Set-up Costs and the Existence of Competitive Equilibria when Extraction Capacity Is Limited

Although set-up costs are prevalent and substantial in natural resource extraction, their analysis in decentralized markets is difficult. In particular, it is known that a Walrasian competitive equilibrium cannot exist in simple extraction models with set-up costs thus rendering standard competitive equilibrium analysis inapplicable. However, this paper demonstrates that this result is sensitive to the assumption of unlimited extraction capacity. When extraction capacity is limited, a competitive equilibrium can exist if each firm earns sufficient surplus to cover its set-up costs. Moreover, if firms choose extraction capacity, the optimal capacity choice ensures existence of a competitive equilibrium. The resulting competitive equilibrium price either grows at the rate of interest when total extraction is below capacity or is constant when capacity is fully utilized. In the equilibrium, identical deposits are opened simultaneously, and set-up costs for new deposits are incurred when the industry has excess capacity rather than when capacity is fully utilized.