[Proposals for the computation of competitive equilibria in the presence of taxation contained in recent joint work by the author are applied to a model of the United Kingdom economy and tax system for the period 1968-1970. Difficulties of model specification and parameterization are also discussed. Results provide indications of efficiency, distributional, and welfare impacts for a number of alternative tax changes.]

A price endogenous numerical general equilibrium model of world trade is used to analyze terms of trade issues in the North-South debate. Seven regions are identified, the U.S., EEC, Japan, Other Developed, OPEC, New Industrialized, and Less Developed Countries. The model is benchmarked to a global 1977 micro consistent data set. In the central case analysis, protectionist trade policies in the North inflict an annual welfare loss on the South of around 30 billion dollars per year with an associated terms of trade deterioration of around 9%. The annual welfare cost to the South from northern trade restrictions is somewhat larger than annual North-South aid flows. Protection in the South, and the potential terms of trade impacts of differential growth, are also analyzed.

John Whalley, A Simulation Experiment into the Numerical Properties of General Equilibrium Models of Factor Market Distortions, The Review of Economics and Statistics, Vol. 59, No. 2 (May, 1977), pp. 194-203

IN the empirical literature on market interferences a variety of numerical techniques have been used to analyse competitive equilibria which are not directly observable. Harberger (1963, 1966), and Johnson and Mieskowski (1970), for instance, in their analyses of factor market distortions in the United States economy use a mixture of differential calculus and linearization assumptions to estimate efficiency losses and distributional impacts of particular market interferences. Acceptance seems to be implied in these procedures of the reliability of approximate methods for calculating unobservable equilibria. This issue of reliability forms the subject matter of the present paper.' A recent joint paper (1972) examined the robustness of Harberger's results (1966) when a competitive for the United States economy in the absence of distortionary taxation was calculated using a procedure for the computation of competitive equilibria due to Scarf (1967, 1969, 1973). The results for particular parameterizations suggested that the gain in simplicity of approximate methods may in some circumstances counterbalance the precision of more refined computational devices. These results, however, were obtained for a problem of small dimensionality and limited complexity, and the comparison between Harberger's results and true general solutions was made only on the basis of one summary statistic. In addition, the approximate solution device used by Harberger (1966) does not correspond to conventional notions of either or general analysis. It is thus of some importance that the comparison between general solutions and various forms of analysis be carried further before any conclusions on computational experience are used as a guide in other contexts. These issues are taken up here in the context of a-particular model which allows different forms of analysis to be used and compared to general solutions. The results presented are put forward as evidence on computational experience. This paper considers a general model of the United Kingdom economy used in recent work on an assessment of tax changes in the United Kingdom economy (1973). Using this model the gain2 to the United Kingdom from the abolition of the distortionary features of capital income taxation is calculated by various methods and compared to the general solution. Section II presents a characterization of competitive equilibria for an economy with taxation used in a recent paper by Shoven and Whalley (1973) which underlies the United Kingdom tax model. As no explicit statement of partial equilibrium analysis is to be found in the literature, two alternative characterizations of such procedures which are later applied to the model, are devel-

In this note the possibility is demonstrated that a movement between a broadly based income tax and a consumption tax in a two-period consumption loan model can be completely accommodated by interest rate changes which leave real intertemporal consumption plans unchanged. Income and consumption taxes are both broadly based taxes, the former taxing all potential consumption in any period and the latter actual consumption. Lenders and borrowers face the same prices under both tax regimes and movements between the two can, in this simple model, be wholly accommodated by interest rate changes leaving intertemporal consumption plans unaffected. This result contrasts with the conventional argument in favor of a consumption tax in preference to an income tax on the basis of lack of distortion of savings behavior. It is not suggested that because of this result exact monetary accommodation to consumption income tax variations will occur in all circumstances, but it seems to be of interest to note that such adjustments are possible and these appear not to have been previously considered. The traditional argument for the distorting effects of an income tax over a consumption tax is often made in a simple two-period intertemporal consumption choice model. If an individual receives income Y,, YK in each of two periods and if the interest rate is r, then, so the argument goes, the slope of an individual's budget constraint between current and future consumption (C, and C2) is not disturbed by a consumption tax, whereas it is under an income tax. If interest is both taxable as a receipt and deductible as an expense under the income tax, and the marginal tax rate t is assumed to apply under both the income and consumption tax,' the slopes of the consumer budget constraint under the three alternative regimes are

A recently constructed numerical general equilibrium model of domestic and foreign trade activity for the United States, the (nine-member) EEC, and Japan is used to analyze the effects of removing distortions in domestic factor taxes, taking into account international trade flows. As is conventional in the general equilibrium tax literature, corporate and property taxes are treated as ad volorem taxes on capital use by industry and social security taxes as ad valorem taxes on labor use by industry. National accounts sources are used both to obtain model equivalent tax rates by trading area and to construct a benchmark data set with which to estimate the model. Results suggest that under some assumptions current factor tax structures can produce significant terms-of-trade gains, and in the U.S. case results show welfare losses occurring from the removal of existing distortions. This result contrasts with conventional closed economy analysis of distorting factor trades and is explained by national terms-of-trade losses which more than outweigh the gains from removal of domestic distortions. The policy significance of this and other findings is discussed.

We wish to acknowledge the help of three referees and of John Pencavel on several earlier drafts, as well as the assistance of the modelers, whose work is referred to in the paper. They corrected our lack of understanding of their work and provided many other helpful comments. Excellent research and bibliographical assistance have been provided by Debbie Fretz, Radwan Shaban, and Janet Stotsky. Helpful comments have been made by Charles Ballard, Michael Boskin, Lans Bovenberg, Sylvester Damus, Harvey Galper, Glenn Harrison, Gordon Lenjosek, Jack Mutti, Serena Ng, T. N. Srinivasan, Charles Stuart, and Eric Toder. The authors also acknowledgefinancial support from the National Bureau of Economic Research, the National Science Foundation, International Business Machines, and the Social Sciences and Humanities Research Council: Ottawa, Canada.

In this paper we outline the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure. For general equilibrium models of the required structure, a full equilibrium may be computed through the solution of a sequence of smaller scale 'sub-equilibrium' problems. The text contains a presentation of the methods involved along with a discussion of initial computational experience for some numerical examples. IN THIS PAPER we describe the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure similar in spirit to the Dantzig-Wolfe decomposition algorithm for the solution of linear programming problems (Dantzig and Wolfe [2]). The method involves the generation of labels for vertices on a master simplex through the separate solution of subequilibrium problems whose parameters are determined by the coordinates of the vertex on the master simplex. For general equilibrium models of the required structure, it is possible to compute a full equilibrium through the solution of a sequence of smaller scale 'sub-equilibrium' problems. The analogues to the common constraints in the Dantzig-Wolfe procedure are common commodities with common prices, and the block diagonal structure on non-common constraints in Dantzig-Wolfe is replaced by an analogous block diagonal pattern of demands and endowments of agents over non-common goods. A natural application of the method is to international trade models with 'traded' and 'non-traded' goods. Traded goods are common to all countries, non-traded goods are traded only within the country involved. We report execution times for numerical examples using Merrill's [5] algorithm for solution of both full dimensional problems and the same problems by the decomposition procedure. We do not discuss the application of these procedures to economies with production, although it seems likely to us that a similar procedure can be applied if a comparable block diagonal structure characterizes the production set. The economic interpretation we offer for our procedure draws on the partition of the full list of commodities in a general equilibrium model into 'common' goods traded among all agents, and 'non-common' goods traded among a subset of agents. The assignment of non-common goods to agents is represented in a block diagonal pattern of demands and asset ownership by agent. Agents have