Matching Markets with Flexible Contracts and Non-transferable Preferences

This paper modifies and extends the aggregate equilibrium models for matching markets developed earlier in the literature. Agents in the matching market search for a match among potential partners, including agreements about a flexible contract, such as hours and wage combinations in the labor market. Under general utility representations that are non-transferable and assuming the matching is stable we derive a framework for the probability of achieving a specific match, including the choice of contract. We also show that the popular transferable utility model with transferable utilities can be viewed as a limiting case within our framework