Chapter 7 Alternative Model Formulations--Gordon

Introduction (Section edited and 3rd para added for this post)

This chapter is about some of the recent practical and theoretical developments in spatial equilibrium modelling which are aids to practitioners in applying such models to real world policy problems. Consideration will be given to a variety of formulations of the models that take into account economic policy mechanisms such as subsidies, taxes, exchange rates, and fixed and ad valorem tariffs and price pooling. Finally, some formulations that are non-competitive in character will be developed along with more sophisticated nonlinear models which include balance of payment type constraints and dynamic formulations.

The work of Takayama and Judge (1971) provides the substantive starting point and has extensive documentation of various spatial equilibrium models. However, work by Enke (1951) and also Samuelson (1952) laid the early foundation for these models. In modern usage, the most important and distinctive feature of spatial equilibrium models is that the direction of trade is not pre-determined and that there is an intermediate position for which no trade takes place between the two regions. These two characteristics provide the basic reason why such models are likely to be useful. When these issues are not important then other, and possibly simpler, techniques may be more appropriate. However, the spatial equilibrium model, in the form presented in Chapter 4, is very efficient in terms of data and therefore can be built quite rapidly and easily.


There is one further feature of spatial equilibrium models in what is known as the primal-dual forms. In a primal-dual structure there is a price or shadow price associated with each constraint. This provides a very clear picture of the economic structure, in both price and quantity terms, of complex trading systems. Particularly is this the case when there are nonlinear constraints, say, in the physical domain, that must have an equivalent in the price domain. The direct incorporation of the Lagrangian variables (prices) into the structure of a maximisation problem allows for the combining into one model relationships between both price and quantity variables. This opens up a whole array of new model forms that can be modelled with a greater richness and directed toward defining a more useful but still abstract representation of the real world. Such models will always rely on a degree of abstraction so as to deal with the essence of a problem rather than with the impossibility of representing the detail of the whole world.