WARNING: I will have to introduce some more tables, and also some little systems of equations, and I have not solved the problem of doing this gracefully in a blog. So I will scan the tables or equations and put them into the blog as pictures. My blog program insists on putting these scans at the beginning of the post rather than where I want them to be, so each time I need to insert one, I will close the blog post, post it, then create a separate post containing only the table or equations, post that, and then continue my text in yet another post. This is too stupid even to contemplate, but it is the only solution I can think of. My granddaughter is, alas, otherwise occupied. :)
We are now ready to engage with Ricardo's version of the Labor Theory of Natural Price [or Value], to see what it means, and to ascertain whether it is correct. For a variety of reasons, it is useful to change my original corn/iron model a bit by assuming that the surplus getters [capitalists, in this case] use a portion of the physical surplus to underwrite a sector devoted to the production of luxury goods. Technically, these are goods that require inputs of various sorts, but whose output is not required as input into either the corn or the iron sector. They are, in modern terminology, final goods. We could, of course, posit a sector devoted to the production of luxurious clothing or sporty cars or gourmet breakfast foods, but since we are explicating Ricardo, and therefore presumably analyzing the doings of stern, upright, seriously religious Protestant businessmen, I shall assume that the luxury good to which they choose to devote a portion of their surplus is theology books. By the way, some of you may be wondering why Corn Flakes and frozen Macaroni and Cheese dinners do not count as luxury goods, even though they, like theology books, are not used as inputs into any line of production, and thus are also final goods. The answer -- and it turns out to be super important, theoretically -- is that Corn Flakes and frozen Macaroni and Cheese dinners are wage goods -- i.e., things consumed by the labor producing sector, which is to say by the workers. Thus they do enter indirectly into the production of all the other sectors, because labor does. Way down the road, this is going to allow me to invoke a nifty theorem proved by John von Neumann to demonstrate exactly when Marx's sophisticated version of the Labor Theory of Value is true. I say this now just to keep up the spirits of the cognoscenti among you who may be yawning and wondering when I am going to get to the good stuff.
Here is the revised model: