In ope-l 4133, Alejandro Ramos wrote:
"I would appreciate that Andrew posts 'his example' containing a couple of
tables in which we can see clearly the different calculations yielding both
the "replacement cost" rate and the "expected rate of return". Now, it is a
little bit involving to follow Andrew's post. Please, tell us if this
corresponds to the tables that I and Rieu worked out.
"An elementary algebra definitions of both rates would also be useful.
"I guess that this WAS discussed and illustratED some months ago, but there
are NEW listmembers (like Rieu and I) who
never saw these tables, examples and formulas. (Always it is useful to
distinguish between t and t+1, or t-1 and t!!)"
I am bemused. I was referring to the example I put forth in ope-l 4046.
Alejandro himself posted the *correct* solution in ope-l 4051. Here are his
"replacement cost" profit rate and expected rate of return computations,
respectively:
------------------------------------------------------
Physical Unit Income Cost Profit
Output Price Price Rate(*)
------------------------------------------------------
A 100 $1.10 $110 $100 10%
B 100 $1.08 $108 $100 8%
------------------------------------------------------
(*) [(Income)/(Cost-price)]-1
--------------------------------------------------------
Physical Unit Income Cost Profit
Output Price Price Rate
--------------------------------------------------------
A 100 $1.0890 $108.90 $100 8.90%
B 100 $1.0908 $109.08 $100 9.08%
---------------------------------------------------------
Why are the numbers in the upper table "replacement cost" profit rates? Well,
they assume that prices in one year will be the same as today's prices.
Hence, in effect, they compute both today's costs and next year's revenues
using today's prices. That is exactly what the "replacement cost" profit rate
does: it uses the same price vector to value all inputs, including fixed
capital, and all outputs. The usual claim is that the "replacement cost"
rate using prices of time t is the basis for firms' investment decisions at
time t. Rieu's new example, however, uses the expected prices of the
following year instead. What physical quantities are to be used in the
calculation is generally not specified (and this is a big problem). It is
impossible, therefore, to give a unique algebraic definition of this alleged
profit rate.
The actual expected rate of return is computed exactly as Alejandro did in the
lower table, given that we're working with the assumptions of my example.
With fixed capital, or a difference between per-period and annual profit
rates, it is more complex.
Andrew Kliman