Pricing analysis of interconnected markets of housing, mortgage lending and insurance
Authors: Geraskin Mikhail 
Published: May 2020

Purpose
This paper aims to investigate the problem of searching for the equilibrium in the housing market, the mortgage lending market and the insurance market in the process of selling the residential property. Three classes of markets are established in three modes, which reflect the interdependence of the firms’ interests in these markets through the parameters of their integration. The paper aims to determine the prices in these markets on the basis of the compromises among the conflicting interests of the related firms, and, in addition, to assess the rationality of integration for firms, which are participants in the process of selling the residential property.

Design/methodology/approach
On the basis of the revenue sharing contracts and the supply chain coordination methods, the optimization models of the housing realtor, the mortgage bank and the insurance company are developed. The models consider the interdependence of the firms’ interests, the monopolistic competition in these markets and the conditions of the firms’ individual rationality in the interaction process.

Findings
The results of the study are as follows. First, as a consequence of a decrease in the demand curves in monopolistic competition, the housing market, the mortgage market and the insurance market are interconnected, therefore, the optimization models of the firms in these markets are interdependent through the revenue sharing parameters. Second, in these markets the individual firms’ sales optimums are not identical, therefore, the interests of the firms are contradictory. Third, in the realtor-bank-insurer system, the equilibrium satisfies the condition of zero revenue sharing payments between the agents; additionally, the equilibrium prices in these markets are mutually independent. Fourth, in the disequilibrium, the prices in these markets are interrelated, i.e. the price in one market increases with the price in another market, if the payment is directed from the former to the latter, and vice versa.

Research limitations/implications
The results of the study are applicable in practice, if the markets demonstrate the decreasing demand curves and if the needs of buyers in related markets are interconnected.

Practical implications
The interaction between the realtor and the mortgage bank enables the realtor to raise its sales and the bank to increase in the number of loans, i.e. it leads to growth of their profits. The interaction between the insurer and the mortgage bank enables the insurer to increase in the number of policies and the bank to reduce the risk of lending, i.e. it leads to an increase in their profits. The identification of the individual firms’ sales optimums enables agents to determine the terms of the contracts of these interactions, which are compromises from the positions of each transaction participants. In addition, the firms’ optimums indicate the predictions of the equilibrium market prices.

Originality/value
In comparison with the studies in the contract theory framework, first, the mathematical description of the complicated (three-agent) system of interactions is proposed; second, the optimal choice non-linear models are developed, which take into account the non-linear demand functions in the monopolistic competition markets; third, the equilibrium of the agents with contradictory interests is investigated. In the later item, the authors establish that the revenue sharing contracts in the complimentary demands functions systems do not require the payments between the participants. Fourth, the authors prove that, in the equilibrium of these markets, the housing prices, the mortgage interest rates and the insurance rates are mutually independent and equal to the prices in the isolated markets.