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...in the face of practical problems. Below will show with an engineering production function some facts related to the returns to scale of the gas transmission industry; after that a cost function is derived and the increasing returns to scale associated to that industry are shown in that cost function.
Research on the natural gas industry, particularly that focused on its economic aspects, shows that pipeline transportation of gas is characterized by economies of scale and large "sunk" costs. The fact that natural gas is largely restricted to pipeline delivery imposes significant economic constraints on the ability to create competition among suppliers. Since pipeline capacity increases much more rapidly with increasing pipe diameter than does investment, there are substantial economies of scale in gas pipelining.
Kahn (1988) emphasizes these particular characteristics of pipelines:
The main potential economics of scale are to be found in employing pipe of the maximum diameter available and, to a lesser extent, of further increasing its capacity, within limits, by increasing pressure and by constructing parallel lines running throughout the same compressor stations. The physical principle is that whereas the cost of a pipeline, like its perimeter, is (roughly) proportional to its diameter, its capacity is proportional to the square of the diameter. Whether it is economical to use the widest available pipe depends on the size and expected growth of demand. Against the lower potential cost of wider-diameter lines must be weighed the cost of building too far ahead of demand. (vol. II, p. 153)
Increasing the diameter of a pipeline allows important economies of scale. As Kahn observes, the carrying capacity of a gas pipeline is proportional to its interior cross-sectional area, whereas the amount of pipeline material used is in proportion to the circumference of the pipe. Hence, if the input of material used in the pipe is doubled, the carrying capacity of the pipe is more than doubled. However, there are limits to the scale economies that can be achieved by increasing the diameter of the pipe, determined by pressure differentials between the inlet and outlet of the pipeline and the length of the line itself, among other factors.
In determining the cost of a pipeline, it is important to think in terms of the capital and operating and maintenance cost of the pipe and of the compressor stations. It is necessary to account for the costs of construction of the line and the compressor stations, as well as the cost of installing all the equipment they require. Furthermore, the operation and maintenance costs of both elements must be considered. In working with this kind of information, models have been proposed (e.g., Lehn, 1943; Chenery, 1949), whose analyses have been built around certain engineering concepts, as described below.
GAS TRANSMISSION PRODUCTION FUNCTION
In Chenery's (1949) formulation for the process of gas transmission, attention is centered on the two basic capital inputs to the process, pipe and compressors. Compressors are employed to raise the pressure of the gas, which decreases gradually due to frictional losses of energy when gas is moved along the pipe.
Chenery uses a system of equations to describe the engineering relations governing the flow of gas in a pipe. In the pipeline problem, compressors are required to transport the gas. Since there is energy loss in the pipe due to friction in transmission, and this loss is a decreasing function of pipe size, it follows that the greater the pipe diameter, the smaller the required compressor capacity to pump any given amount of gas a specific distance. Hence, the mechanism of substitution between pipes and compressors is based on calculations of energy loss in engineering processes and the effect of equipment's capacity size in reducing this loss. Hence, Chenery arrives at all engineering production function that he uses to get the pipeline capacity and power requirements. In order to get the natural gas...
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