| The benefit function introduced by David G. Luenberger is discussed in this work as a tool suitable for analyzing the optimality of taxation and measuring the inefficiency which taxation can cause. While lump sum taxation leads to no inefficiency, or deadweight loss, taxation of this type is not available to governments. The use of unit and ad-valorem taxes are practical, yet they lead to undesirable efficiency losses. With the presence of such losses, economists have developed various approaches to determine how they can be minimized, and measured.;This paper begins with a review of pertinent optimal taxation and benefit function literature, and presents a comparative statics exercise for the calculation of the derivatives of the benefit function. A result regarding the convexity of the technology set and the concavity of the directional distance function, which is shown to be related to the benefit function, is also stated. Following this introduction the main results of this dissertation are presented.;First, we devise an optimal taxation rule for the determination of tax rates that will minimize deadweight loss due to taxation. Optimal taxation rules were first derived by Frank P. Ramsey, but have been further examined and extended by various authors, including Angus Deaton, whose 1978 approach is reviewed in our development of an optimal tax rule derived using the benefit function.;Next, a benefit function approach is used to reinterpret the John A. Kay and Michael Keen (1988) distance function approach to decomposing measured inefficiency caused by taxation into producer and consumer surplus components.;The last topic presented concerns the measurement of efficiency loss in terms of compensating and equivalent benefit. These are concepts dual to the familiar (Hicksian) compensating and equivalent variation measures. Compensating and equivalent benefit are also discussed as potentially useful for the measurement of deadweight loss in applied studies. A simple iterative method for their calculation, based on the methodology of Yrjö O. Vartia (1983), is developed for this purpose. |
