For about forty years now, individuals and organizations have warned of peak oil and predicted a particular date for this event, which is inevitably associated with some sort of impeding doom. Yet, their predictions have not come to fruition (yet). Indeed, there is very little economics in those predictions beyond extrapolating trends. Economics has much more to offer in this regard.
Indeed, theory would tell you that an exhaustible resources would be used up at a decreasing rate as long as there is a positive discount rate, thanks to increasing prices for this commodity. Yet we seem to observe increasing consumption. Stephen Holland offers several explanations why peak oil may arise as an equilibrium and optimal outcome. There are four ways that can lead to upward-trending oil production, at least for some time: increasing demand, increasing reserves, technological change and site development. Demand and reserves are easy to understand, the other two need explanations.
Technological change can lead to increasing production through a decrease in the cost of drilling. The end effect is similar to discovering accessible reserves. As for site development, the idea is that the most promising sites are developed first for extraction, and the next ones come online while the previous ones are not done yet, yielding a temporary increase in production. And I would add a fifth reason for a temporary increase in production: the introduction on alternative fuels. Overall, the general picture that emerges is that in the long run production decreases, but there may be bumps along the way. But if price play their role, their is nothing evil in peak oil.