Modelling Peak Oil

On Wednesday 18th January we had another of our Energy Journal Club meetings. Sean was talking about Hamilton (2011) - Oil Prices, Exhaustible Resources, and Economic Growth, Jelte talked to Murphy & Hall (2010) - Year in review—EROI or energy return on (energy) invested, Sebastian covered Greene et al (2005) - Have we run out of oil yet? Oil peaking analysis from an optimist’s perspective, Erkal spoke to Hamilton (2005) - Oil and the Macroeconomy, and I talked about Holland (2008) - Modeling Peak Oil.

To summarise the Holland paper:
# It started from the usual no-arbitrage Hotellings condition (prices must move in such a way so that the owners of exhaustible natural resources are indifferent between: extracting the resources, selling them and investing the financial proceeds;  and just sitting on the unextracted resources), but presented 4 models that were sufficient to generate a peak in production. You may have thought that since oil production started from zero in the mid nineteenth century and rose to the present day, and since oil is a finite resource, then any good model would show a peak in production. But most economic models of the oil market, including the basic Hotelling model, have peak production at time zero since this is when prices are lowest and demand is highest.
# The 4 models are models of cost reductions through technological change, demand growth, endogenous reserve additions, and site development. This last model in particular is novel to this paper, and is consistent with the story described in Hamilton (2011) - Oil Prices, Exhaustible Resources, and Economic Growth.
# I have two objections to this paper:
(a) It uses a partial equilibrium approach. This means that the interest rate, that the Hotelling mechanism says is the rate at which the oil price rises, is independent of the aggregate oil supply.
(b) It assumes that oil that is uneconomic to exploit now will be economic to exploit at a higher price. This ignores the possibility that the capital goods with which this future oil can be exploited do not change in price (or at least that their price doesn't rise faster than the oil price).

I'm being slightly unfair in my objections since the paper is following standard assumptions in the literature. However these objections essentially form the basis of my own work.