Paul Romer: Plenitude and Platon (IH)

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NBER Working Paper #4452 September 1993


III. The Principle of Plenitude

The convenient but very powerful assumption that we never have to face the decision about whether to invent a good like good Z in figures 3 or 4 is a special case of a general presumption or habit of thought that the philosopher Arthur Lovejoy (1933) labeled the principle of plenitude. (For a discussion of the economic implications of this principle, see Warsh, 1984.) The principle of plenitude states that the world is full: every conceivable entity already exists. As a corollary, it follows that nothing truly new can ever come into being. Every conceptual possibility already has a realization in the physical world. To an economist, it means that we can always assume that we are in the interior of goods space.

As Lovejoy shows, the principle of plenitude is fully formed in the writings of Plato and has played a central role in Western thought ever since1 appearing prominently, for example, in the writings of Spinoza and Leibniz. The set of all conceivable entities corresponds to Plato's world of ideals. For every ideal there must exist a corresponding entity in the world of experience, for otherwise the world would be incomplete and imperfect.

Much of the thrust of modem scientific inquiry has been directed at overcoming our innate prejudice in favor of predetermination and plenitude. Many educated people are contemptuous of creationists who claim that there is a supreme being that created all existing forms of life according to a master plan and who deny the possibility that different forms of life emerged by chance and will continue to do so. We also ridicule the turn of the century head of the patent office who recommended the abolition of the patent system because everything had already been invented. Yet in their everyday approach to economic problems, most economists adopt a modeling strategy that reflects an implicit belief closely related to that of the patent clerk and the creationist. The durability of the principle of plenitude can presumably be traced to a deeply rooted human desire to understand the world and therefore to believe that the world is capable of being understood. If we admit that new things can happen -- that there are many things that could exist that do not yet exist -- we undermine our most common explanation of why the world is the way it is: It has to be this way for it could not have turned out otherwise. For example, if there is only one conceivable form of intelligent animal, then we can explain why humans had to emerge from evolution in precisely the form that they did. People simply could not have turned out differently.

When it is applied in a specific scientific context such as evolution, it is now obvious that the principle of plenitude is not just false; it is wildly misleading. The fossil record shows us that there are many conceivable types of animals that once existed but no longer exist. There are an extraordinarily large number of types of forms of life that could have evolved but did not because of a variety of historical accidents. If the earth had not been hit by the meteor that killed the dinosaurs, the forms of life on earth today would be different in ways that we can hardly begin to imagine. Scientifically, a far better guiding principle would that of sparsity: only a vanishingly small fraction of all conceivable entities can actually exist in the physical world.

When we are confronted with things we do not understand, we all retreat into a world view that has more in common with the creationists than we would like to admit. Take cosmology. Implicitly, most of us believe that there is only one kind of physical universe that is conceivable. We can therefore explain (in some limited sense) why the universe is the way it is. lt could not have turned out otherwise. For example, space must have three dimensions instead of two or four because, we assert, there is no such thing as two or four dimensional real space, even in principle. As unsatisfying as this style of explanation may be, most of use find it preferable to the alternative. It is deeply unsettling to admit that humans, other animals, our planet, even the universe itself, are merely the result of a long sequence of accidents that determined which of many different conceivable outcomes were actually realized. Modern cosmology suggests our universe itself is new. At some date there was a big bang when both space and time as we know them came into existence. And as if this were not enough, some physicists are now seriously raising the possibility that it was only our particular universe that was created in what we refer to as 'the' big bang. This extension of the inflation model of big bangs suggests that our universe emerged from a small local fluctuation in the energy density in some prior universe, and that many comparable universes are continually branching off from our own and many other universes, expanding in their own big bang. Because these other universes start from slightly different initial conditions, the physical laws that they obey may be radically different from our own. We would prefer to believe that there is only one kind of universe and that any universe could not possibly have turned out differently from the one -we inhabit. But to theoretical physicists, the humorous physics exam question, 'Define universe and give two examples,' is starting to look serious. Perhaps the fact that space in our universe is three dimensional is an accidental outcome that is no more explicable than the fact that there are no mammals that lay eggs and fly.

Whatever one's reaction is to the possibility that there could be, or will be, or are many different universes, nothing could be more certain than the facts that there are many different types of economic goods, that there will be many more of them in the future, and that these will somehow be selected from an incomprehensibly larger set of goods that could conceivably be produced. To see why the set of all conceivable goods is so much larger than the set of goods that could ever be produced in our universe, one need only do a few simple combinatorial calculations. Consider for example, the set of all possible computer programs that could fit on the lowest capacity floppy disk still in use for personal computers. Such a floppy disk can store a bit string consisting of 360,000 x S positions, each of which contains either a 0 or a I. This means that there are about 23,00 or about 10ia° different conceivable computer programs (i.e. bit strings) that could fit on such a disk. This is a big number. For comparison, about l0 seconds have passed since the big bang started the universe (or the current version of our particular universe.) It is estimated that there are about BY" electrons and protons in the visible portion of our universe. Most of the possible bit strings will be totally useless as computer programs, but unless we are willing to side with the patent clerk and suggest that all the useful software has already been written, there must be a small fraction of these possible programs, perhaps just one in every l0"", that will do wonderful things. This would still leave lO interesting programs to discover. (liven the physical constraints we face it is inevitable that the vast majority of these useful programs will never be written or tested. For example if we had used every atom in the universe to code a different bit, at any time we could only code up about i0' different bit strings that are 106 bits long. If we had tested a new set of 10 new bit strings every second since the big bang, we would still not have tried only one out of every billion of all the possible bit strings. It is an inevitable fact of life that economies will forever operate on the boundary of goods space, that only a small subset of all possible goods will ever be introduced. The principle of plenitude manifests itself in the everyday operation of economic analysis in the implicit assumption that nevertheless, all the relevant goods already exist. It lets us think of economic analysis as taking place in the interior of goods space. It lets us tell our students that the essential economic problem is depicted in figure 1, not figure 3.

Economists do recognize that the set of traded goods in an economy is always changing, but according to the economic version of plenitude, this turbulence is an epiphenomenon of no fundamental interest. According to this view, you can change the labels on a box of detergent, but detergent is just detergent. According to this view, all decisions in private markets can accurately be characterized as being like changes in the allocations of the quantities of a fixed and unvarying set of underlying goods that cover all of the relevant possibilities. Perhaps the clearest statement of this point of view comes in the characteristics space description of goods articulated by Kelvin Lancaster (1966). All apparently new goods are just different bundles of a fixed underlying set of primitive goods.

Economists have not always gone this far. Joseph Schumpeter was quite explicit about the central importance of the creation of genuinely new goods (1934). Sn was Allyn Young (1928). Yet in our post-WWII enthusiasm for distilling the "miracle of the market" down to its mathematical essence, economists have generally been willing to push these issues aside. Decentralized markets could be shown to get everything right only by assuming that half of our basic economic problem (and by far more difficult half at that) had already been solved. In the Arrow-Debreu world, all the relevant or useful dated and statecontingent goods have already been selected from the large set consisting of all possible goods. The only problem that remained for the economic system to solve was to allocate existing goods between a fixed set of existing uses.

It was perhaps this step, the implicit incorporation of the principle of plenitude, rather than the unification of statics and dynamics per se, that troubled those economists who dissented from the generaJ equilibrium approach to economic theory. The refutation of the principle of plenitude seems to lie at the heart of case that has been made for path dependence and the role of history in economic analysis by Arthur (1989) and David (1985). Much of the explicit discussion by the critics of general equilibrium theory has focused on issues other than path dependence or the sparsity of the set of reaiized goods. Instead, critics have emphasized the suboptimality of market outcomes and the implausibility of the assumption of rational choice. On these issues, the mainstream economists and the critics are not very far apart. Mainstream economics is filled with arguments showing that equilibria are in many cases not first-best Pareto optimal, and mainstream equilibrium theorists increasingly emphasize the importance of informational constraints, costs of decision making, and of the importance of learning processes that converge slowly, if at all, to the outcome derived from the assumption of fully informed rational calculation. Disagreements between the critics and mainstream economists over these issues are really over no more than differences in degree.

It is a deeper difference in the presumptions that different people have about the nature of the world and the nature of the problem that an economic system must solve that separates the different groups of economists and makes communication so difficult. When economists insist on the importance of disequilibrium behavior, part of what they must be saying is that out of all conceivable goods, only a very sparse subset can actually exist in any real economy, so genuinely new goods can always be added. Any analysis that treats a dynamic economy as being formally equivalent to a static economy characterized by plenitude -. fullness in the set of goods -- can not, according to this view, capture the essential aspects of growth and change.

After being lectured about the philosophical origins underlying the selection of different areas in figure 4, the economist subjected to the Rorschach test described in the previous section could complain of having been tricked. If we had explained that the demand curve in figure 4 was for a good that did not yet exist, then he would of course have commented on the welfare significance of the triangle A. Moreover, this economist could observe with irritation, the point argued here (about newness) is "not new. • There is an old literature on marginal cost pricing and utility regulation (Hotelling, 1938) that is concerned precisely with the problem of paying the fixed cost of bringing some service into being. Similarly, economists have long understood that the problem of assigning patents or copyrights involves a fundamental conflict between conflicting efficiency conditions.

Monopoly profits induce people to incur the fixed costs of invention, but cause distortions in the allocation of goods once the invention exists. We have always known, this economist could continue, that if the market had to solve two problems — both introducing the right goods and allocating them properly — a competitive economy would never be able to get the prices right. (Section V below challenges the fall-back position that is sometimes offered suggesting that an economy characterized by monopoly power can get the prices right if price discrimination is tolerated.