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On day 6, went the through the standard 2 period durables good problem, carefully working out the demand curve in each period. Did this to emphasize later how this problem is just like the problem of a multi-product monopolist with substitutes. Then, onto a discussion of JC Penny. In retrospect, not the best of examples. Doubt they shop at JC Penny, or follow the business section of the paper. One student gave a good summary of events as background to rest of class. Textbooks would have been better.

Subsequently, multi-product monopolist; substitute and complement. Emphasized this meant each product could not be priced in isolation of the other. Now the puzzle. Why would a seller introduce a substitute to itself? Recalling discussion of durables good monopolist, this seems like lunacy. A bright spark suggested that the substitute product might appeal to a segment that one is not currently selling to. Yes, but wouldn’t that cannibalize sales from existing product? Time for a model! Before getting to model, formally introduced price discrimination.

Day 7, talked briefly about homework and role of mathematics in economic analysis. Recalled the question of regulating the monopolist. Lowering price benefits consumers but harms seller. Do the benefits of customers exceed harm done to seller? Blah, blah cannot settle the issue. Need a model and have to analyze it to come to a conclusion. While we represent the world (or at least a part of it) mathematically, it does not follow that every mathematical object corresponds to something in reality. Made this point by pointing them to the homework question with demand curve having a constant elasticity of 1. Profit maximizing price is infinity, which is clearly silly. Differentiating and setting to zero is not a substitute for thinking.

Went on to focus on versioning and bundling. Versioning provides natural setting to talk about cannibalization and catering to new segment. Went through a model to show how the competing forces play out. Then to bundling.

Discussion of reasons to bundle that do not involve price discrimination. Then a model and its analysis. Motivated it by asking whether they would prefer to have ala carte programming from cable providers. In the model, unbundling results in higher prices which surprises them and was a good note to end on.

On day 5, unhappy with the way I covered regulation of monopolist earlier, went over it again. To put some flesh on the bone, I asked at conclusion of the analysis if they would favor regulating the price of drug on which the seller had a patent? Some discomfort with the idea. A number suggested the need to provide incentives to invest in R&D. In response I asked why not compensate them for their R&D? Ask for the R&D costs and pay them that plus something extra if we want to cover opportunity cost. Some discussion of how one would monitor and verify these costs. At which point someone piped in that if R&D costs were difficult to monitor, why not have the Government just do the R&D? Now we really are on the road to socialized medicine. Some appeals to the efficiency of competitive markets which I put on hold with the promise that we would return to this issue later on in the semester.

Thus far class had been limited to a uniform price monopolist. Pivoted to discussing a multi-product monopolist by way of a small example of a durables good monopolist selling over two periods. Had the class act out out the role of buyers and me the seller cutting price over time.  It provided an opportunity to discuss the role of commitment and tie it back to the ultimatum game played Day 1. On day 6 will revisit this with a discussion of JC Penny, which will allow one to get to next item on the agenda: price discrimination.

Day 3 was a `midterm’ testing them on calculus prerequisites. Day 4, began with double marginalization. Analyzed the case when the upstream firm dictates wholesale price to the downstream firm. Subsequently, asked the class to consider the possibility that downstream firm dictates price to upstream firm. In this case `double marginalization’ disappears. Connected this pack to the power take it or leave it offers discussed day 1 and related this to Amazon vs Hachette. Concluded this portion with discussion of two part tariffs as alternative to merger to `solve’ double marginalization.

Double marginalization was followed by computing total consumer surplus by integrating the inverse demand function. Ended on optimal regulation of monopolist, showing that pricing at marginal cost maximizes producer plus consumer surplus. Brief discussion of incentives to be a monopolist if such regulation was in place. Then, asked the class to consider regulating a monopsonist and whether a minimum wage would be a good idea.

Day 2 was devoted to marginal this, that and the other. I began by asking if a monopolist (with constant unit costs) who suffers an increase in its unit costs should pass along the full unit cost increase to their buyers? To make it more piquant, I asked them to assume a literal monopolist, i.e., sole seller. Some said maybe, because it depends on elasticity of demand. Others said, yes, what choice do buyers have? Alert ones said no, because you must be at an inelastic portion of the demand curve (thank you, markup formula). They will indeed increase the price but the increase is tempered by the high elasticity at the current profit maximizing price. Profit will go down. This example illustrates how both the demand side and cost side interact to influence profits. In day 1 we focused on how the demand side affected price, in day 2 we focus on the cost side.

To motivate the notion of marginal cost, I ask how they would define cost per unit to convey the idea that this is an ambiguous concept. A possible candidate is average cost but ist not helpful maing decisions about whether to increase of decrease output. For this, what we want is marginal cost. Define marginal cost, and onto constant, decreasing and increasing returns to scale and discussion of technologies that would satisfy each of these. Solving quadratics is a good example. The time to solve each is the marginal cost. If you have decreasing returns to scale in solving quadratics, a wit suggested, correctly, that one should give up mathematics.

Next, where do cost functions come from? Opportunity to introduce capital and labor and production function. Cost function is minimum cost way of combining K and L to produce a target quantity. Numerical example with Cobb-Douglas. Without explicitly mentioning isoquants and level curves, solved problem graphically (draw feasible region, move objective function hyperplane) as well as algebraically. Discussed impact of price change of inputs on mix used to produce target volume. Marginal productivity of labor, capital and marginal rate of technical substitution. Eyes glazing over. Why am I wasting time with this stuff? This is reading aloud. Never again.

Onto marginal revenue. By this time they should have realized the word marginal means derivative. Thankfully, they don’t ask why a new word is needed to describe something that already has a label: derivative. Marginal revenue should get their goat. Its a derivative of revenue, but with respect to what? Price or quantity? The term gives no clue. Furthermore, marginal revenue sounds like price. The result? Some students set price equal to marginal cost to maximize profit because thats what the slogan marginal revenue = marginal cost means. To compound matters, we then say the area under the marginal revenue curve is revenue. If marginal revenue is the derivative wrt quantity then integrating it should return the revenue. Does this really deserve comment? Perhaps watching paint dry would be more exciting. Wish I had the courage to dispense with the word `marginal’ altogether. Perhaps next year. Imagine the shock of my colleagues when the phrase `marginal blank’ is greeted with puzzled looks.

They’ve been very patient. Before class ends there should be a payoff. Show that marginal revenue = marginal cost is a necessary condition for profit maximization and is sufficient when we have decreasing returns to scale. This seems like small beer. What happens when we have increasing returns to scale? Why does this break down? Some pictures, of why the slogan is no longer sufficient and a discussion of how this relates to pricing for firms with increasing returns like a producer of an app who must rent server space and gets a quantity discount.

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.

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