Transportation models of time allocation : a contribution to objective consumption theory : a thesis in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Economics at Massey University
This thesis investigates the optimal allocation of time by a rational agent in terms of his behaviour settings and social requirements. Time is considered as a scarce resource and as an objective measure of activities. Conceptually the models of time allocation are transportation models and share the same mathematical structure. The findings of eco-behavioural science suggest that the behaviour of an agent, as an individual decision maker, will be shaped by environments. Behaviour settings, corresponding to sources in the transportation models, are used to define environments. As a member of society the agent is required to meet parameters of social position, a set of requirements corresponding to sinks in the transportation models. Time use studies provide quantitative measures of the agent's activities. Hence the model is able to specify constraints on the agent's time use in terms of behaviour settings and social relations. The core model shows the relationship between groups, or classes, of agents and their lifestyles. The agent as rational decision maker is faced with the choice of meeting the demands of social position by activities in selected environments, while minimizing the total cost of the lifestyle. Each activity uses up time and incurs a money cost. The optimal solutions specify both the type and level of the activities which the agent undertakes in order to meet the parameters of social position. An equivalent program (the dual) exists. The agent is faced with the choice of maximising the net imputed value of time use, so long as the net value of a unit of time is less than or equal to the per unit cost. Conceptually there are two transportation models. Both are concerned with the particular case of a student as a rational decision maker. In the slack model the focus is on the activities of a particular student. By way of contrast the focus in the tight model is on the activities of the average student, and there is a time distribution not only at sources but also at sinks. This model is useful to social accounts. Three equivalent formulations of the transportation model are outlined. A technology matrix, defined as the agent's socio-economic production function, denotes the set of production processes available to the agent, given behaviour settings (environments) and parameters of social position. An element of the socio-economic production function is termed an activity. The choice of certain activities by the agent represents a particular lifestyle described by a specific time distribution. Social income, defined as the value of social position plus net earned income is a scalar measure (in dollars) of the agent's lifestyle. To show that the models are operational, simple 2 x 2 and 3 x 3 models are introduced and extended in the final three chapters. A methodology is developed for obtaining per unit costs. A step-by-step approach is used to derive a 5 x 5 cost matrix from two sets of actual data, obtained independently. The effects of changes in the parameters of the time allocation models are analyzed.