Modeling interactions of institutions of housing markets based on power, exponential and log cost functions

The article presents a system of optimality conditions for housing market agents (realtor, bank and insurer) with power, exponential and logarithmic cost functions corresponding to different types of economies of scale. The results of numerical experiments are presented, demonstrating the nature of price interdependencies in these markets for various types of functions. In contrast to the study of the "realtor – bank – insurer" system based on linear cost functions, this work presents the following conclusions: firstly, in the case when all agents have concave cost functions, then the real estate price, mortgage interest rate and insurance tariff lower than in the case when agents have convex cost functions; secondly, an increase in the intrasystem commission rate leads to an increase in the price of the agent who pays the commission, and a decrease in the price of the agent who receives it; thirdly, an increase in the commission rate leads to a sharper decrease in the price of an agent, in the case when he has a convex cost function, while the counterparty has a concave one, than otherwise. When comparing the effectiveness of using different types of cost functions, it was found that logarithmic and exponential functions provide greater accuracy than power functions.