Economic Growth and Change in a Material World
4. The Z-function 4.1 ON THE EXISTENCE OF A WEALTH FUNCTION To recapitulate what we have said several times above: economic survival for an economic agent or ﬁrm depends upon avoiding losses that can be avoided in principle (losses of the second kind). If, and only if, gain cycles are much more frequent than loss cycles can the ﬁrm expect to survive in the long term. Unavoidable losses (of the ﬁrst kind) will occur from time to time, as we have noted. But survival implies that such losses must be exceptional, and – for analytic simplicity – we can rule them out altogether for the ﬁrst phase of the following analysis. The economic survivability conditions for an agent are only testable ex post, when the q-cycle is closed (whether the outcome be a gain or a loss). Meanwhile, without foresight of the outcome, the agent has to make a sequence of smaller decisions with regard to unit operations, also based on expectations grounded in past experience and the knowledge stock. For convenience, we call this learned behavior ‘obeying the AAL rule’. We will show that the AAL rule implies the existence of a scalar wealth function Z of which the arguments are goods and money. We show that the AAL rule implies that, ruling out occasional losses of the second kind, the economic process is nondecreasing and irreversible, that is, that dZ > 0.1 Allowing for occasional losses, it still follows that market survival means that Z must increase on average. We have...
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