Set-up costs and capacity constraints in the theory of natural resource extraction.

The dissertation examines set-up costs and flow constraints on Hotelling models of natural resource extraction. The first chapter examines the order of extraction from deposits with exogenous flow constraints. The chapter shows that it may be efficient to begin extracting a high cost, constrained resource strictly before a lower cost resource is opened. It is also shown that it may be efficient to begin extracting a high cost resource, then to stop extracting it for a time, and finally to re-open it if a low cost substitute is flow constrained. The second chapter introduces set-up costs into the model with capacity constraints. Hartwick, et al. (1986) showed that competitive equilibria fail to exist in models with set-up costs. However, in a model with set-up costs and an exogenous capacity constraint, a competitive equilibrium may exist for certain parameters. However, set-up costs depend on the amount of capacity installed. If the set-up cost is a convex function of the capacity, a competitive equilibrium always exists even though the problem is non-convex. This result shows that competitive equilibria exist in a broad class of problems in spite of a non-convexity. The third chapter analyzes the efficient time to construct a water project importing surface water as a substitute for declining groundwater reserves. The empirical application examines the Central Arizona Project (CAP) which imports Colorado River water. The simulation model is calibrated using available parameter estimates and then applied to estimate the welfare losses from various policies. These policies include federal Reclamation construction and operating subsidies, impediments to formation of interstate water markets, and common property groundwater extraction. The model estimates that CAP should have been constructed in 2058, i.e., 71 years later than the actual completion date of 1987. Since Arizona's costs were subsidized, the optimal construction date from Arizona's perspective is 1971, which yields a deadweight loss of $3.016 billion. This deadweight loss is larger than the entire value of the project if it were constructed optimally in an undistorted economy. In addition, the returns to groundwater management are found to be small ($0.988 billion) relative to the deadweight loss of the subsidies. Finally, the chapter shows that policies should not be analyzed piecemeal, since each additional distortion exacerbates the inefficiencies of existing distortions.PhDAgricultural economicsEarth SciencesEconomicsHydrologic sciencesSocial SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131904/2/9938449.pd