Production and endogenous bankruptcy under collateral constraints

We propose an extension of the incomplete markets general equilibrium model with production to situations in which firms default. In the model, firms are assumed to be owned by a single individual whose roles as entrepreneur and consumer are anonymous. Assets are exogenously collateralised and are seized together with future output in case of defaulting. Default is thus endogenous as output determines the deliveries from the assets issued. In turn, the receipts from each asset purchased are assumed to depend on a fraction of the firm's output. This fraction is assumed to be anonymous and is treated as given by individuals who will anticipate it, in equilibrium, as a fraction of the whole output of the economy, generating counter-cyclical default. We show that, under usual assumptions on utilities and technologies, an equilibrium always exists. We then discuss the implications of this setting for Fisher's "separation theorem" and the irrelevance of the financial policies of the firm.