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August 2014

Revenue management of Broadway shows

If you live in or near New York City, you may be part of the lucky ones who get to see Broadway shows - whether theater or musical - on "Broadway" (although technically many theaters are not on Broadway itself but on side streets). Otherwise, your only option to see these shows live is to see them on national or regional tour. The revenue management side of it came to light a few months ago when talks about reducing actors' salaries while on tour found their way into the newspapers. Here are two examples: "On the road, actors seek higher pay" (NYT, January 2014) and "National Theater's latest shows part of non-Equity trends" (WaPo, March 2014).

According to the NYT, the tours of the best-known Broadway tours, such as Wicked or The Lion King, bring in "luxury tour rates" for the actors, starting at $1,807 a week and up to $6,000 for leads. (Obviously, actors don't go on tours year after year after year, many face months between engagements where they don't work, and the time where they can be cast as leads is usually rather short, especially when they also dance.) But other tours have decreased the amounts they pay their actors, with starting salaries at $976/week, for shows that are expected to be successful and reach a wide audience -- otherwise they wouldn't be going on tour to begin with.

Starting salaries for the tour of Mamma Mia! have sunk to about $500 a week, according to WaPo, although that tour will visit big cities such as Philadelphia and San Francisco for full-week engagements (as well as smaller ones for a night) and it shouldn't be too hard to find crowds of ticket-buyers for the show. The idea behind the lower prices is supposed to be that producers want to make sure they'll recoup their financial guarantees (weekly costs are $250,000-400,000 a week). Actors paid lower rates are also said to receive part of the financial gains once the initial costs have been recouped. 

From the NYT: "The economics are complex. Most producers link actor salaries to the box office payments that road presenters guarantee... “Newsies” producers negotiated a $330,000 guarantee, low enough to avoid luxury tour salaries" so that its dancers/actors will be paid a minimum salary of $1,091 a week. Also, "Actors on low-wage tours do receive salary increases of 17 percent if a tour recoups its capitalization, and they also receive overages — a piece of the profits when a tour exceeds revenue projections. But these bumps do not come close to salaries on high-end tours."

An agreement seems to have been later reached where actors on tour would be paid something in the middle following a "tiered" contract (see WaPo article, published two months after the NYT one). I wish there was more transparency regarding how much or how little actors are getting paid. This is a very demanding, sometimes grueling, job that takes many hours of rehearsal for the sake of entertaining audiences, and if you've seen a good choreography on Broadway you know what I'm talking about. (If you don't, search for "Newsies" and "Seize the Day" on YouTube and watch what the dancers do.) There are many more talented performers than there are jobs for them in the show business world, but actors on Broadway tours should be performers their peers look up to, right after actors on Broadway shows (on Broadway) - models of what others hope to achieve. Broadway tours, which make Broadway reputation outside New York City, shouldn't staff rosters with less experienced performers willing to accept lower rates and undercutting their peers.

Here are more numbers for the theater-loving revenue management nerds out there, and maybe that's just me. Book of Mormon recouped its initial investment of $11.4m in only eight months, which was considered fast, and Newsies recouped its $5m investment in six. Incredibly enough, Newsies wasn't even supposed to go to Broadway - the musical was created for high school musical clubs, and had an off-Broadway run in New Jersey (I guess you could call that off-New York City, even) before positive reception by critics and audiences led producers to open the show at the Nederlander for a 12-week engagement. The 12 weeks turned into 2 1/2 years, and Newsies will be closing August 24. Go and see it if you can. The dance numbers are spectacular and, this being a Disney musical, it is highly family-friendly.

The Book of Mormon has also implemented dynamic pricing techniques, "which spikes on high-demand weekend and holiday dates. Unofficial reports peg the show’s advance sales at close to $40 million." The Hollywood Reporter article, from which the previous quote is taken, continues: "any show that returns its initial investment in under a year invariably does so by playing consistently to sold-out houses. Some shows can play two years or more without recouping... Despite sell-out business in one of Broadway’s largest theaters, the bigger-budgetWicked took 14 months to return its $14 million investment in 2004. That show continues to be Broadway’s top earner."

NPR had an interesting take on why theater tickets are cheaper in London's West End than on Broadway. ("[A]ccording to the Society of London Theatre, the average ticket price for a West End show is about $70. In New York, according to the Broadway League, the average price just crossed $100 for the first time.") Because London has many government-subsidized shows [like Paris, in fact], West End theaters - which are not subsidized - must be careful not to have prices too high and send potential theater-goers to their competitors. Also, it costs less to put on a show, so shows don't need to be huge hits to recoup costs. There is also less TV advertising in the West End, but the theaters on Broadway, having been renovated, are said to be much nicer. I haven't been to a West End theater, so I can't judge. But between these issues about actors' salaries and the practice to fine-tune shows either off-Broadway or even in other cities before going to Broadway, the New York theater industry seems to have refined the art of dynamic revenue management under risk aversion and adaptive learning.

PubMed Commons: A Community for Scientists

I recently came across PubMed Commons, a new resource developed by NIH's National Center for Biotechnology Information to facilitate scientist-to scientist interactions. The idea is to provide a forum for scientists to comment on each other's work. Anyone who has at least one publication in PubMed can participate, and helps scientists receive feedback on their work (perhaps more constructive feedback, in fact, than the anonymous one obtained through journal reviews, because of a member-based rating system that identifies the most useful comments), as well as share links to resources and data sets. The NIH calls it a virtual water cooler.

To further participation, I think it'd be good to give more rewards to the users identified (by their peers using the rating system) as making the most useful comments, such as free registration to the annual conference in their field, the opportunity to have a short video about their research posted on the PubMed Commons website, priority review or open-access publication for one of their papers - let me know if you think of something else. The danger is that a few people will leave a comment or two and then will lose interest - I'm curious to see how the NIH will attempt to make PubMed Commons engaging and readership grow. (5,000 scientists have registered so far and 1,600 have left a comment. PubMed Commons was launched in October 2013.) It would also be important to define some metrics to quantify the usefulness of the site in terms of the advancement of science, although gathering data will take time: will articles discussed on PubMed Commons be cited more frequently because they will be more prominent in the field? will collaborations be initiated based on the discussions on the site? Also, the website seems predominantly word-driven. It might be valuable to have more of a user-friendly, multi-media approach where people could upload not only a paper but maybe (separately) the key graph of the paper or a related presentation - "nuggets" to motivate interested fellow scientists to read the whole paper.

You can access PubMed Commons here.

On the price of e-books's dispute with publisher Hachette entered a new round a few days ago when the Seattle behemoth published its key arguments on its blog and, in an email I got over the weekend (you can read the text at ), encouraged readers/writers to contact Hachette about this festering issue. takes issue with the fact that Hachette releases many e-books at $14.99 or $19.99 and argues that its scientists have "quantified the price elasticity of e-books from repeated measurements across many titles. For every copy an e-book would sell at $14.99, it would sell 1.74 copies if priced at $9.99. So, for example, if customers would buy 100,000 copies of a particular e-book at $14.99, then customers would buy 174,000 copies of that same e-book at $9.99. Total revenue at $14.99 would be $1,499,000. Total revenue at $9.99 is $1,738,000. The important thing to note here is that the lower price is good for all parties involved: the customer is paying 33% less and the author is getting a royalty check 16% larger and being read by an audience that’s 74% larger. The pie is simply bigger."

I personally don't like e-books priced much above $9.99, because to me it is a clear signal that the book isn't intended for the general public, and I've read, or attempted to, too many books where I basically drowned in academese to care to repeat the experience. If a book isn't expected to find many readers, it won't find a mainstream publisher - instead it'll be picked by a university press that can best market it to the narrow audience it targets, and will compensate for the lower sales volume with a higher price. (Case in point: Yale University Press.)

One thing I don't understand, though, is why cares so much about the price the publisher charges. It could (option 1) find similar books in its database - not books other customers have bought, because customers can buy a lot of unrelated things, but books on the same topic, say, historical fiction set in this time period with the main character having those attributes, or other textbooks on introductory chemistry (although the prices of e-textbooks are of a completely different order of magnitude than $19.99) - and then it could market those books, presumably cheaper, on the product page of the book that is more expensive. They can (option 2) give priority in the search results to e-books that are priced in the range they prefer. Further (option 3), perhaps they could change the royalties agreement for the prices of e-books that are above $9.99, asking for a higher share of royalties to compensate for a lower volume. All this to say, they have more options on their end than making Hachette do what Amazon says, and the first two options above would be, I assume, something they can implement all by themselves on the website. 

In its email, Amazon mentions (I paraphrase) that the paperback has ended up being good for the book industry in spite of the initial qualms at introducing this new product. What it doesn't say, though, is that paperbacks hit the market about a year after hardcovers are published. The whole reason for the price decrease is to capture a segment of the market that is willing to wait and unwilling to pay the hardcover price. So Hachette could also say ok to $9.99 per e-book, but e-books (cheaper than hardcovers or paperbacks) will only be available two years after hardcover publication. It is hard to imagine Amazon, which has invested a lot in the Kindle, be terribly happy with that. Or e-books can be priced dynamically, depending on the time since publication and the other editions available. Amazon, in its letter, makes no mention of the risk of e-book sales cannibalizing paper sales.

Farhad Manjoo points out in the New York Times that it is not clear $9.99 is the perfect price for e-books. (Also read this article in the Dallas Morning News.) In fact, while hardcovers for the general public are usually sold at around $26 and paperbacks at around $15, maybe a case should be made that e-books should see more price variation instead of one-price-for-all. Or you could even dream big and imagine Amazon and Hachette agreeing to market one "basic" type of e-book (no color, etc) at $9.99 and a more sophisticated one (with features to be determined - perhaps author's interviews and reading group guides for fiction books and additional material about the subject for nonfiction books) at $14.99 or $19.99 so that the $9.99 one would be the e-book equivalent to paperback and the $14.99 one would be the e-book equivalent to hardcover. Or $9.99 could be an abridged version (for nonfiction books - this is harder to do with fiction) and $14.99 the full version. Audiobooks are often abridged to keep recording and listening time manageable - why not e-books? I also wonder if some publishers' (or book business people's) hatred of Amazon, hinted at in the New Yorker piece by George Packer published in February, understand that many readers like e-books, and that might mean dealing with Amazon in a somewhat smarter way. Maybe if publishers had tried harder to imagine the future of the book before Amazon took the lead with the Kindle, they wouldn't find themselves dealing with the issues they have now. 

In the end, I don't think this is really about what the customer pays for e-books or the author gets as royalties. I think this is about what the publisher gets to keep, and what Amazon gets to make from selling e-books.  If this was really about pricing, then Amazon and Hachette could think outside the boxes and debate far-ranging innovations and talk about the sort of reading world they imagine in the future and act on those ideas. Instead, this looks more and more like two behemoths locked in a battle of will, like deers that lock antlers and can't disengage (I have no clue if this actually happens but you get the picture...), or those old couples who hate each other but can't live without each other either and spend their time spewing bitterness at each other and making each other's lives miserable. Someone please find a mediator who can bring those two at the negotiating table without their jumping at each other's throat. It doesn't look like they're on the road to solving their issues without outside help.

Robust risk adjustment in health insurance

This is a short paper my doctoral student Tengjiao Xiao and I recently completed. 

Here is the abstract: "Risk adjustment is used to calibrate payments to health plans based on the relative health status of insured populations and helps keep the health insurance market competitive. Current risk adjustment models use parameter estimates obtained via regression and are thus subject to estimation error. This paper discusses the impact of parameter uncertainty on risk scoring, and presents an approach to create robust risk scores to incorporate ambiguity and uncertainty in the risk adjustment model. This approach is highly tractable since it involves solving a series of linear programming problems."

The paper also contains, in the section where we motivate the need for robustness, the graph about ranking changes using proxy and actual Value-Based Purchasing factors that are used to give the about 3,000 hospitals considered bonuses or penalties. A negative ranking change indicates a loss in ranks and a positive one indicates a gain. The interesting thing about this graph is that losses and gains can fluctuate enormously, meaning that some hospitals that would have stood to receive very high bonuses (for the amounts of money considered: every hospital contributes 1% to fund the scheme) under proxy factors found themselves at the very bottom of the ranking, and vice-versa. To the best of our knowledge, this is not something that has received much if any attention in the media. 

The core of the short paper is to show how robust risk scores can be computed by solving a series of linear programming problems, with the aim of minimizing worst-case regret between the actual risk scores, used to implement transfer payments between health payers, and the true scores, which we don't know. We show on a simple test case with 10 insurers that the change in payments can be substantial.

Comments welcome!

Optimal facility in-network selection for healthcare payers under reference pricing

My working paper with Victoire Denoyel and Laurent Alfandari of ESSEC Business School is online! Read it here.

Abstract: "Healthcare payers are exploring cost-containing policies to steer patients, through qualified information and financial incentives, towards providers offering the best value proposition. With Reference Pricing (RP), a payer or insurer determines a maximum amount paid for a procedure, and patients who select a provider charging more pay the difference. In a Tiered Network (TN), providers are stratified according to a set of criteria (such as quality, cost and sometimes location) and patients pay a different out-of-pocket price depending on the tier of their chosen provider. Motivated by a recent CalPERS program, we design two original MIP optimization models for payers that combine both RP and TN, filling the gap of quantitative research on these novel payment policies. Carefully designed constraints provide the decision maker with levers for a trade-off between cost reduction and patients' satisfaction. Numerical experiments provide valuable insights in that respect, displaying also how the tiers are scattered on a cost/quality plane. We argue that this system has strong potential in terms of costs reduction for public or private payers, quality increase for patients and visibility for high-value providers."

To the best of our knowledge, our paper presents the first quantitative model about tiered-networks design for a healthcare procedure under reference pricing, a model the CalPERS pilot study will certainly popularize.

Our paper is here. (Comments welcome!) We're now working on extensions that we hope to share and discuss soon.

If you're interested in learning more in reference pricing for healthcare procedures, I recommend the work of James C. Robinson of UC Berkeley, who led the analysis of the CalPERS pilot, for instance "Payers test reference pricing and Centers of Excellence to steer patients to low-price and high-quality providers" (Health Affairs, subscription required).