For a market in any item to exist there must be property rights which can be traded. A property right is an enforceable entitlement to possess, use and exchange something. In a society where there is an acceptance that access to goods and services shall not be by physical force, government has a role in protecting and underwriting property rights. If there was a total reliance on atomistic market trading, property rights would rest mainly with individuals and firms. Thus, individuals would have rights to housing which allowed them to occupy housing or to allow others to occupy and these rights could be bought and sold. We might say all housing would be 'privately' owned and some would possibly be 'privately' rented. In this situation the production of housing would be by firms who were motivated by a desire to make profits. Individuals would buy, sell and rent housing in order to maximize individual satisfaction or utility.