Petroleum speculation without contango or growing inventories ?

As I’m sure AngryBear readers know, Paul Krugman does not believe that the spot price of petroleum shot up due to speculation. His argument is that the only way future expected prices can affect demand for crude or supply of refined products to final consumers is via inventory accumulation and inventories haven’t increased. Also he argues that speculation can only affect the spot price if there is contango: that is a futures price above the spot price.

I was convinced. Now I am not so sure. The recent decline in the price of petroleum makes it a little bit harder for me to believe in a simpl supply and demand without speculation explanation (just a little bit harder so I won’t argue the semi hemi demi point).

There are many models in which prices do funny things. One set includes customer market models — very implausible if the product is gasoline. Another set is based on implicit collusion. In this case, lets assume that the oil companies are, in fact, a cartel and enforce cooperation with threats of future retaliation. The subgame perfect semi folk theorem suggests that a continuum of equilibria are possible in this case, which sure helps if one is trying to fit the data.

I am (as always) thinking as I type. The semi model I have in mind is one in which

1) the oil companies buy crude on a thick duble auction type spot market with one worldwide price and close to perfect competition.

2) they refine crude and sell refined products (for simplicity assume that the only product is gasoline) subject to a capacity limit and, of course, demand.

3) they agree on a markup on marginal cost. Firms which sell gasoline at a lower markup are punished in the future. They choose the highest sustainable markup.

4) they agree on the highest sustainable markup and have rules restricting inventory accumulation and forward purchases of oil (key that).

The cartel will drive the price of gasoline up and the price of crude down. The extent to which it can do this depends on the costs and benefits of deviation from the agreement, that is, the gains to a firm of suddenly selling gasoline cheaper than agreed given the spot price of crude and the costs to that firm of the wrost subgame perfect punishment strategy available to the cartel.

It is very important to my story that the firms agree on a markup (let’s say a price of gasoline as a function of the price of crude) and NOT on prices for gasoline or crude or quantities of crude bought or gasoline sold.

Update: This is my second try. My first try was mathematically wrong.

The key issues are gains and costs from deviation from the agreed markup.

I will assume that following deviation, firms switch to the non-collusive oligopolly solution (make it a cournot oligopoly) with a lower price of gasoline and a higher price of crude.

If it took a long time for gasoline stations to change their posted price, an oil company with a chain of gas stations could … well this is silly.

There are gains to deviation from the agreement if the other oil companies in the cartel have limited inventories of gasoline and either limited inventories of crude limited refining capacity limiting their ability to increase their supply of gasoline. I assume that spare refining capacity is key to enforcement. The idea is that shipping refining and distributing takes a while so firms don’t do it on the sly. Spare refining capacity is key to the punishment phase but not to the deviation phase. Limited spare refining capacity implies a low markup. In particular, anticipated future refining capacity is the key (the punishment phase lasts a long time) so expectations of future demand are key.

The cost of deviation is that all firms in the future use all of their refinineries at capacity (and maybe build more).

The benefit is dumping undesired inventories of gasoline on the market and an increase in the price of crude oil which is valuable if the company owns crude oil in the ground or in tanks or has bought crude oil futures beyond their needs for crude oil to refine.

A tight incentive compatibility constraint due to limited refining capacity implies a low markup and tight restrictions on inventories (of both gasoline and crude oil) and on futures positions.

A low markup implies a high price of crude oil. Also low inventories (required to maintain collusion) and limited refining capacity imply a high price of crude. It is important that the collusive agreement allows firms complete freedom on the spot crude oil market. The idea is that the price jumps around so much that any collusive agreement would be way to complicated to work tacitly.

So low spare refining capacity implies low allowed inventories and futures purchases which implies fierce competition for crude oil (if a firm bids low it will have trouble keeping its refineries working and can’t make up later as it has limited spare capacity).

All is driven by forecasts of future demand which can bounce around as much as GNP forecasts.