Representative Agent in a Form of Probability Distribution

This paper provides a methodology for demand aggregation with rigorous micro foundation by using the probability distribution function. In the model setting, a set of agents defined by a similar type of attributes is approximated as one representative agent with probability error. By introducing several assumptions on the probability process, a restriction condition to assume a single representative agent as a whole economy is provided for the following three cases: i) normal diffusion with Markov process, ii) normal diffusion with non-Markov process, and iii) anomalous diffusion. In the case of normal diffusion, no restriction condition for the shape of the probability density function of the consumption bundle is required because the Gaussian distribution has a property of stability. On the other hand, in the case of anomalous diffusion, some restricting conditions on the parameter of the probability process are required to maintain stability.