On Wed, 21 Feb 2001, Fred B. Moseley wrote: > 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. Andrew's right, so far as I can see. Call the equations (1), (2) and (3) respectively. They simplify thus: (1) => (1.4) [0.5 p1 + 5/80 p3] = p1 (2) => (1.4) [ p1 + 5/80 p3] = 3 p2 (3) => (1.4) [1.5 p1 + 5/80 p3] = p3 So: (1) => 0.7 p1 + 7/80 p3 = p1 (2) => 1.4 p1 + 7/80 p3 = 3 p2 (3) => 2.1 p1 + 7/80 p3 = p3 Write P for the vector [p1, p2, p3]', and M for the coefficient matrix, such that MP = 0. Then M is -0.3 0 7/80 1.4 -3 7/80 2.1 0 -73/80 The system MP = 0 has a non-trival solution for P iff M is singular, but in this case |M| = -0.27, so there exists no non-trivial solution. Allin.
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