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.

中文翻译：

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住房，抵押贷款和保险相关市场的定价分析

目的

本文旨在研究在出售房屋过程中在住房市场，抵押贷款市场和保险市场中寻求均衡的问题。通过三种模式建立了三类市场，它们通过整合的参数反映了企业在这些市场中利益的相互依存关系。本文旨在根据相关公司利益冲突之间的折衷来确定这些市场的价格，此外，还评估参与住宅物业出售过程的公司的整合合理性。 。

设计/方法/方法

基于收益共享合同和供应链协调方法，建立了房地产经纪人，抵押银行和保险公司的优化模型。这些模型考虑了企业利益的相互依存，这些市场中的垄断竞争以及企业在互动过程中个体理性的条件。

发现

研究结果如下。首先，由于垄断竞争中需求曲线的减少，住房市场，抵押市场和保险市场相互联系，因此，这些市场中企业的优化模型通过收益共享参数相互依存。其次，在这些市场中，单个企业的销售最优值并不相同，因此，企业的利益是矛盾的。第三，在房地产经纪人－银行－保险公司制度中，均衡满足代理人之间零收益共享支付的条件。此外，这些市场中的均衡价格是相互独立的。第四，在不平衡中，这些市场的价格是相互关联的，即一个市场的价格随另一市场的价格上涨，

研究局限/意义

如果市场显示出需求曲线在下降，并且相关市场中买方的需求相互关联，则该研究的结果将在实践中适用。

实际影响

房地产经纪人与抵押银行之间的互动使房地产经纪人能够提高其销售量，而银行则可以增加贷款数量，即导致其利润的增长。保险人与抵押银行之间的相互作用使保险人可以增加保单数量，而银行则可以降低放贷风险，即导致其利润增加。单个公司销售最优的确定使代理商能够确定这些交互的合同条款，这些条款是每个交易参与者的头寸的折衷。另外，企业的最优值表明了均衡市场价格的预测。

创意/价值

与契约理论框架下的研究相比较，首先，提出了复杂的（三主体）相互作用系统的数学描述。其次，建立了最优选择非线性模型，该模型考虑了垄断竞争市场中的非线性需求函数。第三，研究利益冲突的主体的均衡。在后面的项目中，作者确定补充需求功能系统中的收益共享合同不需要参与者之间的付款。第四，作者证明，在这些市场的均衡中，住房价格，抵押贷款利率和保险利率是相互独立的，并且与孤立市场中的价格相等。