TFhe last few years have seen a resurgence of interest in the old question of how best to raise tax revenue. Roughly speaking, two different problems have been studied. TFhe first is to find a set of commodity taxes that is optimal given certain efficiency and (sometimes) equity considerations. In a second strain of the literature, it is assumed that the revenue system is based upon income rather than commodity taxation, and the problem is to determine the optimal degree of progressivity (or regressivity) .1,2 TI he principal motivation of some writers in the optimal taxation literature seems to be the discovery of fairly simple rules which policy makers actually can implement. Others are more interested in theoretical exploration of the implications of alternative economic assumptions than in developing usable policy recommendations. Practically all the contributions, however, have been quite mathematical and thus inaccessible to many practitioners in the public finance area. The purpose of this essay is to discuss in a nontechnical way the methodology and principal conclusions of the optimal taxation literature.3 In Sections 1 and II are discussed the optimal commodity and income tax literatures, respectively. Following this are some observations on the accomplishments of optimal taxation research and on some open questions.

Until quite recently, theoretical analyses of the impact of intergovernmental grants on public expenditures have run either implicitly or explicitly in terms of the familiar theory of indiv-idual choice.' The recipient of the grant is typically viewed in effect as an individual decision maker with preference patterns of the usual sort defined over private and public goods. Within this theoretical structure, a number of propositions have been developed including, for example, the conclusion that, dollar-for-dollar, a matching grant will induce a greater expansion in spending on the public good than will a lump-sum, unconditional grant. The difficulty with this analysis, as we all have been well aware, is that this is not the appropriate theoretical framework for the study of intergovernmental grants. Such grants are not grants to individuals; they are grants to groups of people. This means that the effects of these grants depend upon the process by which the group makes collective decisionis. A real theory of intergovernmental grants must, for this reason, be one which takes explicitly into account the political process through which the collectivity determines its levels of spending upon public goods. In one recent paper, Goetz and McKnew have shown for a special case that it is con-ceivable that lump-sum grants can have a greater stimulative impact on public spending than an equal-dollar matching grant. Using a rather complicated model in which the collectivity decides separately on the aggregate level of public spending and on the mix of public programs, they show that, if individual preferences bear a particular kind of relation to one another, simple majority voting will lead to greater public expenditure in response to a lump-sum grant than to a matching grant of the same amount. Whether this special case is likely to occur with any frequency is another matter, but, at any rate, it is clear that one can concoct particular instances in which a process of collective decision making will lead to results which are at variance with the conclusions which follow from the rnodel of individual choice. Our purpose in this paper is to try to explore somewhat more systematically the effects of these two types of intergovernmental grants. The question arises whether there are interesting classes of collective decision processes for which the comparative effects of the two types of intergovernmental grants can be predicted. In an earlier paper on revenue-sharing (Bradford and Oates), we have constructed a framework for conceptualizing collective budget determination which offers the possibility of dealing systematically with the effects of * The authors are grateful for a number of helpful comnments to the participants in economics seminars at McMaster University and at Rutgers University. In addition, they are indebted to the F'ord Foundation whose support has greatly facilitated this study. 1 For an excellent presentation using this approach, see James Wilde.

Assessing the impact of new technologies on health care costs is an important research area. This paper evaluates two technologies used to treat coronary artery disease. We estimate two separate stochastic frontier models—one for balloon angioplasty patients and one for cardiac bypass surgery patient—using data taken from detailed chart and cost files of a large urban hospital. Cost estimates for the two technologies are purged of inefficiency so that forecasts of the cost consequences of technology shift can be based on ‘best-practice’ production techniques. Learning behavior, physician effects, and patient clinical characteristics are also taken into account. We find that there are potential cost savings associated with making angioplasty a more perfect substitute for bypass surgery, as well as current inefficiency in production.