"Increasing returns isn't the correct term. Nonconvex production set is what I'm guessing."
I think that explanation is wrong. I pointed out in the comments that the numeric example is not a reswitching example. Radek comments on this observation:
"I think Metcalfe and Steedman emphasized reswitching as necessary for this kind of result then later folks realized that reswitching wasn't it. But like I said, I'm not too familiar and it's been awhile.
Ok - I think I found the MS article and will read up on it (JIL May'77)."
The phrase "this kind of result" is doing too much work here. As I mentioned, Metcalfe, Steedman, and others have a variety of criticisms of the logic of HOS theory. The criticism illustrated by my example is from Metcalfe and Steedman (1974). Steedman and Metcalfe (1977) is a different criticism, a criticism that stretches my knowledge of trade theory by the by. They conclude:
"We have examined a version of the familiar H-O-S analysis, with two countries, two commodities and two factors; we have made all the normal assumptions except that, instead of a common zero rate of profit, we have assumed a common positive rate of profit. Since the existence of a positive profit rate does not affect the properties of the familiar relationship between commodity-prices and factor-prices it does not affect the factor-price-equalisation and Stolper-Samuelson theorems. In general, however, nothing can be said a priori about the relationship between factor-prices and the factor-intensity of production methods, when the profit rate is positive, and it follows that nothing can be said a priori about the shape of the relative supply curve. This does not prevent the H-O-S theorem about the pattern of trade from holding in its 'quantity' form, but does make the theorem invalid in its 'price' form, does mean that trade need not 'harm' a country's scarce factor, and does mean that uniqueness of international equilibrium is to be regarded as a special case when the common rate of profit is positive." - Steedman and Metcalfe (1977)
The demonstration in Steedman and Metcalfe (1977) draws on an earlier analysis of a closed economy, Metcalfe and Steedman (1972). Here M. and S. present a reswitching example with two homogeneous unproduced inputs, labor and land. They find, at a certain given positive rate of profit, that the technique of production that minimizes cost at the higher ratio of the rent to wage will be more land-intensive. I think of this example as analogous to one of capital-reversing. It too is destructive of supply and demand explanations of prices.
I don't recall if they say so explicitly, but this article certainly gives the impression that this counter-intuitive result - at least to those who believe in the out-dated neoclassical theory of value and distribution - is due to the presence of reswitching. If I recall correctly, this result was later shown to be compatible with the absence of reswitching. I believe Steedman selected the article first demonstrating this compatibility for republication in Steedman (1989).
If I ever get around to discussing recent empirical results on the labor theory of value, I will point to some criticisms of Steedman.
Update: Radek reminds me that Montet (1979) demonstrated that the results in Metcalfe and Steedman (1972) and in Steedman and Metcalfe (1977) are compatible with the absence of reswitching.
- Metcalfe, J. S. and I. Steedman (1972). "Reswitching and Primary Input Use", Economic Journal (Reprinted in Fundamental Issues in Trade Theory (edited by I. Steedman), Macmillan, 1979).
- Steedman, I. and J. S. Metcalfe (1977). "Reswitching, Primary Inputs and the Heckscher-Ohlin-Samuelson Theory of Trade", Journal of International Economics (Reprinted in Fundamental Issues in Trade Theory (edited by I. Steedman), Macmillan, 1979).
- Metcalfe, J. S. and I. Steedman (1974). "A Note on the Gain From Trade", Economic Record (Reprinted in Fundamental Issues in Trade Theory (edited by I. Steedman), Macmillan, 1979).
- Montet, C. (1979). "Reswitching and Primary Input Use: A Comment", Economic Journal, V. 89, N. 355 (Sep.): 642-647.
- Steedman, I. (editor, 1989). Sraffian Economics (2 volumes), Edward Elgar.