This paper provides a non-renewable resource extraction model with both technological change and resource exploration. Especially, we consider two types of technology, extraction technology and exploration technology. We show how these technologies affect efficient non-renewable resource extraction differently. Then, progress in extraction technology drops marginal revenue of extraction and resource price by changing the structure of those dynamics, while progress in exploration technology drops marginal revenue of extraction and resource price remaining the structure of those dynamics. Finally, we illustrate the difference becomes significant when innovative technologies are developed using numerical examples.
In this paper, we propose a spot pricing method of an electrical network composed of consumers, suppliers, and transmission companies. The electricity pricing is formulated as a maximization problem of the sum of consumers surplus and profits of suppliers and transmission companies. If there exists a solution to the maximization problem, it is the unique solution for a system of differential algebraic equations with boundary conditions. A numerical simulation demonstrates that an electricity market consisting of two areas is designed to reduce the areal difference of electricity prices.
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