There turned out to be some issues with the analysis I did.
First, a brief bit of background which I left out: "Elasticity of
demand" is the percentage by which demand changes for a given
percentage change in the price. So, if elasticity is -1, then if the
price increases by 10%, the amount people purchase will decrease by
10% and the total revenue paid for the good will be unchanged as a
result of the price increase. If the elasticity is -0.1, then if the
price increases by 10%, consumption will only drop by 1%; in this
case, total revenue will increase by about 9% due to the price
increase.
The elasticity of demand for crude oil is the big question mark here.
I dug around some more, and it turned out its "short-run" elasticity
is believed to be about -0.01 to about -0.04. That's incredibly
small! It means prices move by between 25 and 100 times as much as
consumption. Interestingly, however, this is just /short run/
elasticity; it's obviously very hard to change oil consumption rates
"instantly". I couldn't find a clear number for long-run elasticity,
but I ran across hints that it may be around -1 (although, OPEC not
withstanding, oil is not provided by a monopoly, and one might
therefore expect the long-run elasticity to be smaller than that --
normally only a monopoly can force the price up to the "optimum"
value). It's also worth pointing out that the difference between
"short run" and "long run" price changes isn't exactly clear (to me,
at least). How long is "long"? I don't know.
In the earlier email I sent I mixed up "price" and "total revenue",
but that didn't affect the results. The definition of "E" I used was
not ideal, however, and that did affect the results; I used the ratio
P/Q for the *final* price and *final* quantity sold. It's generally
more reasonable to use the average of the initial and final prices and
quantities sold when looking at elasticity, which leads to the
definition
E = (Q2-Q1)/(P2-P1) * (P2+P1)/(Q2+Q1)
and in turn, if we hold E constant while changing Q2, and if we define
r = (Q2-Q1)/(Q2+Q1)
when we solve for P2, that leads to
P2 = P1 * (E + r)/(E - r)
In case anyone's interested in looking at it, I uploaded the Open
Office spreadsheet on which this is laid out here:
http://physicsinsights.org/oil-price-elasticity-1.ods
The "final" version of the model, using the central difference formula
given above for E, is on the fifth "subsheet", named "Central Formula
Projections".
Excerpt of some of the results (unit width font, please):
Starting quantity: 100
Starting price: $115.00
Demand Supply Final
Elasticity Growth Growth Price
---------- ------ ------ -----
-0.200 0.01 0 $120.87
-0.200 0.02 0 $126.98
-0.200 0.03 0 $133.35
-0.200 0.04 0 $140.00
-0.200 0.05 0 $146.94
-0.100 0.01 0 $127.04
-0.100 0.02 0 $140.27
-0.100 0.03 0 $154.88
-0.100 0.04 0 $171.10
-0.100 0.05 0 $189.19
-0.100 0.06 0 $209.52
-0.050 0.02 0 $171.79
-0.050 0.03 0 $211.50
-0.050 0.04 0 $263.39
-0.050 0.05 0 $334.05
-0.050 0.06 0 $435.93
-0.040 0.01 0 $147.67
-0.040 0.02 0 $190.66
-0.040 0.03 0 $249.77
-0.040 0.04 0 $336.15
-0.040 0.05 0 $474.38
-0.040 0.06 0 $731.07
-0.020 0.01 0 $191.16
-0.020 0.02 0 $340.49
-0.020 0.03 0 $765.94
-0.020 0.04 0 $11,615.00
I found a table of historical oil prices, and during the period of
1991 through 2001 prices appeared fairly flat. Taking oil use growth
during that period as being the "natural" growth rate absent price
hikes, we still end up with between 1 and 2% year on year consumption
increase.
Even so, if the assertion that short-run elasticity of oil prices is
between -0.01 and -0.04 is correct, then it seems like we could
conceivably see $200/bbl oil within 12 months. My, but the crystal
ball is murky....
Finally I ran across an interesting report (to which I seem to have
lost the link, drat); it was testimony given to the Homeland Security
committee late last fall, in which it was claimed that there was no
conventional explanation for the rise in oil prices we'd already seen;
it wasn't due to demand increase, supply shortage, or speculation.
The conclusion was that it was caused by the DOE pumping high grade
crude into the strategic reserve! Apparently their "buy" rate is high
enough to mess up the market. It was proposed that if they would
stockpile "sour" crude instead of "light sweet" crude, it would make a
large difference to oil prices.
And post-finally, McCain has proposed a gasoline tax holiday for the
summer, which would very neatly short-circuit the whole market
mechanism and let gas consumption go back to soaring during the
vacation season -- in essence, such a move reduces the price
elasticity of the demand for gasoline, by zapping out part of the
"price signal" for a few months. Obama opposes the tax holiday,
for which he will no doubt get slammed in the polls.
Ah, and one other thing -- elasticity isn't a constant. In the real
world, it is a function of the price. It normally rises as prices rise.
So, all projections based on "constant" elasticity are automatically
suspect. A classic example is hearts: If you need a transplant, you'll
pay any price for it, so the elasticity of demand for hearts is zero.
But that's only true up to a certain point -- almost nobody could afford
to pay, say, $10,000,000 for a new heart, so if the price rises that
high, demand will indeed drop off -- and at that point the elasticity
will have risen above zero.
