Investigations to the price evolutions of goods exchange with CES utility functions

The price evolutions of goods exchange in multi-agent market are investigated by employing the kinetic theory. Assume that a closed market consists of two groups ( A and B ) of agents, who have the same preferences for goods. The constant elasticity of substitution (CES) utility function which contains Cobb–Douglas utility function and Leontief utility function, is used to describe the agent’s preferences. A system of linear Boltzmann type equation is given to describe the probability distributions of goods for agents of the two groups, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth conditions. We assume that agents in group A put all their goods into the market for maximum utility, while agents in group B aim to acquire maximal utility from goods exchange by suitably selecting the percentage of goods which are exchanged. The effects of different trading strategies on commodity price and wealth distribution are discussed. The results show that the trading strategies of agents in group B have effectively improved their wealth status under certain assumptions. Also, a general system of nonlinear Boltzmann equation for the probability distributions of goods is given to describe the pricing issues of goods exchange for agents. The numerical experiments of nonlinear Boltzmann equations demonstrate how the trading strategies and preferences of agents modify the price of goods.