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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This paper shows that if the production function is appropriately restricted some symmetry (reciprocity) results which hold for a competitive firm under certainty continue to hold under price uncertainty, for any strictly concave utility function. In contrast, earlier analyses have established these symmetry relations by imposing restrictions on the utility function. The present analysis uses the envelope theorem, the indirect utility function, and the duality between production and cost.

INTRODUCTIONHistorically, there has been increasing interest in the appropriate pricing policies for publicly-provided goods and services. In order to arrive at such policies it is desirable to have some knowledge of the cost structures of these outputs. In fact, some recent research has focused attention on the relationship between the cost structures associated with the provision of publicly-provided goods and services and their pricing.' However, serious deficiencies of knowledge in this area still exist. One of the most important areas of which we know little is public bus transportation. For instance, studies by Koshal [ 141 and Miller [ 181 have evaluated the relationship between bus systems' cost conditions and the level of service and prices for privately-, rather than publicly-owned bus systems in the United States. Understanding the cost structures of urban bus systems becomes more vital when we consider that urban bus systems continue to experience the greatest absolute and relative increases in net operating deficits compared to other competing modes of travel.2The purpose of this paper is to evaluate the relationship between cost conditions and the level of service and prices of inputs for publicly-owned urban bus systems in Illinois. We adopt a neoclassical cost model, which enables us to take into account prior restrictions on the parameters implied by neoclassical theory. The available literature fails to take account of these restrictions. Rather, studies by Koshal [ 141, Lee and Steedman [ 161, and Miller [ 181 have adopted the statistical cost function approach, making interpretation of the estimates difficult.The two most common functional forms used in the estimation of urban bus transportation cost functions are the linear and log-linear forms. A log-linear cost function specification implies a Cobb-Douglas production function for which u, the elasticity of substitution, is unity. These forms appeal to statistical conve-

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