opening hours). However, the studies have also demonstrated that care seeking behavior is often a sophisticated response to the type and severity of illness of the client.' Efriciency ainalysis sand the economnetnric esm tion of coqt unncfons Cost functions can be useful in shedding light on a number of questions. Are health facilities under- or over-capitalized? Are facilities inefficient in other respects? Are they technically inefficient in that they fail to produce the maximum output from their inputs? Do they use inputs in the wrong proportions? Do facilities vary in their degree of inefficiency? Are public facilities less efficient than others? Should facilities specialize or provide a broad range of services? Could costs be reduced by concentrating cases in fewer facilities?

In the industrialized world, there is a large literature on these topics. A much smaller literature exists in the developing world. Wagstaff and Barnum (1992) review the four principal studies up to 1992 (Ethiopia, Kenya, Nigeria and Peru). Barnum and Kutzin (1993) report estimates of cost functions for hospitals in Colombia and China. The published literature during the last 10 years includes a large volume of cost function studies from industrialized countries but apparently none from the developing world. Some of the studies (e.g., Nigeria, Colombia, China) that have been done in developing countries-in contrast to those undertaken in the industrialized countries-have relied on survey data, which is unsurprising in view of the poor quality of data in most developing country health facilities (Lewis, La Forgia, and Sulvetta 1996; Mills, Kapalamula, and Chisimbi 1993).

Few of the studies to date shed light on the issue of whether health facilities have too little or too much capital. The test proposed by Cowing, H[oltman and Powers (1983) is to see whether the slope of the variable cost function with respect to capital is equal to the price of capital. Wagstaff and Barnum (1992) suggest an alternative test similar to Feldstein's (1967), namely to test the hypothesis that the slope of the short-run total cost function with respect to capital equals zero. Anderson's (1980) study of Kenyan hospitals is inconclusive on the overcapitalization issue. The results of the studies from Ethiopia (Bitran-Dicowsky and Dunlop 1993) and Nigeria (Wouters 1993) are consistent with over-capitalization, but Wagstaff and Barnum warn against taking the results too literally.

In many studies the primary focus has been on efficiency. Broadly speaking, the concept of efficiency pertains to the relationship between inputs and outputs.<sup>5 9</sup> In modem efficiency measurement it is customary to distinguish between technical and allocative efficiency (Farrel 1957).6? Technical efficiency refers to the maximization of output with a given set of inputs. In contrast, allocative efficiency reflects the substitution between inputs with different prices to achieve minimum costs. These two measures can be combined to provide a measure of total economic efficiency. However, applying the concept of allocative

> 58 The welfare implications of bypassing are not immediately obvious, but it is clear that under some circumstances, bypassing can lead to low utilizations of available pubhc facilities (resulting in low efficiency) and impose unnecessary costs on the clients.

> 59 In the broadest sense, efficiency can be seen to concern the relationship between inputs and _outcomes._ Using this broad concept of efficiency would however require data that are not typically available.

> 60 The efficiency concepts were originally developed in relation to firm performance. See Fned et al. (1993) for a comprehensive treatment.

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