Home seekers in the housing market

There are two types of home seekers in this housing market matching model: the homeless who search for a dwelling both in the rental market and in the homeownership market simultaneously; and the home seekers in the renter (tenant) state who want to buy a home and only search in the homeownership market. The search process leads to several types of matching and in turn this implies different prices of equilibrium. Furthermore, the search process connects the rental market with the homeownership market. Hence, this simple model is able to explain both the relationship between the rental price and the selling price and the price dispersion which exists in the housing market, relying only on the different states of agents in the search process