The Solow Growth Model for Eternity
The geo-famed Solow growth model is built for Eternity over the River, wittingly or otherwise.
First
of all, the so-named growth model does not have the time dimension. As an ABC
in macroeconomics, the growth in GDP is defined to be (Δlog Y)/ Δt. Voila, there in "growth" certainly is the time dimension
in the negative (T-1, T for time dimension). Incidentally, the negative sign enters in the equation for the purpose of
performance evaluation only.
Take the marathon vs. the 100 meter dash
for example. The length (L1 in the space dimension) of running of
the former is larger than that of the latter by many “orders of magnitude,” so
to speak. You know what? The Solow model predicts that always and everywhere, “The
winnerrrrrrr is the marathoner!” The running speed is just irrelevant, or more precisely
the time duration (Δt) does not
count.
Likewise, the GDP will certainly
grow 10,000 times greater in Eternity with no lapse, or no relevancy at least, of
time (T0). RIP over the River!
Let us return to the law of
diminishing returns as the crown jewel of the Solowian approach. The law is envisioned
for cross-sectional or cross-scenario measurement (L-1), never for longitudinal
or over-time (T-1). On the sidewalk exogenous to macroeconomics, most
every grownup would know that the space dimension is one the time dimension is
another
Moreover, the law applies to the
production scale (in the physical quantity) at a defined job at the firm with the given capital stocks. There is no guarantee whatsoever that the
law will hold true across machines (alternatives), firms (productivity), products
(value of utilities) or time (innovation and taste changes). In the first
place, would anyone outside of classrooms keep investing in steam engines?
Most-over, ever since the turn of
the 20th century (not 21st), the lion’s share of GDP has
been taken by services. By nature, the “network effect,” the polar opposite of
the law of diminishing, applies virtually all the major services including information,
communications, transportation, housing, amusement, banking and rentals. To
paraphrase, the efficiency of the network is proportional to the square of the scale
of service generation.
Where is the beef? Well, beef is everywhere
except for in the earthly statistics.
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