Dear Drewk, You write: " It is only >when input prices are constrained to equal output prices, a >constraint I reject, but which Fred embraces, that prices and the >rate of profit are functionally determined solely by physical >quantities." It may be that a necessary condition (it is only when) of this determination is what you say. But I was questioning whether this was sufficient. In a Sraffa simultaneist system, for example, the wage is a share along with profits, and prices can vary independently of the physically specified techniques of production. But you suggest that: > " a change in >the money wage rate entails a change in another set of physical >quantities, namely the components of workers' consumption. > >Formally, if we denote the money wage rate as w, the vector of >prices as p, and the bundle of workers' consumption components as >the vector b, workers' budget constraints are w = pb, so a change >in w entails a change in b. > >It thus remains the case that simultaneist prices and the rate of >profit cannot vary unless physical quantities vary." This may be so, if the changes in prices consequent on a change in w don't leave b the same, or if there is no workers' saving (which most models assume for the sake of simplicity, and you assume above, though this assumption is not inherent in simultaneist models). But there is no specific variation of physical quantities in the model. We can't read off the model what changes occur in b. I would have thought that your model's price variations would also have had similar effects on physical quantities in this sense. " What I take >you to mean is this. Prices and the average profit rate WOULD >fluctuate around the static equilibrium prices and the static >equilibrium profit rate IF technology were not changing (rapidly >enough). IN FACT, however, prices and the average profit rate DO >NOT fluctuate around the static equilibrium prices and the static >equilibrium profit rate, because technology DOES change (rapidly >enough). In other words, the static equilibrium profit rate is >not the average profit rate that prevails at any moment, nor even >the time-average of the average profit rate. This is pretty well what I meant. I like the classical model of competition that Dumenil and Levy produce in the paper on competition. They point out that full equilibrium prices of production are the end of a rather long adjustment process. They model responses to changes in supply and demand, starting with price adjustments to get a baslance of supply and demand in one sector, going on to equalisation of profit rates between sectors, and ending with the weeding out of all but the optimally profitable technique. Clearly this process cannot actually reach full equilibrium prices of production if technological change occurs within the time frame of their model (the length of the weeding out process depends on the strength of producers reactions to changes in supply and demand and changes in prices, with all of these reactions having to be fairly moderate if the process is to be stable). Of course, Marx's proces of production cannot be these full equilibrium prices, since Marx clearly envisages that there will be a multiplicity of techniques. Would your TSS model take prices of production as a stage in D-L's process of price adjustment under competition from supply-demand balance in a given sector to equalisation of profit rates across sectors? " >But once one DOES understand this -- and this is a question for >you -- of what use and what significance are the static >equilibrium results? They don't describe or predict what actually >occurs, nor do they even describe or predict what actually occurs >once we abstract from accidental factors and fluctuations that >compensate for one another over time. So what good are they? > >Take the following simple one-sector case, for example. Define >the relative rate of variation in the unit price as > >H[t] = (P[t+1] - P[t])/P[t], > >where P[t] and P[t+1] are the unit input and output prices of >period t. > >Assume the time-path of H is > >H[t+1] = -2H[t] - 50(H[t])^2 . > >Assume further that 10 units of corn input are required to produce >every 11 units of corn output. Then the rate of profit is > > (11P[t+1] - 10P[t])/10P[t] = 1.1(1+H[t]) - 1. > >Now the static equilibrium value of H is 0 (there is also another >fixed point, H = -0.06), so the static equilibrium profit rate >equals > >1.1(1+ 0) - 1 = 0.1 = 10%. > >However, for H[0] not too far from 0, H behaves chaotically and >averages -0.02. > >The rate of profit thus also behaves chaotically and its *average* >over time is 7.8%. This is 22% below its static equilibrium >value. Simulations indicate, moreover, that two-thirds of the >observations are below the static equilibrium value of 10% and >only one-third are above, instead of half and half. > >So who cares what the level of the static equilibrium profit rate >is? What use does it have? What does it tell us about the actual >economy?" I think I take your point here. But a tendency can be useful. Take a moving target on a shooting range. At any point in time, it will not be the poiunt around which all shots cluster. Even so, it is useful to have the idea of a point around which, at any time, shots will tend to cluster in understanding why the pattern of shots takes the form it does. However, as your example and a number of people have shown, the matrices of classical price models are "chaotic" in the sense that relatively small changes in their inputs can produce quite large changes in the vector of prices. Technological change change need not be a "smooth" process at all. So, as I understand your point, in principle knowing a moving target that jumps discontinuously may not have the same predictive value as a target that changes continuously. Of course, examples are one thing but a model of real processes can be another. Any classical theory of technological change will have to come up ways of limiting price changes. Perhaps we should all understand TSS as a proposal to have a theory simply of competition (such as D-L's) with market prices tending toward some point along their adjustment path? >I still haven't answered your question about why Fred should be >worried about Alan Freeman's demonstration. The answer is this. >Although, as we agree, Fred's (physicalist) profit rate is not the >actual "center of gravitation," when MARX referred to the general >or average rate of profit, he WAS referring to the actual "center >of gravitation." Hence Fred's average rate of profit and his >associated prices of production are NOT the same as Marx's. This >is contrary to what Fred has claimed, so he should be worried. > >Moreover, Alan's paper also shows (by means of Monte Carlo >simulations) that temporally determined prices of production and >average profit rate are indeed the "centers of gravitation" of >actual prices and profit rates, even when technology is changing. >This is also contrary to what Fred has claimed, so, again, he >should be worried. I haven't seen Alan's Monte Carlo simulations, so I can't saywhether they would also prove that other forms of price of production are "centres of gravitation". As to whether Fred's prices of production are Marx's, is there any clear answer to this? After all, Marx did not separate out the issue of equilibrium (or various forms of quasi-equilibrium) prices of production. Perhaps if the implications for the price system of technological change had been clearere to him, he would no longer say that prices of production are "centres of gravitation", Cheers, Ian Associate Professor Hunt, Director, Centre for Applied Philosophy, Flinders University
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