contrast, crops where there was no new technology available (e.g. asparagus) suffered a large drop in production (because farmers couldn't substitute to new technology, and fewer workers were employed).

    The lesson here is that when prompted to change, producers will usually adopt the cheapest available production technology (as I have noted before). But that isn't necessarily the production technology that policy makers want them to adopt. In this case, instead of a production technology that made use of more local workers, the farmers opted for a production technology that made greater use of mechanisation. So, even if as a policy maker you believed that reducing immigration would improve wages for local workers, it isn't certain that would be the result of polices that reduce immigration (more on the effect of immigrants on local wages in a future post).

    [HT: Eric Crampton at Offsetting Behaviour]

    Sunday, 10 June 2018

    More on the Oregon marijuana market shake-out

    A few weeks ago, I wrote about the ongoing shake-out of the marijuana market in Oregon. Last week, the New Zealand Herald ran another story on this issue:
    When Oregon lawmakers created the state's legal marijuana program, they had one goal in mind above all else: to convince illicit pot growers to leave the black market.
    That meant low barriers for entering the industry that also targeted long-standing medical marijuana growers, whose product is not taxed. As a result, weed production boomed — with a bitter consequence.
    Now, marijuana prices here are in freefall, and the craft cannabis farmers who put Oregon on the map decades before broad legalization say they are in peril of losing their now-legal businesses as the market adjusts...
    The key issue there is that the profit opportunities for new growers attracted a lot of additional supply, leading to decreased profits for all. Usually, we think of barriers to market entry as being a bad thing, and indeed they are from the consumer's perspective - they decrease competition and lead to higher prices. However, from the perspective of the sellers, barriers to entry are a great thing because they provide the sellers with some amount of market power - that is, some power to raise the price above their costs.

    So, how did Oregon get into this situation? The Herald story explains:
    The oversupply can be traced largely to state lawmakers' and regulators' earliest decisions to shape the industry.
    They were acutely aware of Oregon's entrenched history of providing top-drawer pot to the black market nationwide, as well as a concentration of small farmers who had years of cultivation experience in the legal, but largely unregulated, medical pot program.
    Getting those growers into the system was critical if a legitimate industry was to flourish, said Sen. Ginny Burdick, a Portland Democrat who co-chaired a committee created to implement the voter-approved legalization measure.
    Lawmakers decided not to cap licenses; to allow businesses to apply for multiple licenses; and to implement relatively inexpensive licensing fees.
    Limiting the number of licences would create an effective barrier to entry into the market. By not limiting licences, Oregon's legislators set up a situation where marijuana sellers have to compete with many others. Note that, for now, this is only a problem for the sellers, who end up with low profits as a result of the competitive market. However, if the coming shake-out results in a smaller number of large firms being the only ones left, and Oregon goes on to crack down on the issue of new licences (which is a possibility), then we could end up in a situation where not only is there market power, but where it is concentrated in the hands of a few large sellers. Of course, that will be highly profitable for the sellers, but marijuana buyers will be much worse off.

    Read more: