How does Ricardo justify this math? In Ch 5, Of Wages, Ricardo tosses this gem:


  if the labour of ten men will, on land of a certain quality, obtain 180 quarters of wheat, and its value be £4 per quarter, or £720; and if the labour of ten additional men, will on the same or any other land produce only 170 quarters in addition, wheat would rise from £4 to £4 4s. 8d.; for 170:180::£4:£4 4s. 8d.


That seems like a bold proposition to me, and I'm not sure where to look for the justification of that math.  

Is it earlier in Ricardo and I just missed it?  Is it intuitively obvious given some fact I just don't know yet?
Because in Ricardo's view, the money is neutral. The price reflects only the quantity of labor which is incorporated in the product. If it takes you 2 hours to hunt a deer and only 1 hour to hunt a rabbit then the deer will be two times more expensive. 

That being reminded, one can go back to Ricardo's example. First, we have 180 quarters of wheat that needed 10 men (which gave an output of 720£, at 4£ per quarter). But afterwards you have 20 men producing 350 quarters of wheat, which obviously takes into account the less productive land. Let's say we wanted to double up our first production with the new land: then we would in fact need about 21 men to meet our target of 360 quarters (2 x 180 quarters). But as you see this can't be worth 1 440£ , because there is mork work incorporated ! So there must be a new price for the quarter of wheat ...

Therefore the following question is: what shall be the new price ? One can turn that around into asking: how much more work is incorporated in the new production ? Well there is about 5% more work (1 man = 5% of the 20 that should be normally if there weren't any diminishing returns), which you can also find out by putting: 180/170 = 1,05 or 1+5%. If it is still not clear: this fraction represents the production advantage of the first land in comparaison with the second one. It is 5% more productive. Which means that you have to incoporate 5% more work to get the same production, which in returns, means the quarter of wheat has to be about 5% more expensive...