Full Substitutability

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' canonical definitions of substitutability to settings in which an agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We then prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability. We also show that substitutability corresponds to submodularity of the indirect utility function, the single improvement property, and a no complementarities condition. Finally, we show that substitutability implies the monotonicity conditions known as the Laws of Aggregate Supply and Demand.