Abstract
It is the disaggregation of the consumption function that allows interesting dynamics to arise. Disaggregation in this context does not merely imply the study of consumption behaviour of a single unit but implies, as a central feature, the study of interaction among consumption units. In accordance with Duesenberry's work, consumption units are not considered in isolation from their surrounding society but are allowed to respond to the consumption behaviour of other agents.
The methods of cellular automata theory are used to model the interaction of consumption units. "Society" is modelled as a cellular automaton and consumption units are situated on the cells in the automaton. Time is discrete in the model and at each point of time one agent takes a decision on how much to consume and on how to move between the cells. The information-gathering and decision-making processes are described by simple algorithms. Disregarding certain modifications, the goal for each unit is to consume as much as the average of all units. The units are faced with two constraints in reaching this goal; first of all they do not have full information and secondly they face a budget constraint.
Due to the structure of cellular automata it is quite easy to introduce imperfect information to our model, i.e. we do not have to model noise since time and space is given to us by the structure of the automaton. Thus imperfect information is modelled by imposing a time and a space constraint on the movement of units between the cells and by only providing units with information about other units situated on the neighbouring cells. Not knowing the average level of consumption, the unit must approximate it from information on consumption by units on neighbouring cells.
The budget constraint is made up by the combination of three elements; income, accumulated wealth and a credit limit. Production is adapted frictionless to consumption, and a consumption decision generates an income of equal size. Incomes are evenly distributed among consumption units, wealth is accumulated savings (or dis-savings) and the credit limit is fixed in proportion to income. Thus we have a simplified closed system with the required accounting relation between income and expenditure and between debts and wealth.
The purpose of the study is to investigate the dynamics of consumption behaviour in this simple framework. Is the aggregate level of consumption likely to converge to a steady state, or does consumption fluctuate without ever converging? Is there a difference between the stability of aggregate consumption and disaggregate consumption, e.g. do we find stability at the aggregate level, but continuing fluctuation between the different units? Is the qualitative characteristics of consumption altered with the introduction of interest payments, by introducing a different distribution of incomes or other modifications of our model? Thus it is a study of certain qualitative aspects of consumption behaviour, with the purpose of investigating its possible role in the generation of business cycles.