An Increase in Worldwide Demand for Oil

Another round on the oil market model, this time to show what happens when there is an increase in the world demand for oil due to some factor such as increased demand from developing economies. The point is to show that, in this simple model, the increase in demand would increase in the long-run equilibrium price, but it would not change the level of inventories in the long-run. There are also other results to note, e.g. the possibility of overshooting the new long-run equilibrium and mimicking a bubble.

Case 1: An Increase in the Expected Future Price of Oil

First, the continuous time version of an increase in the expected price. I did a discrete time-version of this yesterday, but the continuous time version of this case Paul Krugman did yesterday is much simpler, so let's use that. Here's a quick review of that case:

In this model, the initial equilibrium is at point a. Then, there is an increase in the expected future price or a drop in the interest rate that increases the stock demand, N^d, and the equilibrium moves to point b. At this point, the spot price is above the equilibrium value in the flow market shown on diagram on the right, and there is excess supply as indicated by the red line. This excess supply increases the stock so, as shown by the arrow, the stock supply curve begins shifting out. Eventually, the economy settles at the new equilibrium shown at point c.

Summarizing the results for an expected increase in the future price:

1. The spot price, p, rises in the short-run, but is unchanged in the long-run.
2. The stock of inventories, N, rises.
3. The long-run flow equilibrium is unaltered.
4. The change in inventories depends upon the horizontal shift in the stock demand curve. This can be related to the slope of the stock demand curve, but it is not necessarily the case that a steeper demand curve leads to a smaller horizontal shift.
5. Steeper flow supply and demand curves affect the size of the change in the spot price during the transition (and the slopes can affect the transition path for inventories), but this does not change the ultimate size of the inventory change since this depends only upon the size of the shift in the stock demand curve.

Case 2: An Increase in Worldwide Demand for Oil

Moving to the next case, what happens if there is an increase in the world demand for oil due to worldwide economic growth. This shifts the flow demand curve outward:

Starting at the equilibrium a, as the flow demand curve shifts out, this causes an excess demand for oil as shown by the red line on the diagram. This excess demand is met by reducing stocks, so the stock supply curve begins shifting left and the economy moves to point b. Thus, so far there is an increase in price, and a decline in inventories.

But this isn't the end of the story. Because the increase in flow demand is permanent, the increase in price is permanent, and this will increase the expected future price. The increase in the expected future price will shift the demand curve out as shown in the next diagram:

As the demand curve shifts out to reflect the higher expected future price, the price moves up to point c. At point c, the flow market has excess supply as shown by the orange line segment, and this pushes the stock supply curve outward as the excess flow supply is absorbed as new stocks. Eventually, the economy reaches point d which, compared to point a, reflects a higher price but no change at all in inventories. Notice that the spot price overshoots its long-run value as it moves from b to c, then back down to b.

Why does the demand curve go through the same point for inventories as before? Recall from Krugman's post that  N^d = N(i-(p^e-p)/p), where i is the interest rate, p is the spot price, and p^e is the expected future price. At the initial long-run equilibrium, it must be that p^e=p, otherwise there would be a tendency for something to change (and hence it wouldn't be a long-run equilibrium [Update: I should add that there is no mechanism in this model to force p^e=p, but adding this in is a simple fix, e.g. just add an equation that says dp^e/dt = f(p^e-p), f'<0, or go to a more complicated rational expectations set-up. In this model, the requirement that p^e=p arises from making the model internally consistent with the definition of a LR equilibrium]). Thus, at the long-run equilibrium, the stock demand is just N(i). That means that the long-run equilibrium for stocks is independent of the spot price and its expected future value. Thus, the inventory level will be the same as its initial value after the offsetting changes in p and p^e.

Summarizing the results for an increase in flow demand:

1. The long-run spot price rises.
2. In the short-run, the spot price can overshoot in the new long-run equilibrium. The model doesn't predict overshooting, the a-b-c-d progression shown in the diagram is just for exposition, the actual path can be different (e.g. there's no reason for the expected spot price to increase only after the economy reaches point b). But the model is consistent with overshooting, and therefore the change in the spot price can look like a bubble that is inflating, then deflating even though the change is driven purely by fundamentals, i.e. by a shift in world demand.
3. The level of inventories can change in the short-run, but is unchanged in the long-run. (However, in a more general model, there might be a change in, say, the interest rate or convenience yield and this would cause an additional shift in the stock demand curve and change inventory levels. But it's still possible for the variation in inventories to be small.)

Finally, this is just a "vintage" Branson-style exchange rate model applied to commodities, so if you are familiar with those models and the bells and whistles that can be added to them, or with alternative models, for the most part the results and intuition ought to carry through to this case.

Update: Paul Krugman in response to Tyler Cowen.

Comments

[MG]

In summarizing case 1 you said:

...
4. The change in inventories depends upon the horizontal shift in the stock demand curve.

Since the increase in the demand for inventories is being driven by an increase in expected price, wouldn't it be more accurate to say "a vertical shift." It doesn't make much difference given the way you've drawn the curve, but suppose the curve were nearly horizontal (say near p=pe/(1+i)).

In fact, the curve would be nearly flat from the point of normal inventories to the level of storage capacity (or wherever marginal storage cost rises sharply) and then slope down sharply. Below normal inventories, the curve would at some point slope up sharply due to rising convenience yield.

Also, in case 1 (expected price increase), you end with higher stocks but an unchanged price. Isn't there another iteration where the stocks get sold off because the actual price has not increased?

[bakho]

The simple models assume that the system is operating below production capacity. More or less, the Saudis are saying there are limits to their production increase. Instability in Nigeria, Iraq and elsewhere is (in effect) reducing production capacity. The current situation is one where demand is increasing but increases in production are sluggish or not happening or the long term average production costs exceed the long term projected price. When this happens, the price keeps increasing because the gap between excess demand and current supply is not being closed.

For oil, the supply curve is NOT a straight line. The current situation suggests that the slope of the supply curve is much higher at current demand than at slightly lower demand. Technical factors support this conclusion.

[ddt]

Oil market oversupplied but not wise to cut: Qatar

MADRID (Reuters) - Oil markets are oversupplied but it would not be wise for any OPEC exporter to tighten the taps given the risk of exacerbating prices, Qatari Oil Minister Abdullah al-Attiyah said on Sunday.

Attiyah's remarks came after Libya's most senior oil official said on Thursday he was studying the possibility of reducing output in response to a U.S. threat to sue OPEC members, although he said the North African country had no concrete plans to do so for now.

"It is not wise today to cut supplies even though there is a surplus because we do not want to create a psychological problem," Attiyah told Reuters. "I'm not in favour of it at all. We want to try to help to ease the psychological heat."

But the Qatari minister criticised a move by U.S. politicians to sue the Organization of the Oil Exporting Countries if the oil club did not pump an amount of oil that Washington sees sufficient.

"The Congress should look to increase exploration inside the United States," Attiyah said. "It is strange to ask what I should produce. It's an issue of sovereignty."

he U.S. House of Representatives has passed a bill allowing the Justice Department to sue OPEC members for limiting oil supplies and working together to set crude prices.

The Senate has yet to vote on it and the White House has said it would veto the bill.

Attiyah said if enacted, the measure could create a problem for the U.S. market as many producers would avoid U.S. buyers.

"You will see a lot of oil suppliers will avoid the American market and you will create another big problem."

OPEC's biggest exporter Saudi Arabia has announced plans to hike output to 9.7 million barrels per day (bpd) -- the fastest pace in decades -- but some consumer economies blame the oil exporter group for doing too little to combat the rally.

Oil producers have to consider their reservoirs' productivity for the long run and not only supply and demand factors as they manage production levels, said Attiyah.

"Sometimes I have to think carefully in terms of reservoir management. I do not want to damage all the reservoirs. We produce to satisfy the whole world but not at the cost of our reserves," he said.

Record oil prices are putting pressure on the global economy, saddling companies and consumers around the world with higher energy costs and triggering protests from farmers in Spain to students in Nepal.

Attiyah said oil prices were detached from market fundamentals.

"There is no coordination between supplies and the oil price. We believe that the market is not facing any shortage of supplies at the moment. There are some cargoes in floating storage. More crude will not benefit the market.

"I never get a call from my customers asking for more supply but we always hear concerns about high oil prices. This shows there is no correlation between the oil price and supplies."

http://www.reuters.com/article/ousiv/idUSL2956547020080629

[robertdfeinman]

It seems that for these models to be useful in practice one would have to know several real pieces of information.

1. How much fuel (at any point in the chain) can be put into inventory? We do hear about refiners in the US stocking up on heating oil in the late summer and gasoline in the spring, but is this enough to have any cushion effect on prices, or is it just that they have to spread their production out because of capacity limits? I would imagine that the ability to store crude worldwide is relatively limited, so how much effect does this have?

2. We don't know how quickly producers adjust their output in response to market conditions or even perceived trends in the futures market. Turning off a pump seems to be a fairly easy thing. If production declines then excess stocks do not accumulate. Claims about rates of production from oil states are totally unreliable and must be inferred.

A good, limiting case to study might be the spot electricity market. Storage capacity is essentially zero, but next day prices are handled in a futures market and production changes are instantaneous. As Enron showed even in this limiting case it is possible to game the market.

I have no problem with the theoretical models, but it makes a big difference in practice if the straight lines in the standard "double cross" diagram are at 80 degrees or 10 degrees to the vertical.

To know what are the dominant factors in the current price changes we need some real data.

[Ben Ross]

I'd like to raise a related issue. Is the demand curve close to a straight line? (I'm thinking of the medium- and long-term equilibrium here, and not worrying about inventories.)

Let's take as a given that developing-world demand is growing faster than supply. Supply has hit the steep part of the curve, so the price has to adjust upward to a point where developed-world consumption goes down.

An important point about petroleum demand that I haven't seen mentioned in these consumptions has to do with gasoline demand in the developed world. To a large extent, driving is currently constrained by road capacity. There is a lot of unsatisfied demand for travel, by people who don't take trips because of highway congestion. In this situation, the space opened up on the roads by cars that don't travel because of high gasoline prices will be replaced by other cars no longer deterred by congestion. (Since the net effect will be an upward shift in the average income level of drivers, there might even be a shift toward bigger, less fuel-efficient cars on the road.)

By this argument, the price elasticity of gasoline demand is now fairly low because rural drivers don't have any other travel options, and urban driving is constrained by highway capacity rather than price. When the price reaches the point where urban highways are decongested, then you will see price elasticity of demand increasing. Until you reach that point, oil prices could easily keep going up rapidly.

I doubt very much there's any good empirical evidence about where that price level is - my gut says it's more like $10 or $15 per gallon gasoline than where we are now.

[Real Person from the Real World]

it's considerate of others to mention developing countries et al, but what do I do, on the wal-mart level wages I am being paid NOW, as gasoline goes up, and knowing my cost of heating in the winter will be going up? What incentive does big oil have to lower prices as long as they make their margins, after all, while consumers may cut back, they still have to get to work and the hospital, and you must have oil to fuel trucks that haul produce and goods, at pretty much whatever the price is. Common sense is that someone somewhere should be working on fuel alternatives, electric cars, whatever, but where? How long before we see something?

from above:
'Attiyah said oil prices were detached from market fundamentals.

"There is no coordination between supplies and the oil price. We believe that the market is not facing any shortage of supplies at the moment. .... "I never get a call from my customers asking for more supply but we always hear concerns about high oil prices. This shows there is no correlation between the oil price and supplies."'
---------------
Whether or not, there is correlation between price and supplies the actual reality is $4+ at the pump. The money is going where?

meanwhile, my salary is stagnant. I was not making ends meet before, and am doing less so now.

Let's stop the games, and the babble and actually DO SOMETHING.

[Bruce Wilder]

If you have one eye on this abstract model, and the other eye on the New York Mercantile for West Texas Intermediate, you might be confusing yourself.

The oft-quoted spot price for WTI on the New York Mercantile is the spot price on a speculative market, which represents only a tiny fraction of oil exchange. The New York Mercantile spot and futures prices are handy statistics, but they are highly imperfect indicators of the full range of transaction prices for oil, the bulk of which is exchanged pursuant to long-term contract, and most of which is less valuable than the light, sweet WTI (or its London rough equivalent, Brent).

Small changes in the quantity of oil committed in long-term contracts can have a big impact on the spot market. Limits on refinery capacity can also push the light, sweet grades (which are the ones quoted in newspaper headlines) well ahead of the heavy, sour grades. It isn't just that oil prices are rising: the range of prices is expanding like a telescope.

It is useful, certainly, to refine one's intuition, with careful, abstract reasoning. But, it would be misplaced arrogance not to think it wise to consult someone familiar with the institutional details. I know just enough to be skeptical and uneasy with the pure product of abstract reasoning, but search in vain for the plausible insight of the truly well-informed.

[marcel]

In case 2, you wrote (cannot do the superscript):

it must be that pe-p

This is a confusing typo, and I think it s/b:

it must be that pe=p

[Mark Thoma]

Thanks, I'll fix that. Also, I need to fix the statement in that section - it's been bugging since just after I posted this.

In this model, there is nothing to bring pe and p into alignment. That's easy to fix, you can make pe a function of p for a simple fix or got to some sort of RE set-up for a more complicated way of forcing pe=p in the long-run, but for now, making pe=p is simply a question of internal model consistency as you would expect pe=p in long-run, but as written above, there is no reason why you can't have an equilibrium where this doesn't hold.

[SanFranciscoJim]

but what do I do, on the wal-mart level wages I am being paid NOW, as gasoline goes up, and knowing my cost of heating in the winter will be going up

Don't travel as much. Live near your job and combine your other trips. That is what I have been doing (for much longer than gasoline has cost $4.50/gallon).

If you must own a car, get one that is fuel efficient. Hopefully, you had the foresight to do this last year, before the price of fuel efficient cars shot up. If not, consider buying a scooter or moped. You can really get good gas economy in a moped.

[halbhh]

The model uses the false presumption that the supply and demand lines aren't identical in this case.

The supply and demand lines are in reality just identical: suppliers sell all the oil buyers want, and without competition, and just use a price influence by the futures market, which itself is mostly responding to "investment" (aka speculation).

[alishuz]

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