Let me clarify a few things before we get to Nick’s post. As I argued in a previous post, classical authors (e.g. Smith, Ricardo and Marx) understood that they needed to determine the rate of profit independently from relative prices to avoid circular reasoning. The Labor Theory of Value (LTV) provided a solution. Prices were determined by labor incorporated (or commanded for Smith) and profits, and the surplus, were determined on that basis [Sraffa’s solution to the problems with the LTV build on Ricardo’s use of a commodity, corn, to measure the profit rate as a ratio of two physical quantities]. However, most neoclassical/marginalist authors today are completely oblivious to the fact that their theory too must deal with the independent determination of the rate of profit and relative prices, and that this is problematic if you also accept the notion of a uniform rate of profit (a natural rate of interest).
Also, and before I show why the problem is a general one, that any theory has to deal with it is essential to note that the rate of profit and the rate of interest must be in the proverbial long run (when everything is flexible and there is no ceteris paribus) in equilibrium. That is, either the rate of interest adjusts to the rate of profit (the position taken by Ricardo and Wicksell, which called the real variable the natural rate of interest), or vice versa (as Tooke and Sraffa believed; Marx and Keynes pose more problems to be clearly defined, but I would put them in this camp too).
In the case of neoclassical economics, if you want to determine the natural rate of interest by the interaction of the discounted profitability of investment and the intertemporal savings (i.e. consumption) decisions of agents, you must be able to bring the gains to present value (as in the examples provided by Nick). That means that the discount rate (to bring the investment schedule to present value) must be known, while the rate of interest you want to determine requires knowing the value of investment (the demand for capital goods). Thus, we encounter the circularity of the determination of the natural rate of interest in the Loanable Funds Theory, noted by Joan Robinson long ago.
Note also that the process implies that the rate of interest (which in equilibrium is equal to the rate of profit) is a variable that is determined by intertemporal decisions, which must equalize the rate of profit associated with the production of capital goods (i.e. produced means of production). What happens if, as Nick suggests, “There isn’t just one future period; there are many future periods.” Nothing much really happens, since for all those possible future periods, there must be a uniform rate of profit. For several different capital endowments, or several different sets of preferences (which seems to be what Nick has in mind), the interaction of investment and savings will solve for the rate of interest. But the inconsistency is still there.
But really what Nick is suggesting is that one might have a multitude of interest rates (which he refers to as the term structure, but think more of a term structure of interest rates associated with different capital goods, rather than financial ones, even if you do have monetary rates too). In fact, that is exactly what the mainstream did, when they changed the notion of equilibrium, as noted by Garegnani in his 1976 paper. It was only then, after the capital debates, that the Arrow-Debreu (AD; not Anno Domini) intertemporal general equilibrium notion became dominant. In that case you must give up the notion of a uniform rate of profit. Note that you cannot have both (in his replies to my comments Nick seems to believe that you can have it both ways; scroll down for the various comments which are worth reading I might add).
“I hadn't realised, until I read your comment just now, that *maybe*, when some people talk about “uniform rate of profit”, they mean something very different to what I thought they meant. I thought they meant: A uniform rate of profit across different industries (adjusting for or ignoring risk). But you seem to mean: A uniform rate of profit across different periods of time (i.e. a flat term structure). I would say that arbitrage is what creates a uniform rate of profit across different industries (or different assets). I would say that *nothing* creates a uniform rate of profit across different periods of time. The term structure is not (in general) flat. It could slope either up or down, or wiggle around. Even if we are talking about Wicksellian “natural” rates of interest. E.g., if everyone wants to go on a big consumption binge every 7 years, and fast for the remaining 6 years, (and if everyone knows about this), we are in general going to see a big spike in the term structure at 7 year terms.”
So what does that mean about the term structure? First, the term structure of monetary rates (i.e. the Fed Funds versus the ten year Treasury bonds) depends on the actions of the central bank, among other things (and I’ll let that for another post; mind you as you see I tend to think the monetary rates rule the roost, as Tooke and Sraffa). Nick is talking about the real or natural rate, having for reasons associated with the demand (the preferences about consumption in the future) different levels. That is, there would be more than one natural rate, associated with different preferences regarding consumption [echoes of the Sraffa-Hayek debate about the existence of several own rates of interest perhaps].
Yet, the point still is whether you have competition (free entry) or not. So if more people, as in Nick’s example, want to consume more in 7 years, wouldn’t the supply of capital adjust, to provide more in that year allowing for the consumption binge, and reduce the gains associated with providing more goods in that period? After all there is no reason for profitable opportunities, unless there are imperfections (e.g. lack of capital mobility or lack of information, which does not seem to be what Nick is arguing, since he says that "everybody knows"), to be left unfulfilled. The intertemporal nature of the decisions, meaning the decisions are being made now with all the information available about the future, does not affect the equalization of the rate of profit (interest). So competition should also lead to a uniform rate of profit not across different periods of time, but now for different states of preferences and the capital endowments (and technology of course).
Hence, the existence of a myriad of capital goods, or changing preferences (or technological change, which used to be the one that the capital debates concentrated more), do not per se justify abandoning the notion of a long term uniform rate of profit. That is what the AD model does. In the process it abandons the classical notion of competition (free entry) for one that has less meaning from the point of view of understanding capitalism (atomistic agents that are price takers; both links to the New Palgrave require subscription I'm afraid).
Note that the centrality of the results of the capital debates is that one cannot say that changes in relative prices govern decisions about the allocation of resources in any clear way. Not only capital will not be used more intensively with lower rates of interest (even if lower rates of interest may stimulate other forms of demand, not capital, and eventually lead to more demand for means of production), but also lower real wages (the relative price of labor force) might not lead to higher employment. Think of the policy implications of this result for Europe now.
But let me finish saying that beyond the differences we might have, real or of interpretation (and I think both things play a role), I think it is important to thank Nick for thinking about the relevance of these issues and taking them seriously, which can only lead to clarify differences and provide a better understanding, if not of the real world, about what economists think about the real world. And that is a step in the right direction.