You are currently browsing rvohra’s articles.
About a year ago, I chanced to remark upon the state of Intermediate Micro within the hearing of my colleagues. It was remarkable, I said, that the nature of the course had not changed in half a century. What is more, the order in which topics were presented was mistaken and the exercises on a par with Vogon poetry, which I reproduce below for comparison:
“Oh freddled gruntbuggly,
Thy micturations are to me
As plurdled gabbleblotchits on a lurgid bee.
Groop, I implore thee, my foonting turlingdromes,
And hooptiously drangle me with crinkly bindlewurdles,
Or I will rend thee in the gobberwarts
With my blurglecruncheon, see if I don’t!”
The mistake was not to think these things, or even say them. It was to utter them within earshot of one’s colleagues. For this carelessness, my chair very kindly gave me the chance to put the world to rights. Thus trapped, I obliged. I begin next week. By the way, according to Alvin Roth, when an ancient like myself chooses to teach intermediate micro-economics it is a sure sign of senility.
What do I intend to do differently? First, re order the sequence of topics. Begin with monopoly, followed by imperfect competition, consumer theory, perfect competition, externalities and close with Coase.
Why monopoly first? Two reasons. First it involves single variable calculus rather than multivariable calculus and the lagrangean. Second, student enter the class thinking that firms `do things’ like set prices. The traditional sequence begins with a world where no one does anything. Undergraduates are not yet like the white queen, willing to believe 6 impossible things before breakfast.
But doesn’t one need preferences to do monopoly? Yes, but quasi-linear will suffice. Easy to communicate and easy to accept, upto a point. Someone will ask about budget constraints and one may remark that this is an excellent question whose answer will be discussed later in the course when we come to consumer theory. In this way consumer theory is set up to be an answer to a challenge that the students have identified.
What about producer theory? Covered under monopoly, avoiding needless duplication.
Orwell’s review of Penguin books is in the news today courtesy of Amazon vs Hachette. You can read here about that here. I wish, however, to draw your attention to an example that Orwell makes in his review:
It is, of course, a great mistake to imagine that cheap books are good for the book trade. Actually it is just the other way around. If you have, for instance, five shillings to spend and the normal price of a book is half-a-crown, you are quite likely to spend your whole five shillings on two books. But if books are sixpence each you are not going to buy ten of them, because you don’t want as many as ten; your saturation-point will have been reached long before that. Probably you will buy three sixpenny books and spend the rest of your five shillings on seats at the ‘movies’. Hence the cheaper the books become, the less money is spent on books.
Milton Friedman in his textbook Price Theory, as an exercise, asks readers to analyze the passage. He does not explicitly say what he is looking for, but I would guess this: what can you say about the preferences for such a statement to be true. Its a delightful question. A budget line is given and a point that maximizes utility on the budget lie is identified. Now the price of one of the goods falls, and another utility maximizing point is identified. What kind of utility function would exhibit such behavior?
By the way, there are 60 pence to a shilling and a half a crown is six pennies.
The news of Stanley Reiter’s passing arrived over the weekend. Born in a turbulent age long since passed, he lived a life few of us could replicate. He saw service in WW2 (having lied about his age), and survived the Battle of the Bulge. On the wings of the GI bill he went through City College, which in those days, was the gate through which many outsiders passed on their way to the intellectual aristocracy.
Perhaps a minute to recall to what Stan left behind.
Stan, is well known of his important contributions to mechanism design in collaboration with Hurwicz and Mount. The most well known example of this is the notion of the size of the message space of a mechanism. Nisan and Segal pointed out the connection between this and the notion of communication complexity. Stan would have been delighted to learn about the connection between this and extension complexity.
Stan was in fact half a century ahead of the curve in his interest in the intersection of algorithms and economics. He was one of the first scholars to tackle the job shop problem. He proposed a simple index policy that was subsequently implemented and reported on in Business Week: “Computer Planning Unsnarls the Job Shop,” April 2, 1966, pp. 60-61.
In 1965, with G. Sherman, he proposed a local-search algorithm for the TSP (“Discrete optimizing”, SIAM Journal on Applied Mathematics 13, 864-889, 1965). Their algorithm was able to produce a tour at least as good as the tours that were reported in earlier papers. The ideas were extended with Don Rice to a local search heuristic for non-concave mixed integer programs along with a computation study of performance.
Stan was also remarkable as a builder. At Purdue, he developed a lively school of economic theory attracting the likes of Afriat, Kamien, Sonnenschein, Ledyard and Vernon Smith. He convinced them all to come telling them Purdue was just like New York! Then, to Northwestern to build two groups one in the Economics department and another (in collaboration with Mort Kamien) in the business school.
The Fields medals will be awarded this week in Seoul. What does the future hold for the winners? According to Borjas and Doran, declining productivity caused by a surfeit of dilettantism. The data point to a decline in productivity. By itself this is uninteresting. Perhaps all those on the cusp of 40, see a decline in productivity. What Borjas and Doran rely on is a degree of randomness in who gets a medal. First, there is the variation in tastes of the selection committee (Harish Chandra, for example, was eliminated on the grounds that one Bourbaki camp follower sufficed). Second, the arbitrary age cutoff (the case of the late Oded Schramm is an example of this). Finally, what is the underlying population? Borjas and Doran argue that by using a collection of lesser prizes and honors one can accurately identify the subset of mathematicians who can be considered potential medalists. These are the many who are called, of which only a few will be chosen. The winners are compared to the remaining members of this group. Here is the conclusion (from the abstract):
We compare the productivity of Fields medalists (winners of the top mathematics prize) to that of similarly brilliant contenders. The two groups have similar publication rates until the award year, after which the winners’ productivity declines. The medalists begin to `play the field,’ studying unfamiliar topics at the expense of writing papers.
The prize, Borjas and Doran suggest, like added wealth, allows the winners to consumer more leisure in the sense of riskier projects. However, the behavior of the near winners is a puzzle. After 40, the greatest prize is beyond their grasp. One’s reputation has already been established. Why don’t they `play the field’ as well?
The August 3rd NY Times has an article about the advertising of Fishoil and Facebook. As sometimes happens with a NYT article, the interesting issues are buried beneath moderately interesting anecdotes that may be traded with others at the dinner table in what passes for serious discussion.
The story is about a company called MegaRed, that peddles fish oil. It wants to target consumers who are receptive to the idea of fish oil because they believe that it confers health benefits. The goal is to get them to try out and perhaps switch to MegaRed.
Facebook proposes a campaign which raises the eyebrows of the marketing director, J. Rodrigo:
“I can go to television at a quarter the price.”
Brett Prescott of Facebook agrees, that yes, Facebook is more expensive than TV. But offers an analogy between advertising on Facebook and firing a shotgun.
“And you are firing that buckshot knowing where every splinter of that bullet is landing.”
If biology is the study of bios, life, and geology is the study of goes, the earth, what does that make analogy?
Some arithmetic to clarify matters. Suppose 1 in 100 of all people would be receptive to the idea of MegaRed’s message. Suppose each of these people is worth $1 on average to MegaRed. If you could reach all 100 of these people via TV, then MegaRed should pay no more than 10 cents per person and so $1 in total.
Enter, stage left, Facebook. It claims that it can target its ads so that they go just to the right person. How much is that worth? $1. In this example, Facebook is no better or worse than TV.
If Facebook has any added value compared to TV it does not come from better targeting because one can always compensate for that by paying TV less and reaching more eyeballs. It must come from access to eyeballs unreachable via TV, or, identifying eyeballs that MegaRed would not initially have identified as receptive to their message, or that the medium itself is more persuasive than TV. Is this true for Facebook? If not, MegaRed is better off with TV.
Over a lunch of burgers and envy, Mallesh Pai and discussed an odd feature of medical reidencies. This post is a summary of that discussion. It began with this question: Who should pay for the apprenticeship portion of a Doctor’s training? In the US, the apprenticeship, residency, is covered by Medicare. This was `enshrined’ in the 1965 act that established Medicare:
Educational activities enhance the quality of care in an institution, and it is intended, until the community undertakes to bear such education costs in some other way, that a part of the net cost of such activities (including stipends of trainees, as well as compensation of teachers and other costs) should be borne to an appropriate extent by the hospital insurance program .
House Report, Number 213, 89th Congress, 1st session 32 (1965) and Senate Report, Number 404 Pt. 1 89th Congress 1 Session 36 (1965)).
Each year about $9.5 billion in medicare funds and another $2 billion in medicaid dollars go towards residency programs. There is also state government support (multiplied by Federal matching funds). At 100K residents a year, this translates into about about $100 K per resident. The actual amounts each program receives per resident can vary (we’ve seen figures in the range of $50K to $150K) because of the formula used to compute the subsidy. In 1997, Congress capped the amount that Medicare would provide, which results in about 30K medical school graduates competing for about 22.5K slots.
Why should the costs of apprenticeship be borne by the government? Lawyers, also undertake 7 years of studies before they apprentice. The cost of their apprenticeship is borne by the organization that hires them out of law school. What makes Physicians different?
Two arguments we are aware of. First, were one to rely on the market to supply physicians, it is possible that we might get to few (think of booms and busts) in some periods. Assuming sufficient risk aversion on the part of society, there will be an interest in ensuring a sufficient supply of physicians. Note similar arguments are also used to justify farm subsidies. In other words, insurance against shortfalls. Interestingly, we know of no Lawyer with the `dershowitz’ to make such a claim. Perhaps, Dick the butcher (Henry VI, Part 2 Act 4) has cowed them.
The second is summarized in the following from Gbadebo and Reinhardt:
“Thus, it might be argued … that the complete self-financing of medical education with interest-bearing debt … would so commercialize the medical profession as to rob it of its traditional ethos to always put the interest of patients above its own. Indeed, it can be argued that even the current extent of partial financing of their education by medical students has so indebted them as to place the profession’s traditional ethos in peril.”
Note, the Scottish master said as much:
“We trust our health to the physician: our fortune and sometimes our life and reputation to the lawyer and attorney. Such confidence could not safely be reposed in people of a very mean or low condition. Their reward must be such, therefore, as may give them that rank in the society which so important a trust requires. The long time and the great expense which must be laid out in their education, when combined with this circumstance, necessarily enhance still further the price of their labour.”
Interestingly, he includes Lawyers.
If we turn the clock back to before WWII, Hospitals paid for trainees (since internships were based in hospitals, not medical schools) and recovered the costs from patient charges. Interns were inexpensive and provided cheap labor. After WWII, the GI Bill provides subsidies for graduate medical education, residency slots increased and institutions were able to pass along the costs to insurers. Medicare opened up the spigot and residencies become firmly ensconced in the system. Not only do they provide training but they allow hospitals to perform a variety of other functions such as care for the indigent at lower cost than otherwise.
Ignoring the complications associated with the complementary activities that surround residency programs, who should pay for the residency? Three obvious candidates: insurers, hospitals and the doctors themselves. From Coase we know that in a world without frictions, it does not matter. With frictions, who knows?
Having medicare pay makes residency slots an endowment to the institution. The slots assign to a hospital will not reflect what’s best for the intern or the healthcare system. Indeed a recent report by from the Institute of Medicine summarizes some of these distortions. However, their response to is urge for better rules governing the distribution of monies.
If hospitals themselves pay, its unclear what the effect might be. For example, as residents costs less than doctors, large hospitals my bulk up of residents and reduce their reliance of doctors. However, assuming no increases in the supply of residents, wages for residents will rise etc etc. If insurers pay there might be overprovision of residents.
What about doctors? To practice, a doctor must have a license. The renewal fee on a medical license is, at the top end (California), around $450 a year. In Florida it is about half that amount. There are currently about 800K active physicians in the US. To recover $10 billion (current cost of residency programs) one would have to raise the fee by a $1000 a year at least. The average annual salary for the least remunerative specialties is around $150K. At the high end about $400K. From these summary statistics, it does not appear that an extra $1K a year will break the bank, or corrupt physicians, particularly if it is pegged as a percentage rather than flat amount. The monies collected can be funneled to the program in which the physician completed his or her residency.
The last of the trio, Harold Kuhn, passed away on July 2nd, 2014. Upon hearing the news, I was moved to dig up some old lecture notes of Kuhn’s in which KTK is stated an proved. I’ve been carrying them around with me since 1981. From the condition they are in, this must have been the last time I looked at them. With good reason, for as I re-read them, it dawned upon me how much of them I had absorbed and taken to be my own thoughts. Kuhn motivates the KTK theorem by replacing the non-linear functions by their first order Taylor approximations. This turns the exercise into a linear program. The LP duality theorem suggests the theorem to be proved, and the separating hyperplane theorem does the rest. For details see the relevant chapter of my book. The notes go on to describe Kuhn and Tucker’s excitement and subsequent despair as they uncover a counterexample and the need for a constraint qualification.
William Karush, who passed in 1997, had arrived at the same theorem many years earlier in his 1939 University of Chicago Masters Thesis (Kuhn-Tucker is 1951). When Kuhn learned of Karush’s contribution through a reading of Takayama’s book on Mathematical Economics. Upon doing so he wrote Karush:
In March I am talking at an AMS Symposium on “Nonlinear Programming – A Historical View.” Last summer I learned through reading Takayama’s Mathematical Economics of your 1939 Master’s Thesis and have obtained a copy. First, let me say that you have clear priority on the results known as the Kuhn–Tucker conditions (including the constraint qualification). I intend to set the record as straight as I can in my talk.
The missive closes with this paragraph:
Dick Cottle, who organized the session, has been told of my plans to rewrite history and says `you must be a saint’ not to complain about the absence of recognition. Al Tucker remembers you from RAND, wonders why you never called this to his attention and sends his best regards.
Karush’s reply, 6 days later, equally gracious:
Thank you for your most gracious letter. I appreciate your thoughtfulness in wanting to draw attention to my early work. If you ask why I did not bring up the matter of priority before, perhaps the answer lies in what is now happening – I am not only going to get credit for my work, but I am going to crowned a “saint”.
One of the most engaging books of academic politics, is C. P. Snow’s `The Masters’. In it, a scene describing the debate between factions (Science and Arts) over who should be elected to a college fellowship. The master is in the Arts camp. One of the Science camp urges his candidate upon the college with these words (from memory, as my copy is beyond my reach): “He has written the absolute last word on the subject.” To which the master, responds: “Why can’t you chaps ever have the first word on the subject?” As the narrator, Eliot notes, it was an impolitic response, but recognizes that the master could not resist because it felt good on the tongue.
From Swansea comes another example of the inability to resist something that felt good on the tongue. A note from the head of Swansea University’s school of management to his colleagues (do they still have those at UK universities?):
Some wags call for the removal of some or all of the school’s top management team. Yes, well don’t hold your breath. Or actually, do.
Its not: why haven’t I one won? I have. A sixth form science prize. In my salad days I would day dream about winning the big one (to the sound of Freddy Mercury crooning `We Are The Champions’). But, one ages and comes to term with one’s mediocrity.
In the good old days, when men were men and sheep were nervous, prizes were awarded for accomplishing particular tasks. The French academy of sciences, for example, established in 1781, I think, a system of prizes or contests. A committee would set a goal (in 1766 it was to solve the 6 body problem, in 1818 it was explain the properties of light) and submissions judged after a deadline and a prize, if merited, awarded. One sees that today with the X -prize and the Clay prize. The puzzle with these prizes is would the challenge they highlight not be undertaken in their absence? For example, resolving P = NP has been around well before the Clay prize and many a bright young thing had already given it serious thought.
Many prizes are `achievement’ awards, given out in recognition of a great accomplishment after the fact. Some are awarded by learned societies and named in honor of an ancient worthy (Leibniz, Lagrange, Laplace etc.) Others are funded by private individuals (Nobel, Nemmers, Simons etc.).
Some learned societies have a surfeit of prizes (Mathematics) that are concentrated in the hands of a few. Indeed, one might be able to construct a partial order of the prizes and come to the conclusion that some prize X can only be awarded provided prize Y has already been secured. Once again, there is the incentive question. It is hard to imagine the prize winner strives and continues to do so in the anticipation of winning further prizes. If the purpose of the prize is to honor the work (rather than the individual) why give the $$’s to the individual? Perhaps better to take the $$’s, divide them up and hand it to junior researchers in the same area telling them they have received it in honor of X, a pioneer of the field.
Other learned societies have very few prizes (American Economic Association). There is the Clark medal (famous), Walker medal (discontinued after Nobel), Ely Lecture and the Distinguished Fellow (who?). No doubt, this is a great comfort for the members’ status anxiety. Although I have it heard it said that a paucity of awards can adversely affect a discipline in that it lessens its members chances of securing grants. No doubt this is why some learned societies have prizes for every age group and speciality one can imagine: best under 40 in applied nobble nozing theory.
Why do private individuals fund prizes? Nobel is the archetype. Is it a way to purchase reflected glory? The founders of Facebook and Google are famous in their own right, so it is hard to see how a prize will burnish their images. Perhaps they genuinely wish to support research into topic X. One can easily imagine more effective ways to do this via grants, fellowships and conferences. Indeed, both the Kavli and Simons do just this (in addition to handing out prizes). Perhaps its advertising. If one wishes to publicize the importance of some field, does awarding a generous prize buy more publicity than a simple advertisement or cultivating journalists? Unclear. How many have heard of the recent `breakthrough’ prizes?
I had the opportunity to participate in a delightful workshop on mechanism design and the informed principal organized by Thomas Troeger and Tymofiy Mylovavnov. The setting was a charming `schloss‘ (manse rather than castle) an hour and half outside of Mannheim. They had gathered together a murderer’s row of speakers and auditors. Suffice it to say I was the infimum of the group and lucky to be there.
One (among many) remarkable talks was given by Roger Myerson on his 1983 paper entitled `Mechanism Design by an Informed Principal‘. Kudos to Thomas and Tymofiy for coming up with the idea of doing this. It brought to mind some couplets from Locksley Hall:
When the centuries behind me like a fruitful land reposed;
When I clung to all the present for the promise that it closed:
When I dipt into the future far as human eye could see;
Saw the Vision of the world and all the wonder that would be.—
By the way, the last pair of lines appears on the dedication plaque that graces the USS Voyager (of the Star Trek franchise).
What did Roger do? He tried as best as possible, given the gulf of time, to explain why he had chosen the tack that he did in the paper (axiomatic) and his hope for how it would influence research on the subject.
A principal with private information must propose a mechanism to an agent. However, the choice of mechanism will reveal something of the principal’s private information to the agent. Thus, the problem of mechanism design in this setting is not a straight optimization problem. It is, at a high level, a signaling game. The signals are the set of mechanisms that the principal can propose. Thus, one seeks an equilibrium of this game. But which equilibrium?
In section 7 of the paper, Roger approaches the question axiomatically in the spirit of Nash bargaining. Indeed, Roger made just such an analogy in his talk. Nash did not have in mind any particular bargaining protocol, but a conviction that any reasonable protocol must satisfy some natural invariance conditions. Some decades later Rubinstein arrives with a bargaining protocol to justify Nash’s conviction. So, Roger sought the same here and expressed the wish to see this year a vindication of his hopes.
Lest you think the audience accepted Roger’s axioms uncritically, Thomas Troeger, pointed out Roger’s axiom 1 ruled out some possibly natural settings like Rothschild & Stiglitz. Roger argued that it was right and proper to rule this out and battle joined!