Numerical Examples Of The Reswitching Of Techniques In Spatial Economics?

It is my custom to work through, with graphs, example of the reswitching of techniques and other capital-theoretic 'paradoxes' in various models. Sometimes I have created numeric examples, and perturbed them too.

Reswitching examples exist in the literature on spatial, regional, and urban economics. Nowhere have I worked through them.

I think of regional economics as having two traditions for building theoretical models. One is the the Von Thunen model, with a central city and concentric rings of land uses. Transport costs are of importance. Reswitching is manifested by non-adjacent rings being used to produce the same commodities, with other commodities being produced in between. Barnes & Sheppard (1984) have graphs suggesting that they have a concrete numerical example. But they do not present parameter values. Their text suggests that an example can be created based on the example in Metcalfe & Steedman (1979).

Walter Isard invented regional economics in the middle of the twentieth century. This approach has different countries or regions described by individual Leontief matrices. Imports and exports show interactions between the regions.

Pavlik (1990) has a numeric example for this second tradition, reproduced, I think, in section 5.1 of Sheppard & Barnes (1990). They have the production distributed among regions, as I understand it, like in 'gravity models'. And its solution requires an application of an iterative algorithm. I think this implies the eample does not necessarily have a technique that is cost-minimizing across all regions, as opposed to within each region. I suppose it would be good to replicate this example and produce some graphs. (I realize that computers these days provide capabalities that were not also easily available decades ago.)

Perhaps Zaffari & Sbrenna (2024) provide a model on which I should concentrate. This model seems to be in the Isard tradition, with improvements. Their modeling includes transportation costs, the spatial capacity of regions in space, and the endogenity of various variables. I can make various simplifications in developing a concrete numerical example.

Can I work through existing numerical examples in the literature? Can I find numerical values for the parameters in the model in Zaffari & Sbrenna (1984), perhaps simplified, for a reswitching example? I suppose techniques might differ in which regions, processes are run to capacity. Or, perhaps, one region specializes in manufacturing one set of commodities and the other in making manufacturing another set. I do not know how far I will get.

References

• Barnes, Trevor & Eric Sheppard. 1984. Technical choice and reswitching in space economies. Regional Science and Urban Economics 14: 345-362.
• Metcalfe, J. Stanley & Ian Steedman. 1979. Reswitching and primary input use. In Fundamental Issues in Trade Theory (ed. by I. Steedman) New York: St. Martin's Press.
• Pavlik, C. 1990. Technical reswitching: a spatial case. Environment and Planning A 22:1025-1034.
• Sheppard, Eric & Trevor Barnes. 1990. The Capitalist Space Economy: Geographical Analysis after Ricardo, Marx and Sraffa. London: Unwin Hyman.
• Zaffari, Gabriel & Giacomo Sbrenna. (2024) Sraffa goes to space: spatial elements of political economy. Review of Political Economy DOI: 10.1080/09538259.2024.2434532