UBC Theses and Dissertations
Essays on the measurement of waste and project evaluation Tsuneki, Atsushi
Harberger's methodology for the measurement of deadweight loss is reformulated in a general equilibrium context with adopting the Allais-Debreu-Diewert approach and is applied to various problems with imperfect markets. We also develop second best project evaluation rules for the same class of economies. Chapter 1 is devoted to the survey of various welfare indicators. We especially discuss the two welfare indicators due to Allais, Debreu, Diewert and Hicks, Boiteux in relation to Bergson-Samuelsonian social welfare function. We first show that these two measures generate a Pareto inclusive ordering across various social states, but they are rarely welfarist, so that both are unsatisfactory as Bergson-Samuelsonian social welfare functions. We next show that second order approximations to the Allais-Debreu-Diewert measure of waste can be computed from local information observable at the equilibrium, whereas second order approximations to the Hicks-Boiteux measure of welfare or to the Bergson -Samuelsonian social welfare function require information on the marginal utilities of income of households, which is unavailable with ordinal utility theory. Finally, we give a diagrammatic exposition of the two measures and their approximations to give an intuitive insight into the economic implications of the two measures. Chapter 2 and Chapter 3 study an economy with public goods. In Chapter 2, we compute an approximate deadweight loss measure for the whole economy when the endogenous choice of public goods by the government is nonoptimal and the government revenue is raised by distortionary taxation by extending the Allais-Debreu-Diewert approach discussed in Chapter 1. The resulting measure of waste is related to indirect tax rates, net marginal benefits of public goods, and the derivatives of aggregate demand and supply functions evaluated at an equilibrium. In Chapter 3, cost-benefit rules for the provision of a public good are derived when there exist tax distortions. We derive the rules as giving sufficient conditions for Pareto improvement, but we also discuss when these rules are necessary conditions for an interior social optimum. When indirect taxes are fully flexible but lump-sum transfers are restricted, we recommend a rule which generalized the cost-benefit rule due to Atkinson and Stern (1974) to a many-consumer economy. When both indirect taxes and lump-sum transfers are flexible, we suggest a rule which is based on Diamond and Mirrlees' (1971) productive efficiency principle. When only lump-sum transfers are variable, we obtain a version of the Harberger (1971)-Bruce-Harris (1982) cost-benefit rules. Chapters 4 and 5 study an economy with increasing returns to scale in production and imperfect competition. In Chapter 4, we discuss a methodology for computing an approximate deadweight loss due to imperfect regulation of monopolistic industries by extending the Allais-Debreu-Diewert approach to incorporate the nonconvex technology. With the assumption of the quasi-con-cavity of production functions and fixed number of firms, we can derive an approximate deadweight loss formula which is related to markup rates of firms, and the derivatives of aggregate demand functions, factor supply and demand functions and the derivatives of marginal cost functions. We also discuss various limitations of our approach and the relation between our work and that of Hotelling (1938). In Chapter 5, we consider cost-benefit rules of a large project applicable in the presence of imperfect competition. We show that the index number approach due to Negishi (1962) and Harris (1978) can be extended to handle situations with imperfect competition.
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