The Measurement of Deadweight Loss in an Open Economy

Abstract

There are many approaches to the measurement of the resources wasted in an economy arising from an inappropriate system of taxation and government regulation. The existing literature on this topic is too voluminous for us to summarize in this introduction.1 In the remainder of this Introduction, therefore, we simply outline what we hope to add to the literature in this paper. At the outset, it should be mentioned that we are going to consider only the deadweight loss generated by inappropriate systems of taxation. The losses generated by monopolistic behaviour on the part of producers could be modelled in a similar fashion, but we leave this generalization to the reader.2 In Section I below, we illustrate our two alternative measures of deadweight loss by means of some simple diagrams. From the diagrammatic viewpoint, neither loss measure has a clear-cut advantage over the other. However, when we move to our algebraic analysis of the loss measures and to quadratic approximations, then it turns out that our Allais-Debreu loss measure (Allais, 1943, pp. 610-616; Debreu, 1951, 1954) has a clear-cut advantage over the Hicks-Boiteux measure (Hicks, 1941-1942; Boiteux, 1951), at least when the number of households in the economy exceeds one. It should be mentioned that we are restricting our attention to loss measures that are well defined when (a) there is an arbitrary number H of households in the economy, (b) there is an arbitrary number N of domestic goods and an arbitrary number M of internationally traded goods in the economy,3 and (c) there is an arbitrary number K (?N) of constant (or diminishing) returns-to-scale sectors in the production sector of the economy. The last restriction turns out to be important because the case where N (the number of domestic goods) equals K (the number of sectors) leads to measures of deadweight loss that have substanitally lighter informational requirements. In Section II we lay out our model of the economy, using duality theory in order to reduce the number of variables and equations. In Section III we develop a measure of loss arising from tariff and tax distortions which is due essentially to Boiteux (1951). Conceptually, the Boiteux loss measure is simply a sum of Hicksian (1941-1942, p. 128) equivalent variations applied to each consumer's expenditure function, so we call our loss measure a Hicks-Boiteux loss measure. However, Boiteux (1951, p. 128) provided a quadratic approximation to his loss measure, which decomposed into additive consumer and producer terms, whereas Hicks and others did not accomplish this additional step. We obtain the same kind of decomposition as Boiteux, but generalized to an open economy.5 It should be noted that the loss measure developed in this section collapses down to the standard