Wheat price coordination

Wheat price yearly averages for four counties

In a recent post about the theory of agricultural location, I missed out the definition of 'P' in Dunn's equation...thanks Mi for pointing this out. P is the price of the commodity (e.g. wheat) at the market. I've corrected the omission. Mi's remark made me think about the variation in wheat prices on a locality basis. If the wheat price varies from point to point, then Dunn's equation gets more complicated. I've found a remarkable set of wheat prices by county which last from 1770 1820. I have been looking at these to see what regional difference there might be. On the graph I've plotted the yearly mean price for our four counties of interest. Interesting things: the wheat prices converge when the variation is small. But when there are peaks (for example a huge jump in 1800) then there is considerable divergence. And it is always Somerset that is most expensive. Cornwall is always cheapest, with the two counties between them geographically, also between them with regard to price. I'd guess that this effect is caused by proximity to London. London was a major market, with about 14% of the population living there. This is really interesting (isn't it?).

Sunshine and wheat yields

Malcolm has been plugging away at data from the UK Meteorological Office, calculating mean hours of sunshine in August for our 715 parishes. Now, the data comes from earlier last century and not from 1836, when the wheat yields were recorded, but that’s the best we can do.

August sunshine is a critical factor in wheat yields: best is hot of course, allowing the ear to ripen fully before harvest. I’ve done a regression of wheat yields against hours of sunshine in August, as well as the other data we have: elevation, amounts of rainfall in different groupings. There is a map of sunshine to the right and the regression output is below. The map is interesting, because you can see the parishes in bright yellow, indicating the most sunshine. Along the coasts, and down to the tip of Cornwall. And of course this matches up with where people like to go on holiday. The best wheat yields come from Somerset, inland and with plenty of August sunshine.

Here is the regression output. Elevation has a negative sign, meaning less yield with height. Sunshine is positive...as expected. Rainfall is negative above a certain amount. More than 1000 mm in a year waterlogs the wheat plant. This is not a bad result at all, and it will improve once I get data for soil types and amounts of available water into the regression.

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.

Malcolm's comment on Cornish railways

Old Cornish tin-mine pumping station (Wikipedia, Tim Corsler)

Malcolm made a perceptive comment about why distance to market seemed to matter much more down in the 'toe' of Cornwall than in the lusher pastures of Somerset, well to the east. He thought this might have something to do with railways. This is interesting, because railways did develop early on in Cornwall, but mostly for the freighting of minerals, especially tin. The steam engine started off in Cornwall to pump water out of mines. The Cornish railway system was purely local though, and didn't get connected up with the rest of the system until the 1850s. What is interesting about Cornwall, and which Malcolm's comment made me think about, was the amount of food rioting that went on among the tin-miners. As the linked text notes, the rioters were isolated groups of non-local non-farmers who suffered when food prices went up. This isn't just history: we're seeing the same thing these last few weeks in Tunisia and Eqypt. Underlying the protests are concerns about high food prices, caused by stock-piling, poor harvests (possibly climate-change driven though this is risky speculation) and the large amount of food production being converted into ethanol (primarily in the US). There is an article here from the British Daily Telegraph about the world being one poor harvest away from chaos. History does repeat itself, and only fools don't learn from the past.

Market distance signs: a clear break

I used geographically-weighted regression to get location specific coefficients for market distance in the regression: Rent = wheat yield + market-town population + distance to market-town. As I have gone on and on about before, the theory is that there should be a negative sign for distance, because the further you are from your market, the more it costs you to truck your produce in on market day. The fact that this sign changes has been perplexing me...and there is something interesting going on here. Look at the map below.  Can you see that the locations to the west of that thick red line have a negative sign, those to the right a positive sign? I did put a marking on the map but it is a little faint. Wow! Such a clear boundary. But why is it there and not a few kilometres to the west or east for that matter? What are factors that decide the location of this line? Interesting!

Mountains and food security

Just been reading a really interesting article about food supply chains in mountainous areas. The ideas behind the article...in mountainous areas you rely more on your neighbours etc, could apply to any time period. The article is a bit light on theory and math, but it gave me the idea that perhaps Devon was unusually reliant on local food markets. That is why the sign for distance to market is so resolutely negative. So it is not Somerset that is the odd county out for having a positive sign for distance to market....it is Devon because Devon was a bit cut off (in more ways than one) and relied on its local food markets. Here is a map of population density and slopes. The population density I got by looking at the 1831 census and then dividing the number of inhabitants by the area of the county. Having less than one person per square kilometre seems unimaginably empty to us now.

You can see how fewer people and big slopes go together. So in Devon they would have felt pretty isolated, and so relied on their local market towns. I think I'll work on this theory for a bit. I've circled Devon in the map of southwest England below.

Density (in green) and slope (red for small, blue for big)

Water and wheat yield

I've been mapping topsoil water availability throughout the year and wheat yield. The relationship is clear: more water gives more yield. A more reliable indicator than rainfall. Here is a map with high water availability matched by high wheat yield.