# [OPE-L:3176] Labor-Time and Money Values Compared

andrew kliman (Andrew_Kliman@msn.com)
Sun, 29 Sep 1996 08:40:57 -0700 (PDT)

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In ope-l 3175, Jerry wrote

"why couldn't TSS and other interpretations develop *two* sets of numerical
illustrations -- one set assuming a constant value of money and one set which
does not? It might then be interesting to compare the results."

Interpretations don't develop illustrations. People do. For instance, I, who
have already fulfilled Jerry's request, piecemeal, in my recent posts. For
everyone's convenience, I have cut and pasted the whole thing below, in one
place.

We are considering, in Duncan's words, "a purely circulating capital, one-good
model in which it requires a(t) units of output in period t-1 to produce 1
unit of output in period t."

To take one extreme example, assume that
1. a(t) = a(t+1) = 0.8, a constant
2. workers' consumption is zero
3. the living labor extracted is period is constant
4. the growth rate of output is 25%
5. \$1 = 1 hour of living labor
6. in the initial period, period 0, 4 units of the commodity and 100 units
of living labor are used to produce 5 units of the commodity
7. in the initial period, the input and output prices are equal

The following are the labor-time value magnitudes that the TSS and
simultaneist interpretations derive from these assumptions, except that
assumption 5. is not needed by either. In other words, in both sets of
interpretations, the following labor-time value magnitudes ALWAYS obtain, no
matter what the money/labor-time relation [value of money; monetary expression
of value; monetary expression of labor; labor-time expression of money, etc.]
may be or how it may vary over time.

LABOR-TIME VALUE MAGNITUDES
--------------------------------------------------

TSS Interpretation
---------------------------------------
year C V+S C+V+S
0 400 100 500
1 500 100 600
2 600 100 700
3 700 100 800
etc.

All Interpretations Except TSS
---------------------------------------
year C V+S C+V+S
0 400 100 500
1 400 100 500
2 400 100 500
3 400 100 500
etc.

Due to assumption 2., these figures imply that the simultaneist or "commodity
numeraire" profit rate equals 25%, throughout all time, when measured as a
ratio of labor-time magnitudes. The temporalist rate starts at 25% and
monotonically falls, approaching zero at time goes on.

Given assumption 5., these figures, in both sets of interpretations, are also
the value magnitudes in money terms. Hence, the rates of profit, measured as
ratios of money magnitudes, will be the same as the labor-time profit rates.

Now drop assumption 5., and assume instead that one unit of the commodity
always has the money price of \$100. The first 4 years of the TSS table are
given below. The top rows are the labor-time values. The middle rows are
the money values of output (C+V+S) and constant capital (c) , and money-value
"added" by living labor, found by subtracting the money-value of constant
capital from the money-value of output. The bottom rows are the derived
money/labor-time relations (monetary expressions of value).

TSS LABOR-TIME AND MONEY VALUE MAGNITUDES,
WHEN MONEY PRICE PER UNIT IS CONSTANT
-----------------------------------------------------------------------------

year C V+S C+V+S
0 400 hrs. 100 hrs. 500 hrs.
\$400 \$100 \$500
\$1/hr. \$1/hr.

1 500 hrs. 100 hrs. 600 hrs.
\$500 \$125 \$625
\$1/hr. \$1.0417/hr.

2 600 hrs. 100 hrs. 700 hrs.
\$625 \$156.25 \$781.25
\$1.0417/hr. \$1.1161/hr.

3 700 hrs. 100 hrs. 800 hrs.
\$781.25 \$195.31 \$976.56
\$1.1161/hr. \$1.2207/hr.

The nominal (money) profit rate would be a constant 25%, given v = 0. The
labor-time profit rates are as I reported before. If one uses the monetary
expressions
of value to deflate the money-value figures, of course, one arrives back at
the labor-time profit rates.

Andrew Kliman