Factor Intensity and Site Geology as Determinants of Returns to Scale in Coal Mining
利用煤矿微观数据，估计了一个包含资本劳动比和固定地质条件的射线齐次生产函数，发现资本密集度提高会带来更高的规模报酬，但并非所有资本设备都如此，且多数矿井未达到最优规模。
Increasing returns to scale (RTS) is frequently pos- tulated as affecting productivity in surface coal mining. How- ever, it is not clear whether increased capital intensity or increased output is the relevant phenomenon. A ray-homo- thetic production function that incorporates the capital-labor mix and fixed site geology into the scale elasticity is presented and estimated with a micro (mine level) dataset. The results indicate that higher capital intensity contributes to higher RTS for some types of capital equipment, but not all. On the average increasing RTS was found, with few mines approach- ing optimal scale. T HE literature of coal mining productivity contains many references to returns to scale as a factor in strip mining productivity.' However, different analysts use different definitions of scale,' and consequently their results are mixed. Some analysts associate returns to scale with larger pieces of capital equipment; 2 others use the more traditional economic notion of output volume and the scale elasticity;3 others simply relate output volume to labor productivity.4 It may be true that developments in large pieces of earth-moving equipment have been implemented at surface mines with large output volume, but this does not necessarily imply increasing returns to this par- ticular capital input. This confusion in the mining literature in the use of the term scale, coupled with the more general observation that large firms (not just large mines) rarely have the same capital-labor mix as their smaller counterparts, leads to a hypothesis that a different capital-labor mix yields different economies of scale. The application of ray-homothetic production functions leads to an easily testable hypothesis on the impact of input mix to economies of scale. Additionally, these functions are more general than their homothetic namesakes. Fare (1975) has shown that they do not generate linear expansion paths. convex isoquants, or exhibit strong dispos- ability of inputs. The properties of convexity and strong disposability are necessary for a dual, cost function analysis of the production structure. If the true underlying production function is ray- homothetic, the dual approach is inappropriate, therefore these functions are a desirable tool for productivity analysis in general and in particular when input mix is believed to be an important