Hi, Fred. In reply to your OPE-L 5020: "You are right that in my example I assumed the money wage as given rather than the real wage, as in Steedman." That isn't the issue. It doesn't matter what was given. You could have assumed a given money wage of 0.2685; you would have gotten the same physical quantities as Steedman -- and also the same prices and profit rate. "However, I think what my example shows, at least, is that, if the money wage is taken as given, then a given set of physical inputs and outputs and the assumption of "stationery prices" does not uniquely determine the rate of profit." This is a red herring. No one has ever claimed that "a given set of physical inputs and outputs" is enough. The physicalists are always careful to specify that the technical AND REAL WAGE coefficients, together, uniquely determine the relative prices and profit rate. If your full set of physical quantities --technical AND real wage coefficients -- are the same as the physicalists', so too will be your relative prices and profit rate. That's because of your simultaneous determination of prices. "My example shows that, with a given money wage, at least two rates of profit are compatible with the given physical structure and the assumption of "stationery prices" (and we could compute more)." No. The physical structure includes real wage coefficients. "there are an infinite number of rates of profit that are compatible with the given quantities of inputs and outputs." Of course, but again, that's a red herring. There's only one simultaneist uniform profit rate compatible with the given quantities of inputs, outputs, AND real wages. "unfortunately, the system of equations is more difficult to solve under the assumption of a given real wage. ... I will get some software soon, and then we shall see whether the result still holds under the assumption of a given real wage. "In the meantime, perhaps another listmember who has the software can solve this system of equations for us and let us know the results. "Assuming to begin with that the rate of profit = 0.4, the equations are: (1.4) [28 p1+ 56 (5/80 p3)] = 56 p1 (1.4) [16 p1+ 16 (5/80 p3)] = 48 p2 (1.4) [12 p1+ 8 (5/80 p3)] = 8 p3 Please solve for the three prices." The reason you're having trouble solving this, Fred, is that it can't be solved (for positive prices). The top equation gives us p1 = (49/168)p3. The bottom gives us p1 = (73/168)p3. Obviously, the only solution is that p1 = p3 = 0, which would also make p2 = 0. Apart from that solution, there isn't one. For positive prices, the top and bottom equations are inconsistent. The reason for the contradiction? You're using the wrong profit rate. There is only one simultaneist profit rate that corresponds to the full set of physical quantities. Steedman's. 52.08%. "And then assume the rate of profit = 0.25, replace the 1.4 in the above equations by 1.25, and solve for the three prices again. Thanks in advance for any help." The top equation gives us p1 = (25/120)p3. The bottom gives us p1 = (59/120)p3. Again, the system cannot be solved, except with zero prices all around. But that would make v = 0. Jerry would not be pleased. "Logically I don't understand why this system of equations would not be solvable for different rates of profit. This is a system of three equations in three unknowns, which should in principle be solvable." Not necessarily. It isn't solvable if two or more equations are inconsistent, as your 1st and 3rd ones are. A simpler case of the same problem is x + y = 0 x + y = 1. Again, no solution. To eliminate the inconsistency, you need to either (a) Use 0.5208, Steedman's rate, as your rate of profit or (b) Rewrite the equations so that the input prices and the output prices differ. Those are the only options, given the same physical quantities as Steedman's. "Andrew, I don't understand why you think that the money wage rate is not equal across sectors. The money wage rate is assumed = 1 in all sectors. From which it follows that the real wage rate will also be equal across sectors, since the real wage rate = 1 / (price of corn). Thanks for the clarification." I plugged in your prices and profit rate, and solved for w in each equation. I may have made an error. It doesn't matter, because the inequality of the wage doesn't matter. What matters is that you had a different real wage from Steedman, which caused your prices and profit rate to differ. Ciao, Drewk Andrew ("Drewk") Kliman Dept. of Social Sciences Pace University Pleasantville, NY 10570 USA phone: (914) 773-3968 fax: (914) 773-3951 Home: 60 W. 76th St. #4E New York, NY 10023 USA "The practice of philosophy is itself theoretical. It is the critique that measures the individual existence by the essence, the particular reality by the Idea."
This archive was generated by hypermail 2b30 : Thu Mar 01 2001 - 14:01:39 EST