Open letter from economic students
About game theory
Who are we?
The Fitoussi Report
Microeconomics holds a privileged place in economic studies. It is the only subject (with mathematics) to be composed of several courses, which spread over the entire degree. Moreover, recent research on "microeconomic foundations" expand its presence to fields such as macroeconomics or international economics. Furthermore, its weight, in the economics’ degree, is increased by the theory’s abundant use of mathematics. Indeed, some learning difficulties, specifically linked to microeconomics, are reinforced by having to cope with rather complex mathematical techniques. Do the "results" or "tools" , that the theory pretends to provide, justify the scope and weight of microeconomics in economic studies ? This text shows how and why the so-called microeconomic "tools" or "results" are limited, pointless, and irrelevant. In order to do so, we will go through the main themes of the microeconomic theory, and present them as the theory does (consumer, producer, equilibrium, perfect and imperfect competition, "market failures".) This overview will enable us to show that microeconomics is essentially a pure "game of the mind": it is grounded on unjustified and unjustifiable postulates and stress mathematical exploits to the detriment of an economist’s concerns. These are the reasons why we suggest to suppress microeconomics -as an independent course- and instead, to teach microeconomic "concepts" in the framework of a (large) course on economic theories (with no, or little, mathematics).
The starting point of the theory is hypothetical individuals characterised by preference relations - or a utility function. These characteristics are purely fictional : they do not come from any given observations. The theoretician merely gives them a certain number of properties (transitivity, monotony, continuity, convexity) which he will use in his mathematical processing, and which he more or less tries to justify with economic arguments. The issue at stake, here, is that these preference relations - of members of societies which microeconomics pretends? to study and explain - are, and will remain, unknown (apart from the fact that there is no reason why these preference relations should conform to the mathematical properties the theoretician has postulated) .
The consumer theory will thus focus on characterising "choices" of fictional individuals, who are placed in an even more fictional environment (see point III on equilibrium). The game thus consists in making assumptions on these preference relations and in deducing characteristics on the consumers’ choices. Because assumptions are essentially mathematical, these deductions will be in the form of mathematical propositions. More precisely, the problem consists in characterising the extrema of a function, whose variables are under constraint (budgetary constraint).
In micro1, generally teaching is limited to studying first order conditions, by introducing notions such as the lagrangian. In courses "micro 2" or "micro 3", second order conditions (with quadratic forms, bordered hessians, determinants of principal mineurs) and corner solutions (with Kuhn and Tucker conditions) are added. This will both keep the students busy and make them suffer, although this is utterly useless and even has negative effects (students get used to mechanically -and dumbly- manipulate rather complex mathematical techniques which they do not master).
A sterile game
And then what? Since preference relations are only characterised by mathematical properties, nothing can lead microeconomists to give the consumer’s choices (his demands) a precise form. What can be done, then? Generally, microeconomic textbooks suggest "applications". These consist in endowing the consumer with a utility function : which isn’t chosen on the basis of observations, but because it conforms to certain mathematical properties (monotony, convexity, etc.), and because it enables a relatively simple resolution of the mathematical problem (i.e. explicit the consumer’s demand functions). All this leads to multiple and diverse "exercises", or eventually to pseudo-concrete applications (once obtained, the demand function may be confronted to real data, and then give way to a game on the parameters of the assumed utility function). This is what is done in the Picard (a french microeconomic textbook): the same ’Cobb-Douglas’ utility function is assigned to the entire panel of households. These so-called applications are obviously pointless. The considered consumer remains totally fictional (and this characteristic is increased by his new outfit: the totally arbitrary utility function). After having gone through the detour of "applications", supposed to give the theory a down-to-earth aspect, microeconomic treaties go back to the "general" approach (i.e., not giving a precise form to utility functions, while making a certain amount of assumptions on them). The purpose is to deduce "results" - which can only be of a qualitative kind - such as a decreasing demand function. May we hopefully think that this latter property is easily established? No way! To prove it - or to try to prove it- substitution and income effects are introduced, and therefore a new concept: the compensated demand function, with fairly heavy mathematical developments. This is, here again, utterly useless and devoid of interest. Indeed, this function is grounded on an unknown indifference curve. With further efforts, it is possible to show that the Slutsky matrix is definite negative. This might give students some kind of pleasure, but is of no use whatsoever. Frequently, this approach, based on the compensated demand function, is put forward in issues concerning compound indexes (among others, the cost of living index). Nevertheless, ignoring everything of microeconomics does not prevent anyone from discussing these issues, on the contrary. Elementary reasoning is enough.
Indeed, even if we accept microeconomics’ usual assumptions, an imperative observation has to be made: it is impossible to deduce any result from them (not even the decreasing demand function). The model is thus totally sterile, even in the framework of its own postulates: it doesn’t give the slightest prediction - and cannot do so. However, microeconomic treaties carefully avoid to say so: instead, they side-step the problem by providing more equations and by suggesting "pseudo-applications". These concern, in the same perspective, inter-temporal choice (between labor and leisure) with risk. Courses micro 2 or 3 then make these issues even more irrelevant.
Conclusion on the consumer theory:
In a course on economic theories, the neo-classical consumer theory can be presented in less than an hour-and-a-half, without mathematics. This can be done easily. First, the professor explains what exactly a preference relation is - as well as the associated utility function. Second, by using elementary reasoning (which can be in purely literal terms), he shows that the consumer’s standard behaviour consists in making choices so that they even out his subjective exchange rate with the corresponding price ratio.
The microeconomic producer theory has the same congenital defect as the consumer theory: the producer (or the "firm") is represented by a production function, which does not correspond to anything precise ( a "black box", as neo-classical economists sometimes say). Its only raison d’être is to enable boundless mathematical developments. This requires, as in the consumer theory, certain assumptions on these functions’ "shape". However, in this case, some assumptions are particularly hard to prove. Indeed, output does not have the same malleability as a consumer’s psychology, on which one can say almost anything. This is particularly stunning if we examine “factor substitutability” (needed to use a “marginal” approach). First, lets recall that input factors are substitutable when it is possible, while maintaining identical the level of output, to replace a given quantity of some input by an additional quantity of another input. The "given quantity" can be as small as we like, and the word "replace" reminds us that substitution is both immediate and costless.
The myth of input substitutability
If we can imagine a consumer’s "psychology" in a way that he can substitute pears to apples while remaining on the same indifference curve, this is impossible in the case of production. Whichever situation is considered, inputs are almost always complementary (one man, one shovel, or one tractor, an assembly line, n men etc). One just has to consult microeconomic textbooks to be aware of this basic fact . Indeed, NO textbook succeeds in giving a concrete example of an output function with substitutable inputs (smooth isoquantes). Advanced textbooks remain focused on the mathematical aspect. They calculate marginal productivities, marginal rates of substitution etc. and back up their theory with a plethora of graphs (Varian, Kreps, Mas-Colell and al. Gabszewicz, Malinvaud etc.). Because these books are intended for graduate students, their authors do not feel obliged to justify themselves. However, textbooks designed for novices somehow feel the need to prove that microeconomics is not merely a branch of mathematics. Some of these, such as Microeconomics of Beggs, Dornbusch and Fischer (three high rank economists) dodge the question by examining the output of imaginary “blips” resulting (without any further explanation) from a combination of "capital" and labor. This might be funny, but is mostly significant. Most authors, truly, attempt to look "concrete" or "real", but they actually make fools of themselves. In this perspective, we will browse through a series recurrent examples of substitutable inputs given in microeconomic textbooks. Schotter (Microeconomics, Harvester) takes the example of jam production, with "tanks" and labor. The same jam output could thus be obtained, at any moment, by reducing the size of tanks and increasing the quantity of labor! Kirman and Lapied (Microéconomie, PUF), along with Picard, take the example of the diameter of a gas pipeline and the pumping power, which make gas circulate! Because inputs are said to be substitutable, one should be able to -instantly- reduce the diameter of the pipeline and increase the power of the turbines, so that the same amount of gas circulates. Students just have to imagine a pipeline, in the Russian steppe, which widens or shrinks according to the Nasdaq fluctuations! (By the way, this example is characteristic of what is called clay-putty in macroeconomics: once an installation is in place, it cannot be altered). Parkin, Fluet and Bade (Microéconomics, ERPI) talk about the purely fictional firm "Golden stitch" which produces "jumpers" by using labor and "machines" (knitting machines, we assume). They give the following example of substitutability between machines and labor
One can efficiently produce 15 jumpers with :
a. 4 machines and 1 worker
b. 2 machines and 2 workers
c. 1 machine and 4 workers
The reader merely has to understand how the same output can be obtained either with one worker who bustles on 4 machines, or with 4 workers who cluster around one machine (in all of these cases, the same machine is presumed to be used in an efficient manner, all the same concerning the workers.).
Hirshleifer and Glazer (Microeconomics, Prentice Hall, 1992) are also concerned with textile. The example evoked in the midst of equations, is one concerning output of shirts with labor and cloth. Readers have to imagine how the same number of shirts can be produced either with little cloth and a lot of labor, or with a lot of cloth and little labor. Browning and Zupan (Microeconomics and applications, Harper and Collins) go even further : They talk about output of cars, either in a garage with a lot of labor, or in a factory with automatized machines and little labor.. Both inputs (labor , machines) are supposed to be substitutable "on the margin" and instantly. Thanks to microeconomics, students’ imagination is really put to contribution.
Another frequently used example is one concerning land and labor. This example is taken by Ferguson and Gould (Microeconomic theory, Homewood), but also by Samuelson and Nordhaus (Economics 16th edition) who create numeral examples out of nothing. In order to yield the same output, is the alternative between digging deeper in a restricted land area, or digging less deep in a broader land area? Who knows? Lets just ask a neighbouring farmer! In Baumol, Blinder and Scarth, just the same, a farmer can yield 2600 bushels of corn with either one unit of labor per month and 6 tons of fertilizers , or 2 units of labor and 4 tons of fertilizer, or 5 units and no fertilizers’. AGAIN, THAT’S NONSENSE.
Why do microeconomists obstinate themselves with this kind of examples, even if they have to make fools of themselves? One answer comes to our minds: it is linked to the idea according to which "flexible prices" enable "smooth adjustments", and lead to full employment of resources (by input substitutability ). This idea is one which is essentially put forward in macroeconomics, where inputs are reduced to "capital" and "labor". But, in most microeconomic textbooks, machines are -surreptitiously and symptomatically- called "capital" (particularly in graphs). Because capital is a vague notion (de facto identified with an amount of money), the idea of substitutability is more easily accepted than if one speaks of replacing bits of machines by hours of labor.
Apparently for "pedagogical" reasons, a distinction between short term and long term is frequently introduced. First, students have to consider one input, usually labor, and show that its marginal productivity decreases. Then, a second input is introduced (machines or "capital"): its presence modifies the productivity of the first input. Thus, this leads to note that the same level of output can be obtained with different "input combinations". The dirty trick consists in confusing possible inter-temporal substitution (which takes time, and which is, in no way, marginal as to "micro" units) with instantaneous substitution. All this is done so that students believe that substitution (between labor and machines), at a given moment, is immediate. Obviously these ’mechanisms’ or argumentations have nothing in common. Nonetheless, the idea which is behind and which absolutely has to break through (even in a subliminal manner) is that if an economy is "flexible" enough, then -eventually after some brief adjustments- full employment will be reached.
Last, but not least, Mc Closkey in his The applied theory of prices (Macmillan, 1985) gives … cat skinning as an example of the fact that “Substituability is common in production as is consumption” ! He says : “You can skin the cat in a machine intensive way by dropping it into an automatic cat-skinning machine and pressing the button. Or you can skin it in a labor intensive (and machine light) way by giving it to a team of bloodthirsty folks” (p 160). We don’t know if it’s really funny, but it’s sure that’s a way to escape the problem (indee, you cannot substitute half of an “automatic cat-skinning machine” with some folks, even it they are ‘bloodthirsty” …
Conclusion on the producer theory:
Discourses on smooth production functions, with substitutable factors, have no raison d’être : their place is in a course on the history of economic theories, which would try to find the origin, clearly ideological (since J.B. Clark) of all this nonsense. Truly in microeconomic courses, the approach in terms of output functions is generally completed by the "cost function" approach (which enables to introduce fixed costs and therefore U-curves). But this approach is very different ( "marshallian" rather than "walrasian", thus without micro foundations): the cost curves integrate prices. It is also true that these curves come from nowhere, but so do the output functions! We might as well stick to the cost function , which is much easier (only one variable). These can be used -for an illustrative purpose- in normative discourses (especially public economics- regulation of monopolies or of oligopolies, collective goods, public goods, etc.). Given their simplicity and their special characteristics, they can be presented directly in this type of course. Here again, there is no need of a specific course in microeconomics.
After studying separately fictional consumers and firms, microeconomists gather them under the leadership of somebody - or an institution- often called “ walrasian auctioneer ” who is, if this can be, even more fictional, who :
-offers prices for the economy’s entire life-time ;
-centralises and adds up the supplies and demands, made by consumers and firms on the basis of these prices (which they wrongly think to be insensitive to their respective choices) ;
-determines, with a “ groping ”
- process, a set of prices which equalises these supplies and demands
-organises trade, according to these equilibrium prices.
Unfortunately, microeconomic textbooks do not present matters this simply. On the contrary, they mislead the students on this so-called "perfect competition" model: they allude to "markets", on which "numerous" agents would be in competition with each other in a "transparent" environment, with “ perfect information ”, “ free entry ” etc. This is obviously vague, falsely intuitive, and gives students a flawed image of the model’s nature. Indeed, the prerequisites for "perfect competition" are those stated above. These assumptions are those found in formalised models, those that microeconomists use to “prove” their results. Why are these queer and nonsensical assumptions made? Because they considerably facilitate mathematical processing, and also - mostly - because the corresponding equilibrium allocation is (apart from some subtle considerations) an optimum. The normative aspect of the model now appears clearly. Nonetheless, it cannot be a basis for the usual discourses given by microeconomists (this model is not a description of a "perfect market", unless the latter is defined as a system organised by a rather authoritarian, but benevolent, auctioneer - which no-one does)
Conclusion on perfect competition:
The perfect competition model is the very prototype of what has to be taught in a course on the history of economic theories: explain the model’s genesis (from Walras to Arrow-Debreu), its transformations, its main assumptions (including "auctioneer" and complete system of markets - which are almost always left out), and its eventual "results" (which narrow down, in fact, to the existence of at least one equilibrium).
This could fascinate students, and can be dealt with in less than three hours (including the Edgewoth diagram). One more hour could be devoted to presenting Pareto-optimality, and the two theorems of "welfare economics" (one hour and a half if the professor proves the first, which is quite easy, and provides its illustration in the Edgeworth diagram). Lets trust mathematicians for demonstrations, which aren’t even taught in current courses. Indeed, they are generally restricted to "exercises" or "applications" (most of the time robinsonian). A historical and literal account of the model, emphasizing its characteristics and its stakes, would be much more instructive than loads of calculations (that induce students to mechanically apply formulas they do not understand).
The (rare) microeconomists who accept discussions and debates say things such as "Okay, the perfect competition model is untenable. Some of its assumptions, such as the "auctioneer" or the "price-taker agents" make the model totally irrelevant. However, microeconomic theory is making huge progresses. It explores new fruitful paths, and results are progressively accumulating" (this leads to "new microeconomic theories" : "labor economics", "network economics" etc.).
This might be true, but our answer is the following: "We’re on! Lets start by suppressing all perfect competition microeconomics - which will be left to a course on the history of economic theories (as it is done in physics with the ptolemian model or in biology with vitalist theories). Lets start by directly studying "modern microeconomics", which is supposed to help students understand economic issues. Lets avoid constant reference -as it is frequently done nowadays, in a way or another- to perfect competition (you’ve just admitted it was irrelevant!). _ Consequence: in the actual curricula of economic degrees, at least two courses out of three can be suppressed (75% of current courses focus -directly or indirectly- on perfect competition. This is true even if we don’t consider "representative agent" macroeconomics- which are is also pervaded with perfect competition).
But what are these so-called recent "progresses"? They obviously do not concern oligopolies (as old as Cournot or as Bertrand’s critique). If one considers Jean Tirole’s reference book : ORGANIZATION THEORY (THE MIT PRESS 1988) one cannot find even one concrete example, which describes a precise situation, or which even merely alludes to it. Furthermore, we can state that Tirol never resorts to utility functions or to production functions - they aren’t even in the index! Linear supply and demand curves suffice for the "demonstrations" (this book is a catalogue of particular cases, fruits of the author’s -and his predecessors’- imagination). Otherwise, and in a more general perspective, it is an acknowledged fact that microeconomists can make "imperfect competition” models say almost anything: the only requirement is to carefully pick the agents’ beliefs ( one of the malleable parameters of the theory). Besides, since oligopoly equilibrium models cannot hold for a standard (generally, they are not pareto-optimal), there is no reason to give them so much concern (except for the pure pleasure of manipulating mathematical symbols). Finally, these models, most of the time, assume a framework very close to the one of perfect competition -centralisation is as important and strong, and all agents (other than oligopolists) are "price-takers". Thus, models of this type (Cournot, Bertrand, Stackelberg) can be easily presented, in a purely literal way in a course on the history of economic theories (one hour and a half is plenty).
In "labor economics", we are now left with few concepts, dealing with "imperfections": "market segmentation" and "efficiency wage ". These concepts are indeed imported from elsewhere; moreover, they come from real observations. "Economists" always do their best to "prove” that they result from a rational choice. This is, by the way, always feasible: one just has to chose the appropriate functions (utility, production) and assume, in a way or another, the existence of these imperfections (market “ segments ”, “ insiders and outsiders ”, production dependent of “effort”)! The main objective is to provide students and readers with a minimum of calculus. These will enable the microeconomists to differentiate themselves from sociologists or historians (which will impress them in front of the authority of "science"). We can also observe that this type of problem is -queerly- dealt with in ... macroeconomics. Why? Who knows...
What is still to be examined? The incentive theory, which is closely linked to what microeconomists call "market failures": it concerns public economics (among others, environmental issues), health economics, labor economics, industrial economics (regulation). What are the "new" concepts? Information asymmetry, moral hazard, free riding (which, in fact, comes from times immemorial - that is, in the realms of insurance at least!). They can be explained, as well as observed, very easily. Economists then try to find "appropriate" incentives to face up to the posed problems. Clearly, this process is normative. If we go back to our main concern, the question is: is formalisation REALLY helpful? Does it make a positive contribution (other than what can result from elementary reasoning- ie. free of mathematical concepts) in our comprehension of these issues? If it does, great ! : students will surely be glad to learn all this (for example in a course on public economics) ! But if formalisation is only taught for the same reasons and in the same manner as it is today (ie. above: assuming "agents" endowed with expected utility functions and beliefs which come from nowhere, and which lead to numerous and pointless "exercises"), then we answer: NO THANKS. People who find this funny and amusing can keep on inventing formalised models, but they should not overwhelm others. Lets stick to the common language, with no formalisation; make us think on problems, on solutions that have been concretely suggested -with their pros and cons, and lets eventually try to discover some others, better ones.
Because microeconomic courses are focused on long litanies of “ proofs ” and "exercises" concerning fictional individuals who "interact" (in an even more fictional environment) -by means of an “ auctioneer ” or something of this kind , we suggest that these courses should be suppressed. However, we accept the fact that beyond these models (equations and calculations) lies a representation of men and society which students should learn: it’s up to courses on the history of economic theories to teach it. These courses should "get to the point", and avoid useless resort to mathematical symbols which mislead and confuse students and readers. If formalisation can be helpful in some areas- such as incentive theories- then PROVE IT! We are ready to accept every proposition or example: we will examine each case concretely. We beg for mercy!!! Don’t give us the usual argument: "this is too complicated. You will understand this later. First, you need to take your dose of equations". Avoid resorting to "applications", to phoney examples, or to specific cases of models which are a pure "game of the mind".
There is, however, one strange thing about all this: microeconomists, these ministers of rationality, have not yet succeeded in giving, or selling, this kind of alluring product -in which mathematics indeed make a positive contribution to our understanding, thus side-stepping our protest. Are microeconomists bad merchants? What is the point of their theory if they are unable to use it?