Date of Award


Document Type

Open Access Dissertation


Moore School of Business



First Advisor

John H. McDermott


Since the middle of the 1970's, there has been considerable research about how to deal with exhaustible natural resources which are essential to production. In the absence of substitution possibilities, the finite stock of these resources acts as a limiting factor to continued growth of output and hence consumption possibilities. In our first chapter, we combine a finite natural resource and human capital in the production function and look at the possibility of maintaining a non-declining or sustainable level

of consumption for an infinite horizon. Our results show that the return to human capital accumulation plays a key role in ensuring this objective. In our model without physical capital, we obtain a similar result where this return must be such that the fraction of time devoted to acquiring human capital each period is at least as much as the share of natural resources in output.

Our second chapter focuses on the transition from a relatively cheap exhaustible natural resource (coal, gasoline) to an expensive alternative technology assumed to be in nearly unlimited supply (wind, solar). Due to significant cost differences between fossil-fuel based energy sources and these alternative (backstop) technologies, their use is not as widespread. Public subsidies to research can however bring about innovation through cheaper production techniques which would significantly reduce the operating costs of these backstop technologies. But without sufficient incentives for investment and patent protections, individual firms typically underinvest in backstop technologies relative to the socially optimal level. In our paper, we find that this underinvestment

in the backstop also leads to an under-extraction of the exhaustible natural resource. This imply firms would conserve the natural resource for too long and switch later to the alternative technology relative to the socially optimal solution. We extend the chapter to include pollution as a flow variable. Pollution from aggregate use of

the natural resource is seen to not affect the behavior of an individual firm whereas it significantly affects that of the social planner. For relatively low pollution cost values, the socially optimal solution involves less investment in the backstop and conserving the natural resource for a longer period compared to the case without pollution. For higher values of the pollution cost, the social planner invests more in the backstop each period and switches sooner to the backstop compared to the case without pollution. In some situations, this may involve leaving behind some stock of the natural resource in the ground.

The third chapter introduces pollution (a stock variable) through a deterioration of environmental quality. The structure of the second chapter is maintained here. Comparing the true pollution cost of the resource (in terms of a poor environmental quality) and the cost of the backstop technology, it is possible for the natural resource to be relatively more expensive. This arises in a situation of a very dirty environmental quality where the additional benefit from a slightly better environment exceeds the cost of the alternative cleaner technology. In this case, the optimal solution involves using the backstop at first for a few periods before making a discrete jump to a

constant mix of using both the resource and the backstop technology. Here the economy settles at a steady state of environmental quality. It similarly follows that when the quality of the environment is relatively clean to begin with, the optimal solution involves starting with the cheaper but polluting natural resource before switching to a constant mix of using both the energy sources.


© 2013, Supratim Das Gupta