**3.0 Price System**

In the first part, I present quantity flows per worker for three island economies facing the same technological possibilities. By assumption, these island economies have adpated production to requirements for use. Since the wage happens to be the same on all three islands, profit-maximizing firms have adopted the same technique of production. The prices that prevail on these islands are stationary. Assuming the wage is paid at the end of the year, the price system given by Equations 1 and 2 will be satisfied:

(1)

(2)where

*p*is the price of a bushel rye,

*w*is the wage, and

*r*is the rate of profits. I have implicitly assumed in the above equations that the price of a bushel wheat is $1.

The wage can be found in terms of the rate of profits:

(3)More work is required to express the rate of profits in terms of the wage:

(4)The price of rye, in terms of the rate of profit, is given by Equation 5:

(5)

Suppose the wage, assumed identical across all three islands, is $ 3/8 per person-year. Then the rate of profits is 100%, and the price of rye is $ 2/3 per bushel. On Alpha, workers consume their wages entirely in rye. Consequently, each worker eats 9/16 bushels rye each year. On Beta, workers consume only wheat. A Beta worker eats 3/8 bushels wheat per year. Gamma is an intermediate case where workers consume three bushels rye for every bushel wheat. A Gamma worker eats 3/8 bushels rye and 1/8 bushels wheat each year.

Note that the quantity flows specified previously show the wage entirely consumed and profits entirely invested. This characteristic of the example is not necessary to the conclusion that the difference in tastes among the islanders need have no effect on prices.

**4.0 Conclusion**

Under the conditions satisfied by this example, different tastes have no influence on prices. If the economy is fully adapted to different tastes, the same prices can prevail.

## 11 comments:

Surely this is a long term result? In the short term price would not equal exchange value and so demand would influence price until such time as supply adjusted.

From a neoclassical perspective, the post can be said to illustrate a "long run" or "long period" model. In a long run model, the initial quantities of capital goods are variables, not given parameters of the model. The post is a component in an argument that the domain of supply and demand does not extend to the long run.

By the way, Varian's exposition of the non-substitution theorem in his intro grad micro text is quite confused. I think Varian is so unclear that one cannot even talk about whether he is correct or incorrect. I refer to the 2nd edition.

Why do you prefer specific examples in your exposition rather than a more general mathematical proof of your result?

A more general proof of some claim or another has the advantage of making it easier to investigate the causes of the phenomenom (in this case the independence of prices on tastes). But with specific examples one is left almost completely in the dark about the causes.

I don't think that this sort of exposition makes for an easier reading either -- quite the opposite.

Secondly, why didn't you make it clear that this result (independence of prices from tastes) depends crucially on there being a single primary (non-produced) good -- in this case a single type of labor?

With this fact in mind it becomes clear that this sort of example has nothing to do with real world economies or even with economic models that try to capture more complex aspects of reality.

Perhaps a mathematical proof would have made the conditions under which this result holds clearer.

Odd. I was under the impression that neoclassical economists, at least, take preferences as given. I don’t see why I should not strive to put points across without exceeding junior high school math, if I can.

I don’t know why the anonymous commentator thinks the example depends crucially on “there being a single primary (non-produced) good”, as opposed to depending on there being, for example, no fixed capital. (Fixed capital is a kind of joint product.) I plan on putting forth an example with joint production sometime in the future.

Apparently, the anonymous commentator objects to the way national income accounts are kept. They are often (e.g., by the OECD) presented in terms of Leontief input-output matrices, with only labor appearing as a non-produced parameter. I don’t see why I should not present examples that emphasize properties that should be seen in models based on standard national income accounting.

Anyways, I present examples to help give readers, if any, guidance to some aspects of more advanced literature that I find of interest. For example, the von Neumann model of growth has only labor as a non-free non-produced input. Some have said von Neumann’s paper (which does include joint production) is the greatest work of mathematical economics produced in the 20th century. It is certainly deep.

What I find interesting is often driven by how unclear and nonsensical the teaching of economics seems to me to be in many universities. In the next post, I echo a criticism by Kurz and Salvadori related to my post.

So neoclassical economists can not enquire further into the (perhaps higher order) motives behind one's preferences? I don't think that this is in any form a consequence of neoclassical economics -- but then I'm not a neoclassical economist.

"I don’t know why the anonymous commentator thinks the example depends crucially on “there being a single primary (non-produced) good”, as opposed to depending on there being, for example, no fixed capital."

The two conditions are not "opposed." The independence of prices on tastes can depend crucially on there being a single primary good and also depend crucially on there being no fixed capital. I just mentioned one condition which is crucial for the result, and I asked why you didn't mention it yourself, given that such a condition deprives the result of relavance to both the real world and to more complex models.

The answer that you reflect a criticism of teaching practices in neoclassical classes is satisfactory[1] but they may also be interpreted --perhaps incorectly-- as you saying that you think the models that satisfy the "non-substitution conditions" (and not some generalizations of the models) are actually useful for understanding the real world.

Sadly, I don't think that national accounting practices count as serious economics. I also don't think that von Newman's paper is great or deep because it uses just one type labor as the only non-produced good -- it may be all those things despite it.

Alex

1. I have in mind the phrase from your next post:

"[S]everal ‘classroom’ neoclassical models, for didactical reasons, are based precisely on the set of simplifying assumptions … underlying the theorem without however arriving at the conclusion that demand does not matter…"

I wrote:

"The answer that you reflect a criticism of teaching practices in neoclassical classes is satisfactory[1] but _they_ may also be interpreted"

The "they" above refers ungrammatically to your remarks in the blog post "No Influence of Tastes on Prices part 2"

Alex

I accept the criticism on my saying the two conditions are "opposed". I should have written, "in contrast to", not "as opposed to".

I did not mean to imply that von Neumann's paper was great or deep "because" it uses one type of labor. It's deep for other reasons.

By the way, some might find puzzling my description of the paper. Von Neumann does not explicitly list labor as an input at all. He describes all inputs as being produced goods. One can, however, think of some inputs as being consumed out of the wages of the workers, much like the feed of horses would be an input. This interpretation goes back to Champernowne's 1945 commentary, published simultaneously with the English translation.

Don't know about Varian (I think I'm one of the few people left in this world who's never used that book) but here's Mas-Collel et. al. (after a mathematical statement and proof of the NST):

"The nonsubstitution theorem depends critically on the presence of only one primary factor. This makes sense. With more than one primary factor, the optimal choice of technique should depend on the relative prices of these factors. In turn, it is logical to expect that these relative prices will not be independent of the composition of final demand (e.g. if demand moves from land-intensive goods toward labour-intensive goods, we would expect the price of labor relative to the price of land to increase). Nonetheless, it is worth mentioning that the nonsubstitution result remains valid as long as the prices of the primary factors do not change."

The result of the theorem is not surprising, since you are considering the exchange of commodity goods, which by definition exchange at a price proportional to labor plus raw materials. You would have to prove that the same holds true for items that have a large IP (intelectual property) component, for example. Additionally, if island B cannot eat barley due to religious reasons, the exchange rate will not be the same. The theorem is based on too many assumptions to be of any universal applicability.

The result of the theorem is not surprising, since you are considering the exchange of commodity goods, which by definition exchange at a price proportional to labor plus raw materials. You would have to prove that the same holds true for items that have a large IP (intelectual property) component, for example. Additionally, if island B cannot eat barley due to religious reasons, the exchange rate will not be the same. The theorem is based on too many assumptions to be of any universal applicability.

wait a minute! you have chosen arbitrary volumes of rye and wheat consumed by the islanders, to fit your assumption that the price does not vary with taste. But why would one islander consume 9/16 bushels of rye, while the other consumes 3/8 bushel of wheat, and yet another 1/8 and 3/8?! Assuming that both cereals have the same caloric content (humor me, your theorem is FULL of assumptions), then they would be consuming widely different amounts of food. This is unlikely in real life. It is more likely that islander alpha would eat 3/8 bushels of rye, beta would eat 3/8 bushels of wheat, and gamma would eat 1/8 rye, and 1/2 wheat (equal volumes of food). Under those conditions, since the combined value of 1/8 rye and 1/2 wheat on island gamma, has to be equivalent to the value of 3/8 rye on island alpha (otherwise the wages do not remain equal), then the individual prices cannot be the same. The price of rye and wheat will vary on each island, depending on the proportion of one and the other workers prefer to consume.

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