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Quantum economics, uncertainty and the optimal grid size
Economics Letters 64 (1999) 277–278
Quantum economics, uncertainty and the optimal grid size Martin Shubik* Cowles Foundation for Research in Economics, Yale University, P.O. Box 208281, New Haven, CT 06520 -8281, USA Received 30 December 1998; accepted 27 April 1999
Abstract The tradeoff between process time and error produces an optimal grid size on economic activity which is influenced by the rate of interest. The rate of interest changes the value of time and hence the velocity of money. 1999 Elsevier Science S.A. All rights reserved. Keywords: Interest rate; Time; Uncertainty; Velocity JEL classification: C60; C61; E4
1. Time and error When studying economic dynamics, why not use continuous time? It is frequently easier to handle than discrete time. At best, all models are an approximation of some underlying aspect of reality. When studying the purchase of a gallon of gasoline, it is possible to conceive of a flow model where the gasoline is sold continuously requiring progressively less and less money with ever increasing velocity during the period. In fact, we do not buy gasoline by the drop paying a fraction of a mil every microsecond. When we consider any economic act, be it consumption, production or trade, the act requires a finite amount of time which we may denote by Dt. Consider a simple act such as pouring oneself and drinking a cup of coffee. It takes a few seconds to pour the coffee without spilling and a minute or two to drink the coffee in comfort. One might be able to gulp a full cup in a few seconds; but as the speed is increased, so are the odds of choking. Even in the electronic world of financial transfers with messages moving near the speed of light, most transactions are ultimately originated by a human and are validated by another human when completed. In production, once the process has been established and learning is no longer a dominant consideration, further attempts at time reduction may be obtained *Tel.: 1 1-203-4323694; fax: 1 1-203-4326167. E-mail address: [email protected] (M. Shubik) 0165-1765 / 99 / $ – see front matter PII: S0165-1765( 99 )00095-6
1999 Elsevier Science S.A. All rights reserved.
278
M. Shubik / Economics Letters 64 (1999) 277 – 278
at the cost of accident or other error. For each consumption, production or transaction process, there will be a process time Dt and an error generation j (Dt) associated with the time taken. If time has value to the individual, there will be an optimal tradeoff between time saving and error generation. This type of risk is endogenous to the system. For a given value to time, there will be associated an optimal level of risk; and hence, an optimal time grid for the economy.
2. Minimal uncertainty There are three basic sources of uncertainty in an economy: exogenous, strategic, and quantum. The first involve the acts of nature, weather, earthquakes, and other natural disasters or favorable events over which we have no control. Strategic uncertainty is endogenous and involves our inability to predict the actions of competitors. Hypotheses such as rational expectations provide non-process rationalizations for avoiding this type of uncertainty. Quantum uncertainty would arise even without strategic uncertainty and is a difficult to measure, but clear to perceive consequence of the physics of process and perception. A context-free, dynamics-free, preinstitutional macroeconomic theory of pure competition with complete markets and all other assumptions of continuity and smoothness may be of considerable use in providing a benchmark against which to measure some macroeconomic processes. It is of limited worth in understanding macroeconomic process. Modern finance with its concern for new instruments with which to insure risk has not yet provided us with either the appropriate concepts or measures for the bounds on the minimal overall uncertainty that have to be present in an economy.
3. Time, money and velocity An inconvenient fact of economic life is that what we call money is an institutional mixture of government paper and individual institutional or personal issue of credit. Payments are made in a complex array of devices ranging from straight barter to straight cash. Thus, the apparent simplicity of the monetary equation PQ 5 MV stating that the price level multiplied by the amount of goods equals the amount of money times its velocity is marred by the empirical facts that we are vague about the definition of M; that the P is a scalar approximation of a high dimensional vector, as is Q; and that, in fact, V (however measured) fluctuates.
4. Control and the rate of interest Even if we were to construct a simple game with trade required to be in government money and with only a single central bank controlling money and debt, the velocity of money could still fluctuate. Without exogenous uncertainty, endogenous quantum uncertainty will still exist. But, as is well known in economic theory, time and money are intimately related. In particular, the rate of interest may be looked at as a device which (within bounds) can be utilized to change the time scale on economic choice. But a change in the interest rate may influence the acceptable length of time employed in any economic process. A different degree of endogenous risk and a different time scale will be selected. Both the velocity of money and uncertainty will be influenced.
Quantum economics, uncertainty and the optimal grid size Martin Shubik* Cowles Foundation for Research in Economics, Yale University, P.O. Box 208281, New Haven, CT 06520 -8281, USA Received 30 December 1998; accepted 27 April 1999
Abstract The tradeoff between process time and error produces an optimal grid size on economic activity which is influenced by the rate of interest. The rate of interest changes the value of time and hence the velocity of money. 1999 Elsevier Science S.A. All rights reserved. Keywords: Interest rate; Time; Uncertainty; Velocity JEL classification: C60; C61; E4
1. Time and error When studying economic dynamics, why not use continuous time? It is frequently easier to handle than discrete time. At best, all models are an approximation of some underlying aspect of reality. When studying the purchase of a gallon of gasoline, it is possible to conceive of a flow model where the gasoline is sold continuously requiring progressively less and less money with ever increasing velocity during the period. In fact, we do not buy gasoline by the drop paying a fraction of a mil every microsecond. When we consider any economic act, be it consumption, production or trade, the act requires a finite amount of time which we may denote by Dt. Consider a simple act such as pouring oneself and drinking a cup of coffee. It takes a few seconds to pour the coffee without spilling and a minute or two to drink the coffee in comfort. One might be able to gulp a full cup in a few seconds; but as the speed is increased, so are the odds of choking. Even in the electronic world of financial transfers with messages moving near the speed of light, most transactions are ultimately originated by a human and are validated by another human when completed. In production, once the process has been established and learning is no longer a dominant consideration, further attempts at time reduction may be obtained *Tel.: 1 1-203-4323694; fax: 1 1-203-4326167. E-mail address: [email protected] (M. Shubik) 0165-1765 / 99 / $ – see front matter PII: S0165-1765( 99 )00095-6
1999 Elsevier Science S.A. All rights reserved.
278
M. Shubik / Economics Letters 64 (1999) 277 – 278
at the cost of accident or other error. For each consumption, production or transaction process, there will be a process time Dt and an error generation j (Dt) associated with the time taken. If time has value to the individual, there will be an optimal tradeoff between time saving and error generation. This type of risk is endogenous to the system. For a given value to time, there will be associated an optimal level of risk; and hence, an optimal time grid for the economy.
2. Minimal uncertainty There are three basic sources of uncertainty in an economy: exogenous, strategic, and quantum. The first involve the acts of nature, weather, earthquakes, and other natural disasters or favorable events over which we have no control. Strategic uncertainty is endogenous and involves our inability to predict the actions of competitors. Hypotheses such as rational expectations provide non-process rationalizations for avoiding this type of uncertainty. Quantum uncertainty would arise even without strategic uncertainty and is a difficult to measure, but clear to perceive consequence of the physics of process and perception. A context-free, dynamics-free, preinstitutional macroeconomic theory of pure competition with complete markets and all other assumptions of continuity and smoothness may be of considerable use in providing a benchmark against which to measure some macroeconomic processes. It is of limited worth in understanding macroeconomic process. Modern finance with its concern for new instruments with which to insure risk has not yet provided us with either the appropriate concepts or measures for the bounds on the minimal overall uncertainty that have to be present in an economy.
3. Time, money and velocity An inconvenient fact of economic life is that what we call money is an institutional mixture of government paper and individual institutional or personal issue of credit. Payments are made in a complex array of devices ranging from straight barter to straight cash. Thus, the apparent simplicity of the monetary equation PQ 5 MV stating that the price level multiplied by the amount of goods equals the amount of money times its velocity is marred by the empirical facts that we are vague about the definition of M; that the P is a scalar approximation of a high dimensional vector, as is Q; and that, in fact, V (however measured) fluctuates.
4. Control and the rate of interest Even if we were to construct a simple game with trade required to be in government money and with only a single central bank controlling money and debt, the velocity of money could still fluctuate. Without exogenous uncertainty, endogenous quantum uncertainty will still exist. But, as is well known in economic theory, time and money are intimately related. In particular, the rate of interest may be looked at as a device which (within bounds) can be utilized to change the time scale on economic choice. But a change in the interest rate may influence the acceptable length of time employed in any economic process. A different degree of endogenous risk and a different time scale will be selected. Both the velocity of money and uncertainty will be influenced.