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Platooning, driverless cars and ride hailing services have all been suggested as ways to reduce congestion. In this post I want to examine the use of coordination via ride hailing services as a way to reduce congestion. Assume that large numbers of riders decide to rely on ride hailing services. Because the services use Google Maps or Waze for route selection, it would be possible to coordinate their choices to reduce congestion.

To think thorough the implications of this, its useful to revisit an example of Arthur Pigou. There is a measure 1 of travelers all of whom wish to leave the same origin (${s}$) for the same destination (${t}$). There are two possible paths from ${s}$ to ${t}$. The top’ one has a travel time of 1 unit independent of the measure of travelers who use it. The bottom’ one has a travel time that grows linearly with the measure of travelers who employ it. Thus, if fraction ${x}$ of travelers take the bottom path, each incurs a travel time of ${x}$ units.

A central planner, say, Uber, interested in minimizing total travel time will route half of all travelers through the top and the remainder through the bottom. Total travel time will be ${0.5 \times 1 + 0.5 \times 0.5 = 0.75}$. The only Nash equilibrium of the path selection game is for all travelers to choose the bottom path yielding a total travel time of ${1}$. Thus, if the only choice is to delegate my route selection to Uber or make it myself, there is no equilibrium where all travelers delegate to Uber.

Now suppose, there are two competing ride hailing services. Assume fraction ${\alpha}$ of travelers are signed up with Uber and fraction ${1-\alpha}$ are signed up with Lyft. To avoid annoying corner cases, ${\alpha \in [1/3, 2/3]}$. Each firm routes its users so as to minimize the total travel time that their users incur. Uber will choose fraction ${\lambda_1}$ of its subscribers to use the top path and the remaining fraction will use the bottom path. Lyft will choose a fraction ${\lambda_2}$ of its subscribers to use the top path and the remaining fraction will use the bottom path.

A straight forward calculation reveals that the only Nash equilibrium of the Uber vs. Lyft game is ${\lambda_1 = 1 - \frac{1}{3 \alpha}}$ and ${\lambda_2 = 1 - \frac{1}{3(1-\alpha)}}$. An interesting case is when ${\alpha = 2/3}$, i.e., Uber has a dominant market share. In this case ${\lambda_2 = 0}$, i.e., Lyft sends none of its users through the top path. Uber on the hand will send half its users via the top and the remainder by the bottom path. Assuming Uber randomly assigns its users to top and bottom with equal probability, the average travel time for a Uber user will be

$\displaystyle 0.5 \times 1 + 0.5 \times [0.5 \times (2/3) + 1/3] = 5/6.$

The travel time for a Lyft user will be

$\displaystyle [0.5 \times (2/3) + 1/3] = 2/3.$

Total travel time will be ${7/9}$, less than in the Nash equilibrium outcome. However, Lyft would offer travelers a lower travel time than Uber. This is because, Uber which has the bulk of travelers, must use the top path to reduce total travel times. If this were the case, travelers would switch from Uber to Lyft. This conclusion ignores prices, which at present are not part of the model.

Suppose we include prices and assume that travelers now evaluate a ride hailing service based on delivered price, that is price plus travel time. Thus, we are assuming that all travelers value time at \$1 a unit of time. The volume of customers served by Uber and Lyft is no longer fixed and they will focus on minimizing average travel time per customer. A plausible guess is that there will be an equal price equilibrium where travelers divide evenly between the two services, i.e., ${\alpha = 0.5}$. Each service will route ${1/3}$ of its customers through the top and the remainder through the bottom. Average travel time per customer will be ${5/3}$. However, total travel time on the bottom will be ${2/3}$, giving every customer an incentive to opt out and drive their own car on the bottom path.

What this simple minded analysis highlights is that the benefits of coordination may be hard to achieve if travelers can opt out and drive themselves. To minimize congestion, the ride hailing services must limit traffic on the bottom path. This is the one that is congestible. However, doing so makes its attractive in terms of travel time encouraging travelers to opt out.

Finally got around to reading the PCES report on economics education at Manchester. The Francis Urquhart  half of my dual selves was duty bound to dislike it. My Urquhart self, would urge the authors to switch subjects and find  fulfilling careers in one of the caring professions, like, personal incontinence counselor. My milquetoast self prevailed and I buckled down to read it.

The report raises two issues and its writers have made the mistake of conflating them or at least not separating them clearly enough. The first is the effectiveness with which economics is taught. The second is what is to be taught.

On the first, the report makes for depressing reading. It summarizes an economics education as dull as ice fishing. For those unfamiliar with ice fishing, it is a sport (and thats being charitable) practiced by the inhabitants of Minnesota and the remoter parts of Wisconsin. In dead of winter, one drives a large vehicle over a frozen lake. If that were insufficient to tempt fate, one then cuts a hole in the ice for the ostensible purpose of catching fish. In practice one sits around the hole drinking prodigously while trying not to fall in. Beans, flatulance and an absence of sanitation figure prominently.

On the second, the report’s authors write

Our economics education has raised one paradigm, often referred to as neoclassical economics, to the sole object of study. Alternative perspectives have been marginalised. This stifles innovation, damages creativity and suppresses constructive criticisms that are so vital for economic understanding. Furthermore, the study of ethics, politics and history are almost completely absent from the syllabus. We propose that economics cannot be understood with all these aspects excluded; the discipline must be redefined.

Exposure to history, psychology and politics? Of course, yes. Within the US system this happens naturally as a function of breadth requirements. Students are not shy about trying to reconcile what they have learnt in Psychology and what they are mastering in Economics. It makes for a lively classroom.

What about these alternative perspectives? In for a penny in for a pound, so I decided to read a paper  by Steven Keen. Keen, as far as I can gather is one of the leading lights of these alternative perspectives. The paper I read (co-authored with Russell Standish) appeared in Physica A and can be found here. If you’ve not heard of it, there is a good reason for that. Continue to ignore it. Pauli might have described it thus:

Das ist nicht nur nicht richtig, es ist nicht einmal falsch!

Reading it lowered my IQ, something I can scarce afford to do. If this is representative of what passes for alternative perspectives, the writers of the PCES should leave economics and find fulfilling careers as incontinence counselors. Finally, for those who think my description of Keen and Standish uncharitable, I refer them to the following by Chris Auld.  Stamping out ignorance is a thankless task and one is cheered to see there are some who take it on.

The urge to promote these alternative perspectives is to be found  across the Channel as well. There, a sub group of scholars and  nescafe society currently wished to form a separate group so that they may be evaluated by different norms.  Jean Tirole, in a letter to  the State secretary in charge of Higher education and Research in France, argued against this. A response can be found here.

On January 30th of this year, one of the arms of the BBC reported a row at Sheffield University about an economics exam question. The offending exam question is reproduced below. Is the question, as one student suggested, indistinguishable from Chinese?

Consider a country with many cities and assume there are $N > 0$ people in each city. Output per person is $\sigma N^{0.5}$ and there is a coordination cost per person of $\gamma N^2$. Assume that $\sigma > 0$ and $\gamma > 0$.

a) What sort of things does the coordination cost term $\gamma N^2$ represent? Why does it make sense that the exponent on $N$ is greater than 1?

b) Draw a graph of per-capita consumption as a function of $N$ and derive the optimal city size $N$. How does it depend on the parameters $\sigma$ and $\gamma$? Provide intuition for your answers.

c) Describe which combination of $\sigma$ and $\gamma$ generate a peasant economy, meaning an economy with no cities (or 1-person cities). Why might the values of the parameters $\sigma$ and $\gamma$ have changed over time? What do these changes imply in terms of optimal city size.

Without knowing what was covered in classes and homework one cannot tell what kind of tacit knowledge/conventions the examiner was justified in assuming in posing the question. Its easy, with experience at these things, to guess what the examiner had in mind. Nevertheless, the question is badly worded and allows a `sea lawyer‘ of a student to get full marks.

First, the sentence does not assert a connection between output and coordination. Thus, the answer to (a) should be:

Without knowing the purpose of the coordination, it is impossible to answer this question.

A better first sentence would have been:

Consider a country with many cities and assume there are $N > 0$ people in each city. Output per person is $\sigma N^{0.5}$ and to achieve it requires a coordination cost per person of $\gamma N^2$.

Second, readers are not told the units in which output is denominated. Thus, part (b) cannot be answered unless one assumes that output has a constant dollar value. One might reasonably suppose this is not the case. The sea lawyer would answer:

As output can be generated at no cost, and is monotone in city size, the optimal size of the city is infinity. Note this does not depend on the values of $\sigma$ or $\gamma$.

From the answer to part (b) we see that no combination of parameters would generate a peasant economy.

Here is Sam Harris, in an addendum to his post How Rich is Too Rich?

I would be interested to know if any economist has an economic argument against the following ideas:

Future breakthroughs in technology (e.g. robotics, nanotech) could eliminate millions of jobs very quickly, creating a serious problem of unemployment.

I am not suggesting that this is likely in the near term…. I am suggesting, however, that there is nothing that rules out the possibility of vastly more powerful technologies creating a net loss of available jobs and concentrating wealth to an unprecedented degree.