Dispersed spatial input demand functions

Most recent attempts to improve the empirical performance of classical trade models by formulation of probabilistic models of the DSPE (Dispersed Spatial Price Equilibrium) type have concentrated on determination of flows of a single commodity. However, a further challenge is to develop consistent probabilistic multi-sector spatial input demand functions and the corresponding spatial supply functions as part of an eventual probabilistic spatial CGE (Computable General Equilibrium) framework. In this paper, we derive short-run aggregate spatial input demand functions as the generators of the spatial supply functions, introducing via entropy some distributional assumptions about the average behaviour of the representative firm. In order to remain compatible with entropy principles, all demand functions are derived in a form guaranteeing compliance with a probabilistic accounting framework, calibrated on observed quantities, costs and prices. Firstly, the paper develops dispersed spatial input demand functions using various classical production functions, such as Linear and CES, accounting for the transport costs and tariffs incurred by the supply of intermediate inputs. It then formulates dispersed interregional input demand functions based on multiregional input-output production functions, transcending the normal relations connecting input and output via constant coefficients, with solution via a price-sensitive iterative adjustment technique. Finally, guidelines for an extension to a long-run analysis are sketched.