Economic Evolution and Structural Changes: a Non-Linear Model of Responses to Changes of Demand

The notion of economic evolution can be seen as encompassing all the processes of change of the fundamental parameters of an economic system. So, any change in technology, preferences or institutions determines an evolutionary change for the economy. The formalization of those structural changes, which are usually intertwined, is a hard task, since their very nature seems frequently difficult to grasp. From a historical perspective it can be easy to understand phenomena that for their contemporaries seem confusing or chaotic. The question is, therefore, to find the right time frame in which to analyze these kinds of processes. Certainly this lack of an adequate temporal framework adds to the difficulties that we face at modeling evolutionary phenomena. In the search for adequate models of structural change in the fundamental parameters of an economy we have to resort to some simplifying assumptions. At the risk of being deemed as too simplistic, we postulate in our model an exogenous shock hitting one or more of those parameters. Their adaptive response is the cause of evolutionary changes. Examples for this kind of behavior abound, but we concentrate on the behavior which arises in an economy where there are a number of agents (each one being a consumer and a producer) interconnected by links representing the provision of output to others and the requirement of input from the others. A shock will be conceived as an exogenous change of demand (representing, in turn, changes in the preferences of the agents). Production responds by either adapting the output under the same technology or by changing the productive structure. These possibilities arise in the case that shocks are relatively small, in the former case, or large, in the latter. More specifically, in our model the state in period $t+1$ depends on the state in $t$ plus the changes induced by the shock in that period. We partition the state space in two regions, one corresponding to the non-evolutionary changes. The other region, is the one in which the system changes its structure. In simplified form, we allow for each agent who receives a large shock to cut (some of) her ties with the other agents and resort to another agent that can be conceived as a "foreign" provider. The intuition is that a large demand shock forces a production unit to disregard its usual providers of input (which are not able to respond to its derived demand of factors) and look for an outside source of input. In turn, if an agent is only connected to that external source, and receives a large negative shock, we allow her to reinstate her links to the other agents just in case the amount of inputs that the internal agents can provide is enough to cover her new decreased demand of factors. The interpretation of this is straightforward: a firm or sector that faces an abrupt decrease of the demand for its production finds it more efficient to demand inputs to units closer (in geographical or institutional terms) to it. Given these assumptions, a sequence of shocks will result in a series of structural changes that end up converging to two main attracting states. Moreover, we show that oscillating behavior cannot be avoided in the way towards one of those states.