%Paper: ewp-get/9904004 %From: eb01@business.swt.edu %Date: Tue, 20 Apr 1999 17:18:48 -0500 (CDT) \\ Title: The Heisenberg Principle in Economics Author: Eric Blankmeyer (Southwest Texas State University) Contact: eb01@business.swt.edu Comments: 6 pages, ascii text JEL: A, B EPWA-References: none Report-no: SWTSU-EB 99-001 \\ Abstract: In the twentieth century, economics (like physics) has abandoned determinism in favor of models that emphasize the intrinsic randomess of the subject matter. The failure of determinism is summarized in the uncertainty principle of Werner Heisenberg. This paper proposes economic analogies to the Heisenberg indeterminacy. Examples are drawn from several familiar, often-studied topics: price stabilization, efficient response to change, the law of demand, comparative advantage, economies of scale, and rational expectations. They demonstrate that economic theory is in essential agreement with physical science about the intrinsic limitations of measurement and control. \\ The Heisenberg Principle in Economics Eric Blankmeyer Department of Finance and Economics Southwest Texas State University San Marcos, TX 78666 512-245-3253 eb01@business.swt.edu Copyright (c) 1999 by Eric Blankmeyer The Heisenberg Principle in Economics 1. Introduction During the first three decades of this century, physicists abandoned classical determinism in favor of a probabilistic approach to the natural world. They concluded that an object's trajectory is necessarily imprecise; that matter is alternately concentrated and diffuse; and that the most meticulous experiment inevitably distorts the phenomenon being studied. The failure of determinism is summarized in the uncertainty principle of Werner Heisenberg. He demonstrated that certain pairs of variables cannot be measured or controlled with arbitrarily high accuracy. The most important physical example involves the position and the momentum of a subatomic particle such as an electron (Rae 1992, 11-13). The more precisely one determines the particle's position, the less precisely can one determine its momentum. A forecast of the particle's trajectory is therefore subject to an unavoidable inaccuracy. The uncertainty principle is part of the epistemology of science. There is no reason to suppose that economic theory is exempt from these general constraints on objective knowledge. This paper proposes economic analogies to the Heisenberg indeterminacy. Examples are drawn from several familiar, often-studied topics: price stabilization, efficient response to change, the law of demand, comparative advantage, economies of scale, and rational expectations. They demonstrate that economic theory is in essential agreement with physical science about the intrinsic limitations of measurement and control. 2. Price stabilization The Heisenberg principle asserts that certain pairs of variables do not "commute": they cannot be brought into precise focus simultaneously. Economic analysis provides several instances where stabilizing one variable destabilizes another. Massell (1970) examines the impact of a buffer stock on the market for an agricultural commodity. In his model, the market supply curve shifts randomly because of unpredictable weather conditions. The buffer stock's intervention in effect rotates the linear demand curve around the average equilibrium point. The price variance diminishes as the demand curve becomes flatter. At an extreme, demand would be perfectly elastic, and producers would confront a stable price; but this may be too much of a good thing. After all, producer income is stable when demand is unit elastic, not perfectly elastic. In summary, the buffer stock can reduce both the price variance and the income variance up to a point --the point at which the linear demand curve is tangent to a hypothetical unit elastic demand curve. Further intervention reduces the price variance but increases the income variance. This trade-off is entirely analogous to Heisenberg's indeterminacy of position and momentum. In macroeconomics, the monetary authorities confront a similar dilemma --the impossibility of stabilizing the money supply and the interest rate at the same time. 3. Efficient response to change As another instance of the Heisenberg trade-off, suppose that a firm makes a product whose average cost is constant over a wide range of output. If, in addition, the demand for the product is rather elastic, the profit function must be nearly flat. The firm's managers are therefore not very certain what rate of output is most profitable. However, this vagueness does not have serious consequences. If production is twenty percent above the optimum amount, for example, or twenty percent too low, the profit shortfall is probably negligible since the profit function has little curvature. Now imagine that the managers are able to reduce the demand elasticity by pursuing product differentiation through advertising campaigns, attractive packaging, and so on. The curvature of the profit function increases, and its peak is more definite. On the one hand, management is more certain about how much to produce. On the other hand, the consequences of overproduction and underproduction have become more serious. A twenty percent error now leads to an appreciable loss of profit. It often happens that, when we cannot be precise about a "control variable," precision is unimportant. But when we can be more accurate, we have to be more accurate. This is just a restatement of the familiar notion that a firm cannot afford to pass up new opportunities in technology, marketing, information, and other dimensions of competition. Responding to these changes is not optional. If management fails to act, the firm will forgo profits. 4. The laws of demand and comparative advantage The Heisenberg principle implies that scientific conclusions must be probabilistic, not deterministic. The exact trajectory of a particular electron is inherently unpredictable, and any statement about its future position must be framed in statistical terms. This situation is not the result of defective experiments or small samples. The randomness is embedded right in the physics. Economic analysis leads to the same conclusion, as we see in the derivation of the law of demand based on revealed preference (Varian 1992, 135-137). Confronted with price changes for several products, the consumer makes optimal adjustments in his purchases of those items. After the income effect has been eliminated, the inner product of the price changes and the quantity changes is expected to be negative. In other words, there is an inverse correlation between prices and quantities. This conclusion is essentially statistical. It does not predict what the consumer will do about any commodity in particular. He might in fact buy more of an item whose price increased. The correlation merely asserts that, on average, he will purchase more of the products whose prices dropped and less of the products whose prices rose. Of course, if only one price is assumed to change, then the consumer is definitely not expected to increase his purchase of that item --the famous law of demand. However, this special case does not belie the probabilistic content of the economic model. The theory of comparative advantage provides a very similar example. If two nations can trade just two goods, the Heckscher-Ohlin-Samuelson model predicts specifically which country will export each good; the outcome is deterministic. With three or more goods, however, the determinism disappears. A country will certainly export the good in which its comparative advantage is greatest, and it will certainly import the good in which its comparative advantage is least. However, the model cannot predict the trade pattern for each of the remaining goods, where a country's efficiency is at an intermediate level. Nevertheless, Deardorff (1980) deduces a negative correlation between a country's autarky (pre-trade) prices and its net exports. Higher autarky prices tend to be associated with imported goods; lower autarky prices tend to be associated with exports. Without additional assumptions, this statistical prediction is the best that the model can achieve. The correlation is not an appendage to make allowance for sampling errors in trade data; it is inherent in the theory. 5. Discrete and continuous variables Quantum mechanics asserts that matter is both grainy and smooth, particle-like and wave-like. However, the particle behavior and the wave behavior are not observed simultaneously. Their incompatibility is another manifestation of the Heisenberg principle. The same lack of interface between discrete and continuous variables is found in economics. Baumol (1977, 566-568) examines competitive equilibrium for goods that must be produced in discrete units; the output space is then a lattice of points. One such point may lie below the production possibilities frontier, but it is still efficient if no other feasible point happens to be northeast of it. Nevertheless, Baumol shows that no competitive prices induce firms to offer that efficient combination. Neither profit-maximizing entrepreneurs nor central planners can use the price continuum, represented by a straight line, to locate the discrete point. In a similar vein, Charreton (1992, 118-119, 151-153) considers an oil field whose rate of output can be adjusted continuously. Using the principles of control theory, the owner of the field determines the most profitable time path of extraction. However, the oil must be loaded onto individual tankers. It is expensive to keep a tanker waiting or to dispatch it half full. Therefore, the (otherwise) optimal extraction plan must be adjusted to the exigencies of transportation. The fit between the discrete and the continuous variables is imperfect. 6. Rational expectations The minuscule world of atoms is inevitably altered by human examination. To locate a particle, the scientist showers it with photons, thereby jolting its trajectory. In consequence, physicists affirm that knowledge of reality is bound up with the experimental apparatus. Observer and object interact. What you see is what you get. Economic theory draws a similar conclusion in the framework of rational expectations (Sargent and Wallace 1975). To learn about the Economy, the Policy Maker conducts experiments; these include regulatory actions as well as fiscal and monetary operations. What response will households make to more health insurance underwritten by public funds ? How will foreign competitors react to the prospect of higher trade barriers ? Can an easier monetary policy stimulate the Economy during a recession ? If they are to reveal the Economy clearly, the experiments must be conducted fairly often on a sufficiently large scale. After all, fiscal stimulus in the form of an occasional million-dollar outlay is unlikely to elicit a measurable response. On the other hand, is it plausible that participants in the Economy behave passively and predictably upon repeated exposure to large doses of policy ? Will they still play their roles as the dependent variables in a cause-and-effect model ? Instead, there seems to be feedback. While the Policy Maker observes households and businesses, they also observe the Policy Maker and adapt to the experiments as best they can. The experiments alter people's ordinary behavior. Given enough time and experience, households and businesses may understand the Economy about as well (or badly) as does the Policy Maker. At that point, according to rational-expectations theory, the Economy's participants anticipate and neutralize the systematic component of each policy. The only experiments that continue to surprise the Economy's participants are the purely random events, which no one can foresee. These "shocks" represent the irreducible noise level that corresponds to Planck's constant in quantum mechanics. The principle of indeterminacy pervades contemporary economic analysis, which like physics has abandoned determinism. Heisenberg and his contemporaries were acutely aware that the step was portentous; some eminent physicists refused to take it. Economists, on the other hand, seem comfortable in a stochastic world and appear to take for granted the intellectual transition which has repositioned their doctrine within the general framework of scientific inquiry. References Baumol, William J. Economic Theory and Operations Analysis, 4th ed., Englewood Cliffs, NJ: Prentice-Hall, 1977. Charreton, Raoul. Relativity and Quanta in Economics, Paris, France: Actibus, 1992. Deardorff, Alan V. "The General Validity of the Law of Comparative Advantage," Journal of Political Economy, 88, 5, 1980, 941-957. Massell, Benton F. "Some Welfare Implications of International Price Stabilization," Journal of Political Economy, 78, 2, March-April 1970, 404-417. Rae, Alastair I. M. Quantum Mechanics, 3rd ed., Bristol, UK: Institute of Physics Publishing, 1992. Sargent, Thomas and Neil Wallace. "Rational Expectations, the Optimal Monetary Instrument and the Optimal Money Supply Rule," Journal of Political Economy, April 1975. Varian, Hal. Microeconomic Analysis, 3rd ed., New York, NY: W. W. Norton, 1992.