The original version of the land use model MUSSA is based on the static equilibrium paradigm assuming locations as differentiable goods traded in auctions. For any forecasting year, the inputs are the household population by socioeconomic clusters, the number of firms by industry, and travel costs taken from a transport model in an interactive procedure. A vector of attributes that include location externalities describes locations, which contains neighborhood quality for residents and agglomeration economies for firms. Consumers value these attributes and define bids for each location. Additionally, equilibrium is defined by the market clearance condition that all consumers are located somewhere, which is attained adjusting the consumers’ utility levels. With these features the equilibrium is specified with two fixed-point problems, one associated with consumers’ externalities and another one for the market clearance condition. In MUSSA II what differ from the previous version are the real estate supply model and the way in which all constraints -consumers’ budget and regulations on supply- are represented in the model. Supply is assumed produced by real estate agents that behave maximizing a stochastic profit with a Gumbel distribution; thus it is modeled as a multinomial logit. Supply becomes interdependent because the model assumes that rents yield by their products are defined in auctions based on consumers’ bids, which in turn depend on the building stock, and also because production costs (potentially) face economies of scale and scope. Then the supply model defines a third fixed-point problem. Additionally, in this new version all constraints have been specified as a binomial cutoff factor on the utility or profit functions of the logit models. This means that the feasible domain for demand and supply is fulfilled stochastically, because there is a small probability (as small as decided by the modeler) that the constraint is violated. The new set of fixed-points problems defines equilibrium, which under weak conditions for real cases, exists and is unique; moreover the algorithm used to find the solution is significantly faster that the original.