Derivation of a Negative PNP
Simon Mohun (2003) has argued that Kliman (2001) did not “show[ ] conclusively” that a negative price of the net product (PNP) is “economically possible in the sense of arising out of economic behaviour” (p. 98). The following two examples derive a negative PNP in precisely the manner that Mohun insists upon, and thereby demonstrate that a negative PNP is indeed “economically possible” in his sense.
In both examples, there are two sectors (1 and 2) in the economy. Wages are part of advanced capital, and aij and lj are the amounts of good i, and of living labor, needed to produce a unit of good j. There is no fixed capital. The price of good 1, the money commodity, equals 1, and P2 is the price of good 2. The gross output of good j is Xj, and the normal output level of each good exactly satisfies the demand for it.
Example 1. All aij = a < 0.5, and both lj = l. The money wage rate per unit of living labor is w < (1 – 2a)/l. Normally X1 = X2, and since a < 0.5, both goods’ net products are positive. Today, however, good 2’s net product is negative (X2 < a(X1 + X2)), because of a one-day work stoppage in part of sector 2. If profit rates were equalized, then P2 would equal 1 and the profit rate would be positive, which implies that the PNP would be positive as well. Yet sector 2 is a regulated monopoly. Because of a data entry error, the regulatory authority has set P2 at a level such that P2 > (X1 – a[X1 + X2])/(a[X1 + X2] - X2) > 1, and thus the PNP is negative.
At day’s end, statisticians at the regulatory authority discover the error and P2 is lowered to 1. Thus the profit rate will be positive and equal in both sectors, starting tomorrow. Moreover, sector 2’s low activity level was only temporary, and sufficient reserve stocks of good 2 exist, so production can resume tomorrow at levels that once again match demands.
Example 2. Workers’ consumption in both sectors is 1/202 units of good 1 and 1/202 units of good 2, per unit of living labor, a11 = a22 = 0.1, a12 = a21 = 0.89, and l1 = l2 = 0.01. Capitalists maximize internal rates of return (IRR), and the IRRs are continually equalized. During the daytime, X1 = 1 and X2 = 99; during the nighttime, X1 = 99 and X2 = 1. (The alternating output levels result from profit-maximizing choices. It is expensive and unprofitable to hire workers at night, so both sectors produce during their daytime only. But almost all of sector 2 is located 12 hours away from where almost all of sector 1 is located.) Periods are one-half-day long. In period 0 and before, the economy is in a static equilibrium. P20 = 1, the IRR = 1%, and the PNP is positive. (P2t, the output price of good 2 in period t, is its input price in period t+1. P2t, the other data, and the equal-IRR condition suffice to determine P2t+1.)
Yet beginning in period 1 (a daytime), sector 1, an extractive industry, experiences a technical regress; 0.11123 < a11’ < 0.11969. The economy quickly converges to a new static equilibrium in which the IRR and thus the PNP are again positive. Nonetheless, the path of P2 is such that the PNP is negative at least during period 1 and perhaps through period 18.
References
Kliman, A. 2001. “Simultaneous Valuation vs. the Exploitation Theory of Profit,” Capital and Class 73, Spring.
Mohun, S. 2003. “On the TSSI and the Exploitation Theory of Profit,” Capital and Class 81, Autumn.