I got notified last night that Leon Moses passed away. There was information about a memorial service and an academic biography. He was almost 89 and his wife had passed away earlier this year. I suspect he led a full life, though we stopped corresponding after the 1980s, so I'm unaware of the specifics of what he did later.
My first published paper was with Leon and it got into the AER; so that was plum. And it was a good thing too since the papers I had carved out of my dissertation were going nowhere and I spent about three years pushing them before moving onto other research.
I was surprised to see that my adviser, John Ledyard, also had a piece with Leon. I had thought my collaboration with Leon a bit odd, but seeing the paper with Ledyard maybe it wasn't so unusual. Here's the story behind it.
Leon had been the full time director of the Transportation Center, an administrative position, but he stepped down from that to return to being a regular member of the faculty. He was to teach an intermediate microeconomics class. To manage the reentry issue, he negotiated for having a student well trained in microeconomics to serve as his grader. I was selected for this task. I can't remember which quarter it was, but it was definitely during my third year in grad school, 1978-79. While I'm not 100% sure of this now, I think the grading thing was really more an internship role. What Leon actually wanted was a young guy who was current in then modern to technique to help formalize his intuitive ideas.
Somebody had to pull strings to make the grader job happen. I was on fellowship and that carried a stipulation about not doing work for pay. So a waiver needed to be granted. I believe I got paid $500 for being the grader, which was on top of what the fellowship paid as a stipend.
Northwestern quarters are quite short - nine weeks of class and a week for final exams. The first several weeks Leon and I were all about his class and how the students performed on the homework. Then, sometime in the middle of the quarter, he initiated a conversation about an idea he had on inventory investment, as a way for a firm to take advantage of scale economies. He wanted feedback from me on how to model the joint production and product pricing decisions. That first discussion is what eventually led to the paper. We eventually had many more such discussions. Both of us enjoyed arguing about the model we developed.
We continued to have these conversations well after the grading work had been completed. Eventually, I came up with a model that utilized optimal control techniques, something I had learned in a class taught by Kamien and Schwartz, using notes that would eventually become their book. This means that time is modeled as continuous and one solves differential equations to get at a solution to the model. In retrospect, it would have been better to model this in discrete time, as we (really it was only me) made an error in the formulation and later had to publish an erratum. The error would not have occurred in a discrete time model, where Leon's simple insight was that batch production and then selling off the product for many periods before the next batch is run is the best way to manage the economies of scale in production. In continuous time, however, a u-shaped average cost curve in flow production is really not a way to get at economies of scale, because a rapid on-off-on-off sequence approximates constant returns with little or no storage cost incurred. In the continuous time approach you need economies of scale in the stock production. That gives a rationale for producing in batches.
That paper was essentially completed while I was still a grad student at Northwestern. Yet my collaboration with Leon didn't end after I began work at Illinois. We talked a bit about mode choice in transportation to and from work (bus, train, walk, drive, etc.). Leon wanted to develop a model where mixed mode was an equilibrium outcome. I can no longer remember why this was of interest to him, but I wasn't very tooled up on categorical choice models, which may have been more interesting to the empiricist than to the theorist. Ultimately we did not write anything in this area.
We did write another paper that extended the earlier model to include plant location for a multi-plant firm. It is perhaps more interesting for how that got done and what it lead to, then for the model itself. I don't really remember this, but probably most of our conversations happened on the phone. I do remember that we met at least once, and maybe twice, in south Florida when I was visiting my parents and Leon was on vacation with his family. If you are a real scholar, even vacation is a time for work. And then somehow Leon got us invited to go to Umeå for a conference on location choice, where we gave an early version of the second paper. It was an exotic trip, my first time visiting Europe.
Umeå is about 500 miles north of Stockholm. We had to go from the international airport to a regional airport to catch a connecting flight. We were already zombie-like from the jet lag when we took a cab or a limo to the regional airport. I don't think we figured out that the speedometer was in kilometers/hour instead of miles/hour so we thought we were really speeding. That marked the first of many strange but interesting things on that trip. It was early summer and it never got really dark in Umeå. You could read a book outside even at midnight. The bathrooms were in the Scandinavian style, with the toilet on the same level as the shower and a drain somewhere in the middle of the room, where you could sweep standing water after taking a shower. Breakfasts were also exotic, with a wide variety of cheeses I hadn't had before served on those thick and heavy crackers and something like grits, but served with sour milk. While we stayed in a dorm during the conference, our hosts treated us very well. I do recall meeting another American there, a woman who was living in Sweden, but I believe we were the only ones who came to the conference from the U.S., so Leon and I were treated like dignitaries. It made for a very enjoyable time.
The collaboration with Leon had indirect effects on me as well. I wrote a couple of other papers on my own that amounted to derivative work on our first paper. One was a short piece to make the model more symmetric in its assumptions. If the firm was going to solve an inter-temporal optimization to come up with its inventory investment and pricing decisions, consumers too should solve a dynamic optimization to come up with their choices of how much to consume over time. It was a harder model to solve, but I showed the core insight of the original paper remained intact when consumers are more sophisticated in their purchasing behavior.
The other paper marked my switch from the dissertation research to study of oligopoly models, where I had more success. One of these was a paper on dynamic duopoly with inventory. I'm rather proud of this paper, as it made a fundamental point that wasn't in the rest of the literature. Heretofore people who worked in this area assumed that asymmetric outcomes (one firm is the market leader, the other is a follower) were a consequence of some asymmetry in the initial conditions (the leader got there first and leveraged that for strategic advantage). My examples showed that you could have symmetric starting conditions but still get asymmetric outcomes and, indeed, that is to be expected in these sorts of models. Google Scholar says the paper got 32 citations, which is second highest among the pieces I've written. I would never had thought to write on this topic at all if it had not been for the earlier work with Leon.
I've not otherwise written with somebody who was a near contemporary of my parents, where there is such an obvious age differential between the authors. Looking back on this, I wish I had done more of it, with Leon and perhaps with other senior scholars. It would have been a way for me to touch research issues that mattered to others and to ground my intrinsic interest in theory with practical questions which were posed to me rather than by me.
I now find myself at approximately the same age as Leon was when he and I started to work together. Perhaps I should be looking for some junior people to co-author on pieces, as a way to invigorate my thinking and possibly to pass on some nuggets to the next generation. It's an interesting thought to ponder.