Thursday, February 3, 2011

Statement of the theory!

We are trying to apply a combination of von Thunen’s rent and distance theory [1] and Ricardo’s rent and land fertility theories, using Dunn’s equation[2] from 1954:

where R is the rent for crop j at location i. E is the yield of crop i, and a is the production cost. k is the cost per unit distance of transporting crop j and d is the distance from the farm to the next commercial transit point (let’s call it CTP). P is the price of the crop at the market. This might be the mill, or a dealer’s yard---wherever the production next changes hands and where its value needs to be calculated.

The rent right next to the CTP will be highest because the distance is shortest. In the same way there will eventually be a ‘margin of cultivation’ where the cost of transport exactly equals the revenue from production. So at this point the rent will be zero. Farmers will bid for the use of the land at any point along a bid curve we construct just by joining up rent at the CTP and rent at the margin of cultivation:

Farmers won’t bid for land if the rent is set at any point to the right of the red line: it is too expensive. Likewise, landowners won’t accept any offer to the left of the red line, because they think they can get a better offer.

In the empirical testing we have been doing, we found that Dunn’s equation worked very well for Cornwall, Devon and Dorset. So far so good. But when I tried to include counties to the east, such as Somerset, the results were no longer statistically significant. In particular, the regression results gave a POSITIVE sign for Ekd, on the right hand side whereas it should (the theory goes) be negative.

In the literature I found several theoretical reasons for why this might happen. First:  worker wages are less further out from the CTP. So this would mean a reduction in ‘a’ in the equation, making the net revenue greater the further away from the CTP. (We see this happening in contemporary business: that’s why firms ‘outsource’ to China and India). Second: the perception of the farmer as to future harvests might differ from place to place. If he/she thinks that the weather will make yields highly variable, then he/she probably won’t bid as much for the land [3]. This second reason is why I have been getting you working on meteorological data these last few weeks.

But actually----I think the solution is simpler (they usually are). I have been mis-specifying the model. Instead of just distance to nearest market town (which worked well enough for Devon), I should have been thinking about the ‘connectivity’ of the towns and villages. The network density of the county/area in which the farm was. If it was highly interconnected with several different routes to the next town, then we would expect the rent to be higher, because the flow of goods in any direction would be less. Just have to figure out how to do that. Less reliance on distance to market town and more on how the towns were all connected together.

[1] von Thunen, J.H. Von Thunen's' Isolated State': An English Edition Pergamon, 1966.
[2] Dunn, E.S. The location of agricultural production University of Florida Press, Gainesville, FL, 1954.
[3] Cromley, R.G. "The von Thünen model and environmental uncertainty." Annals of the Association of American Geographers 72 (1982):404-10.

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