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Introduced externalities. The usual examples, pollution, good manners and flatulance. However, I also emphasized an externality we had dealt with all semester: when I buy a particular Picasso it prevents you from doing so, exerting a negative externality on you. I did this to point out that the problem with externalities is not their existence, but whether they are `priced’ into the market or not. For many of the examples of goods and services that we discussed in class, the externality is priced in and we get the efficient allocation.

What happens when the externality is not `priced in’? The hoary example of two firms, one upstream from the other with the upstream firm releasing a pollutant into the river (That lowers its costs but raises the costs of the downstream firm) was introduced and we went through the possibilities: regulation, taxation, merger/ nationalization and tradeable property rights.

Discussed pros and cons of each. Property rights (i.e. Coase), consumed a larger portion of the time; how would you define them, how would one ensure a perfectly competitive market in the trade of such rights? Nudged them towards the question of whether one can construct a perfectly competitive market for any property right.

To fix ideas, asked them to consider how a competitive market for the right to emit carbon might work. Factories can, at some expense lower carbon emissions. We each of us value a reduction in carbon (but not necessarily identically). Suppose we hand out permits to factories (recall, Coase says initial allocation of property rights is irrelevant) and have people buy the permits up to reduce carbon. Assuming carbon reduction is a public good (non-excludable and non-rivalrous), we have a classic public goods problem. Strategic behavior kills the market.

Some discussion of whether reducing carbon is a public good. The air we breathe (there are oxygen tanks)? Fireworks? Education? National Defense? Wanted to highlight that nailing down an example that fit the definition perfectly was hard. There are `degrees’. Had thought that Education would generate more of a discussion given the media attention it receives, it did not.

Concluded with an in depth discussion of electricity markets as it provides a wonderful vehicle to discuss efficiency, externalities as well as entry and exit in one package. It also provides a backdoor way into a discussion of net neutrality that seemed to generate some interest. As an aside I asked them whether perfectly competitively markets paid agents what they were worth? How should one measure an agents economic worth? Nudged them towards marginal product. Gave an example where Walrasian prices did not give each agent his marginal product (where the core does not contain the Vickrey outcome). So, was Michael Jordan overpaid or underpaid?
With respect to entry and exit I showed that the zero profit condition many had seen in earlier econ classes did not produce efficient outcomes. The textbook treatment assumes all potential entrants have the same technologies. What if the entrants have different technologies? For example, solar vs coal. Do we get the efficient mix of technologies? Assuming a competitive market that sets the Walrasian price for power, I showed them examples where we do not get the efficient mix of technologies.

An unintentionally amusing missive by Marion Fourcade, Etienne Ollion and Yann Algan’s discovers that the Economics profession is a self perpetuating oligarchy. This is as shocking as the discovery of gambling in Casablanca. Economists are human and respond to incentives just as others do (see the Zingales piece that makes this point). Are other disciplines free of such oligarchies? Or is the complaint that the Economist’s oligarchy is just order of magnitudes more efficient than other disciplines?

The abstract lists three points the authors wish to make.

1) We begin by documenting the relative insularity of economics, using bibliometric data.

A former colleague of mine once classified disciplines as sources (of ideas) and sinks (absorbers of them). One could just as well as describe the bibliometric data as showing that Economics is a source of ideas while other social sciences are sinks. if one really wanted to put the boot in, perhaps the sinks should be called back holes, ones from which no good idea ever escapes.
2) Next we analyze the tight management of the field from the top down, which gives economics its characteristic hierarchical structure.

Economists can be likened to the Borg, which are described by Wikipedia as follows:

“….. the Borg force other species into their collective and connect them to “the hive mind”; the act is called assimilation and entails violence, abductions, and injections of microscopic machines called nanoprobes.”

3) Economists also distinguish themselves from other social scientists through their much better material situation (many teach in business schools, have external consulting activities), their more individualist worldviews, and in the confidence they have in their discipline’s ability to fix the world’s problems.

If the authors had known of this recent paper in Science they could have explained all this by pointing out that Economists are wheat people and other social scientists are rice people.

General equilibrium! Crown jewel of micro-economic theory. Arrow and Hahn give the best justification:

“There is by now a long and fairly imposing line of economists from Adam Smith to the present who have sought to show that a decentralized economy motivated by self-interest and guided by price signals would be compatible with a coherent disposition of economic resources that could be regarded, in a well defined sense, as superior to a large class of possible alternative dispositions. Moreover the price signals would operate in a way to establish this degree of coherence. It is important to understand how surprising this claim must be to anyone not exposed to the tradition. The immediate `common sense’ answer to the question `What will an economy motivated by individual greed and controlled by a very large number of different agents look like?’ is probably: There will be chaos. That quite a different answer has long been claimed true and has permeated the economic thinking of a large number of people who are in no way economists is itself sufficient ground for investigating it seriously. The proposition having been put forward and very seriously
entertained, it is important to know not only whether it is true, but whether it could be true.”

But how to make it come alive for my students? When first I came to this subject it was in furious debates over central planning vs. the market. Gosplan, the commanding heights, indicative planning were as familiar in our mouths as Harry the King, Bedford and Exeter, Warwick and Talbot, Salisbury and Gloucester….England, on the eve of a general election was poised to leave all this behind. The question, as posed by Arrow and Hahn, captured the essence of the matter.

Those times have passed, and I chose instead to motivate the simple exchange economy by posing the question of how a sharing economy might work. Starting with two agents endowed with a positive quantity of each of two goods, and given their utility functions, I asked for trades that would leave each of them better off. Not only did such trades exist, there were more than one. Which one to pick? What if there were many agents and many goods? Would bilateral trades suffice to find mutually beneficial trading opportunities? Tri-lateral? The point of this thought experiment was to show how in the absence of prices, mutually improving trades might be very hard to find.

Next, introduce prices, and compute demands. Observed that demands in this world could increase with prices and offered an explanation. Suggested that this put existence of market clearing prices in doubt. Somehow, in the context of example this all works out. Hand waved about intermediate value theorem before asserting existence in general.

On to the so what. Why should one prefer the outcomes obtained under a Walrasian equilibrium to other outcomes? Notion of Pareto optimality and first welfare theorem. Highlighted weakness of Pareto notion, but emphasized how little information each agent needed other than price, own preferences and endowment to determine what they would sell and consume. Amazingly, prices coordinate everyone’s actions. Yes, but how do we arrive at them? Noted and swept under the rug, why spoil a good story just yet?

Gasp! Did not cover Edgeworth boxes.

Went on to introduce production. Spent some time explaining why the factories had to be owned by the consumers. Owners must eat as well. However it also sets up an interesting circularity in that in small models, the employee of the factory is also the major consumer of its output! Its not often that a firm’s employers are also a major fraction of their consumers.

Closed with, how in Walrasian equilibrium, output is produced at minimum total cost. Snuck in the central planner, who solves the problem of finding the minimum cost production levels to meet a specified demand. Point out that we can implement the same solution using prices that come from the Lagrange multiplier of the central planners demand constraint. Ended by coming back full circle, why bother with prices, why not just let the central planner have his way?

Economists, I told my class, are the most empathetic and tolerant of people. Empathetic, as they learnt from game theory, because they strive to see the world through the eyes of others. Tolerant, because they never question anyone’s preferences. If I had the  talent I’d have broken into song with a version of `Why Can’t a Woman be More Like a Man’ :

Psychologists are irrational, that’s all there is to that!
Their heads are full of cotton, hay, and rags!
They’re nothing but exasperating, irritating,
vacillating, calculating, agitating,
Maddening and infuriating lags!

Why can’t a psychologist be more like an economist?

Back to earth with preference orderings. Avoided  the word rational to describe the restrictions placed on preference orderings, used `consistency’ instead. More neutral and conveys the idea that inconsistency makes prediction hard rather that suggesting a Wooster like IQ. Emphasized that utility functions were simply a succinct representation of consistent preferences and had no meaning beyond that.

In a bow to tradition went over the equi-marginal principle, a holdover from the days when economics students were ignorant of multivariable calculus. Won’t do that again. Should be banished from the textbooks.

Now for some meat: the income and substitution (I&S) effect. Had been warned this was tricky. `No shirt Sherlock,’ my students might say. One has to be careful about the set up.

Suppose price vector p and income I. Before I actually purchase anything, I contemplate what I might purchase to maximize my utility. Call that x.
Again, before I purchase x, the price of good 1 rises. Again, I contemplate what I might consume. Call it z. The textbook discussion of the income and substitution effect is about the difference between x and z.

As described, the agent has not purchased x or z. Why this petty foggery? Suppose I actually purchase $x$ before the price increase. If the price of good 1 goes up, I can resell it. This is both a change in price and income, something not covered by the I&S effect.

The issue is resale of good 1. Thus, an example of an I&S effect using housing should distinguish between owning vs. renting. To be safe one might want to stick to consumables. To observe the income effect, we would need a consumable that sucks up a `largish’ fraction of income. A possibility is low income consumer who spends a large fraction on food.

Bertrand, Cournot and Hotelling was on the menu. In addition to covering the mechanics of computing equilibria, spent time trying to motivate each model. Cournot is, I think, the hardest. The short version of the story I gave was this. Firms choose their capacities/quantities, then go to a middleman (should have said platform, so much sexier these days) who auctions of their joint output via a uniform price auction. Wholesale electricity markets come close to this story, which allows one to use Cournot to convey the idea of supply (demand) reduction and the scandal of the California power markets.

Hotelling is easier to motivate, and is a useful vehicle to illustrate why they should always `break’ a model to learn something about it. In the standard Hotelling setup, no reservation price is specified for the buyers. Now, allow the two firms to merge and act like a monopolist. The monopolist’s profit function is unbounded! However, you can still write down a first order condition and solve it. Thus, it is also a useful reminder of the dangers of blindly differentiating and setting to zero.

Contrasted Cournot with Hotelling, for example, the effect on consumer surplus when a merger results in a cost reduction for the merged firm. Also provided an opportunity to remind the class about monopoly and evaluating consumer surplus.

Concluded the module on imperfect competition by applying what  had been discussed to Amazon vs. Apple vs the publishers. Another opportunity to walk down memory lane with double marginalization and then add a wrinkle involving competition in the downstream market.

Uber posts a price {p} per ride and keeps a commission {\alpha} on the price. Suppose Uber is the only ride matching service in town. If {D(p)} is the demand function for rides at per ride price {p} and {S(w)} is the supply curve for drivers at wage {w} per ride, Uber must choose {\alpha} and {p} to solve the following:

\displaystyle \max_{\alpha, p} \alpha p D(p)

subject to

\displaystyle D(p) \leq S((1-\alpha)p)

The last constraint comes from the assumption that Uber is committed to ensuring that every rider seeking a ride at the posted price gets one.

Suppose, Uber did not link the payment to driver to the price charged to rider in this particular way. Then, Uber would solve

\displaystyle \max_{p,w} pD(p) - wS(w)

subject to

\displaystyle D(p) \leq S(w)

The first optimization problem is clearly more restrictive than the second. Hence, the claim that Uber is not profit maximizing. Which raises the obvious puzzle, why is Uber using a revenue sharing scheme?

Sydney Afriat arrived in Purdue in the late 60’s with a Bentley in tow. Mort Kamien described him as having walked out of the pages of an Ian Flemming novel. Why he brought the Bentley was a puzzle, as there were no qualified mechanics as far as the eye could see. In Indiana, that is a long way. Afriat would take his Bentley on long drives only to be interrupted by mechanical difficulties that necessitated the Bentley being towed to wait for parts or specialized help.

I came upon Afriat when I learnt about the problem of rationalizability.  One has a model of choice and a collection of observations about what an agent selected. Can one rationalize the observed choices by the given model of choice? In Afriat’s seminal paper on the subject, the observations consisted of price-quantity pairs for a vector of goods and a budget. The goal was to determine if the observed choices were consistent with an agent maximizing a concave utility function subject to the budget constraint. Afriat’s paper has prompted many other papers asking the same question for different models of choice. There is an aspect of these papers, including Afriat’s, that I find puzzling.

To illustrate, consider rationalizing expected utility (Eran Shmaya suggested that `expected consumption’ might be more accurate). Let {S = \{1,2 \ldots, n\}} be the set of possible states. We are given a sequence of observations {\{x^{i},p^{i}\}_{i=1}^{m}} and a single budget {b}. Here {x^i_j} represents consumption in state {j} and {p^i_j} is the unit price of consumption in state {j} in observation {i}. We want to know if there is a probability distribution over states, {v=(v_{1},...,v_{n})}, such that each {(x^i, p^i)} maximizes expected utility. In other words, {(x^i, p^i)} solves

\displaystyle \max \sum_{j=1}^{n}v_{j}x^i_{j}

subject to

\displaystyle \sum_{j=1}^{n}p^i_{j}x_{j}\leq b

\displaystyle x^i_{j}\geq 0\,\,\forall j \in S

The solution to the above program is obvious. Identify the variable with the largest objective coefficient to constraint ratio and make it as large as possible. It is immediate that a collection of observations {\{x^{i},p^{i}\}_{i=1}^{m}} can be rationalized by a suitable set {\{v_{j}\} _{j=1}^{n}} of non-zero and nonnegative {v_{j}}‘s if the following system has a feasible solution:

\displaystyle \frac{v_{r}}{p^i_r}\geq \frac{v_{j}}{p^i_{j}} \,\,\forall j, \,\, x^i_r> 0

\displaystyle \sum_{j \in S}v_{j}=1

\displaystyle v_{j}\geq 0\,\,\forall j \in S

This completes the task as formulated by Afriat. A system of inequalities has been identified, that if feasible means the given observations can be rationalized. How hard is this to do in other cases? As long as the model of choice involves optimization and the optimization problem is well behaved in that first order conditions, say, suffice to characterize optimality, its a homework exercise. One can do this all day, thanks to Afriat; concave, additively separable concave, etc. etc.

Interestingly, no rationalizability paper stops at the point of identifying the inequalities. Even Afriat’s paper goes a step farther and proceeds to `characterize’ when the observations can be rationalized. But, feasibility of the inequalities themselves is just such a characterization. What more is needed?

Perhaps, the characterization involving inequalities lacks `interpretation’. Or, if the given system for a set of observations was infeasible, we may be interested in the obstacle to feasibility. Afriat’s paper gave a characterization in terms of the strong axiom of revealed preference, i.e., an absence of cycles of certain kinds. But that is precisely the Farkas alternative to the system of inequalities identified in Afriat. The absence of cycles condition follows from the fact that the initial set of inequalities is associated with the problem of finding a shortest path (see the chapter on rationalizability in my mechanism design book). Let me illustrate with the example above. It is equivalent to finding a non-negative and non trivial solution to

\displaystyle \frac{v_{r}}{v_j}\geq \frac{p^i_{r}}{p^i_{j}} \,\,\forall j, \,\, x^i_r> 0

Take logs:

\displaystyle \ln{v_r} - \ln{v_j} \geq \ln{\frac{p^i_{r}}{p^i_{j}}} \,\,\forall j, \,\, x^i_r> 0

This is exactly the dual to the problem of finding a shortest path in a suitable network (I believe that Afriat has a paper, that I’ve not found, which focuses on systems of the form b_{rs} > x_s - x_r ).The cycle characterization would involve products of terms like {\frac{p^i_{r}}{p^i_{j}}} being less than 1 (or greater than 1 depending on convention). So, what would this add?

Completed what I wanted about monopoly and launched into imperfect competition and introduced the nash equilibrium. I follow the set up in the chapter of pricing from my pricing book with Lakshman Krishnamurthi. The novelty, if any, is to start with Bertrand competition, add capacity and then differentiation. I do this to highlight the different forces at play so that they are not obscured by the algebra of identifying reaction functions and finding where they cross. We’ll get to those later on. Midterm Day, 12. I am, as Enoch Powell once remarked in another, unattractive context,

…. filled with foreboding. Like the Roman, I seem to see “the River Tiber foaming with much blood”.

Much of my energy has been taken up with designing homework problems and a midterm exam on monopoly. Interesting questions are hard to come by. Those lying around make me want to make gnaw my feet off. I started with the assumption, which I may live to regret, that my students are capable of the mechanical and have good memories. The goal, instead, is to get them to put what they have learnt in class to use. Here is an example. Two upstream suppliers, A and B, who each supply an input to a Retailer. The Retailer is characterized by a production function that tells you how much output it generates from the inputs supplied by A and B as well as a demand curve for the final product. Fix the price set by B to, w, say. Now compute the price that A should charge to maximize profit. Its double marginalization with a twist. Suppose the inputs are substitutes for each other. If B raises its price above w what effect will that have on A’s profits? There are two effects. The retailers costs will go up of course, so reducing its output. However, A will retain a larger share of the smaller output. Which will be bigger? Its a question that requires them to put various pieces together. I’ve had them work up to it by solving the various pieces under different guises in different problems. Am I expecting too much? I’ll find out after the midterm. Yet, I cannot see anyway around having questions like this. What is the point of the mathematics we require them to use and know if we don’t ask them to apply it when blah-blah alone is insufficient?

I now have a modest store of such problems, but coming up with them has been devilish hard. Working out the solutions is painful, because it involves actual algebra and one cannot afford errors (on that account I’m behind the curve). To compound matters, one is unable to recycle the exam and homework problems given various sharing sites. I begin to regret not making them do just algebra.

Its all the rage. I’m not immune to jumping on a bandwagon, but by the time I get there the dogs have barked and the caravan has moved on. Is there anything new to be said on the subject? Perhaps we can get by with relabeling things we already know? Useful, but not exciting. To think about this I tried to come with questions about privacy that struck me as important. Here is my list, in hopes that it will prompt others to improve upon it.
1) Is the concern for privacy intrinsic or instrumental?

The question matters because an answer would have a profound impact on how one evaluates the welfare consequences of various policies.

2) Property rights over information.

Much of the information about us that is of interest is the result of interactions with others. When I purchase a book from Amazon, who `owns’ the record of that transaction? It could be argued that the record of the transaction is as much Amazon’s as it is mine. The question is not new. It arises, for example, when one writes a biography.

What about when a transaction takes place via an intermediary? What rights does the intermediary have to the record of the transaction?

3) A full specification of property rights would spell out who has the right to disclose what and to whom and under what conditions.

Some of this will involve a balance between the public good and individual harm. Out of court settlements regarding commercial matters whose terms are secret, prevent learning about systemic problems (Akerlof and his lemons, seems like a likely candidate for relabeling).

When is and under what conditions is mandated disclosure warranted? One can also imagine settings where one might wish to prohibit the voluntary disclosure of confidential information. Some professional schools, for example prohibit the disclosure of grades to potential employers (Grossman and Milgrom, anyone?).

4) Compliance. How might one monitor and verify that the specification of property rights have been adhered to?

For example, a promise not to disclose to a third party. In a given setting, are some kinds of promises even feasible? One may promise not to use certain identifying characteristics in the allocation of resources but those characteristics may have good proxies in other `allowed’ characteristics.

Who should bear the costs of such monitoring? (Coase?)As much information of interest is collected by devices, one might think about the `regulation’ of devices as a part of compliance. What standards, if any should devices that collect and transmit information adhere to? Is managing privacy best done through device standards or contracts?

I spent these two classes going over two-part tariffs. Were this just the algebra, it would be overkill. The novelty, if any, was to tie the whole business to how one should price  in a razor & blade business (engines and spare parts, kindle and ebooks etc). The basic 2-part model sets a high fixed fee (which one can associate with the durable) and sells each unit of the consumable at marginal cost. The analysis offers an opportunity to remind them of the problem of regulating the monopolist charging a uniform price.

The conclusion of the basic 2-part model  suggests charging a high price for razors and a low price for blades. This seems to run counter to the prevailing wisdom. Its an opportunity to solicit reasons for why the conclusion of the model might be wrong headed. We ran through a litany of possibilities: heterogenous preferences (opportunity to do a heavy vs light user calculation), hold up (one student observed that we can trust Amazon to keep the price of ebooks low otherwise we would switch to pirated versions!), liquidity constraints, competition. Tied this to Gillete’s history expounded in a paper by Randall Pick (see an earlier post ) and then onto Amazon’s pricing of the kindle and ebooks (see this post). This allowed for a discussion of the wholesale model vs agency model of pricing which the students had been asked to work out in the homework’s (nice application of basic monopoly pricing exercises!).

The `take-away’ I tried to emphasize was how models help us formulate questions (rather than simply provide prescriptions), which in turn gives us greater insight into what might be going on.


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