Linear programming and locational equilibrium: The Herbert-Stevens model revisited

The paper reviews the early work of Herbert-Stevens in which linear programming was used to find a competitive equilibrium to an urban land market. First, it is demonstrated that a solution to the Herbert-Stevens model does not meet well-established criteria for an equilibrium. Secondly, a new linear programming model is suggested which is proven to achieve equilibrium if certain conditions are met. An iterative procedure for meeting these conditions is suggested, and an operational version of the model exhibits no problem in obtaining convergence. The revised model represents a feasible way of simulating urban land markets.