Prices and Production

My original intention in writing this book was to consider evolving market systems and Hayekian criteria of efficiency (see von Hayek (1931, 1945)), and to discover those formal structures which might possibly lie at the base of economic systems capable of evolution. Much work in this field had already been done by others (see, for example, Kirzner (1975) and Nelson/Winter (1982)), and a consensus seems to have been reached that something like system theory must be the logical point of departure for evolutionary theory in economics. But most of the previous work in this area is purely intuitive, and though there is much talk in it of systems and system theory, a precise definition of the concept of a system in this context is nowhere to be found. I had hoped to be able to sketch a working definition of pricing and production systems in a few pages and then to go on to investigate their performance within the framework of modern stability analysis. It soon became clear, however, that difficult and complex problems arise from the very outset of such an endeavor. If, for example, one speaks of dynamic systems of pricing and production, it should be made clear just how these systems differ from those portrayed in standard price theory and why that theory is inadequate for such analysis. Because the existing literature in evolutionary economics offers no clear answers to these questions, economists accustomed to thinking of preferences and scarcities as the primary determinants of price formation might justifiably ask what the real advantage of all this new theoretical apparatus is.

We begin with a simple example which will soon be generalized. Consider time as a sequence of points t₀, t₁, t₂ etc. which follow one another in a given distance which we shall call a time step. All events in the world last for a minimum of one time step, which may be arbitrarily small. Consider first the process of producing a consumption good whose quantity is represented as C. This consumption good is produced in three successive steps, each of which lasts one time step (so that the time step is our elementary period of production). Assume that production in the first stage requires only raw materials taken from nature in quantity R₁ plus human labor in quantity L₁; to produce intermediate outputs in quantity X₁. The product X₁ is then combined with raw materials R₂ and labor L₂ in the second stage of production I₂ to produce new intermediate products X₂. In the final stage of the process, I₃, C units of the consumption good itself are produced by combining X₂ with new inputs of raw materials and labor R₃ and L₃. Employing the symbol ⊕ to connote combination in production as determined by the available technology, we may represent this three-stage process as follows (see Bliss (1977)):

We proceed now to formalize the ideas presented in the first chapter. As before, time is understood as a sequence of equidistant, discrete points t _i , i ∈Z. Through these points in time, all events in the world are mapped into time space T, and we call the distance between two successive points in time a “time step” ¹. For the time being, we shall assume that no event occurs in less than one time step, so that no bias is introduced by the discrete representation of time. We shall relax this assumption later. We regard production as a transformation of resources into finished consumer through the application of human labor, and, in most cases, of previosly produced intermediate goods as well. Let r = r₁,..., r _m be an m-dimensional vector of raw-material inputs, some of which may denote the direct input of labor, and c = c₁,...,c _n be the n-dimensional vector of finished consumer goods. Both vectors are real and nonnegative. The transformation of inputs r into outputs of consumption goods c is achieved by a system of production Σ, the state of which is described by a n-dimensional state vector x. This vector spans a space which is called the “state space” (see e.g. Kalman/ Falb/Arbib (1968)), and the inflows r and outflows c similarly span the spaces Ω ⊂ R ₀ ^m+ and Γ ⊂ R ₀ ⁿ⁺ .

In this chapter, the systems with which we have thus far been concerned will provide an analytical framework for a critical review of several economic doctrines of historical significance. The ground we have covered in Chapter 2 is by no means unexplored territory in economic theory. Most of these ideas have appeared at various points in the economic literature. But they have not yet been fully integrated into the body of modern economic thought.