Journal Article A Supplementary Note on Mr Pearce's General Equilibrium Model Get access S. A. Ozga S. A. Ozga London Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 25, Issue 1, October 1957, Pages 62–63, https://doi.org/10.2307/2296125 Published: 01 October 1957

Journal Article A Dynamic Approach to the Theory of Consumer Demand Get access J. S. Cramer J. S. Cramer Cambridge Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 24, Issue 2, February 1957, Pages 73–86, https://doi.org/10.2307/2295761 Published: 01 February 1957

Journal Article Tariffs and the Balance of Payments Get access S. A. Ozga S. A. Ozga London School of Economics and Political Science Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 71, Issue 4, August 1957, Pages 630–638, https://doi.org/10.2307/1885714 Published: 01 August 1957

FEW DATES in the history of econometrics are more significant than 1857. In that year Ernst Engel (1821-1896) published a study on the conditions of production and consumption in the Kingdom of Saxony [6], in which he formulated an empirical law concerning the relation between income and expenditure on food. Engel's law, as it has since become known, states that the proportion of income spent on food declines as income rises. Its original statement was mainly based on an examination of about two hundred budgets of Belgian laborers collected by Ducp6tiaux. Since that date the law has been found to hold in many other budget surveys; similar laws have also been formulated for other items of expenditture. With the formulation of Engel's law an important branch of econometrics took its start, though it was not until our days that consumption research was placed on a sound theoretical and statistical basis. It is proper that in this centennial year econometricians should pay tribute tzo one of their most illustrious precursors. His successful attempt to derive meaningful regularities from seemingly arbitrary observations will always be an inspiring example to the profession, the more so because in his day economic theory and statistical techniques were of little assistance in such an attempt. There can, I think, be no more fitting tribute to this enlightened empiricist than a further inquiry into the subject to which he devoted much of his life's work. There is no need to go into details of Engel's analysis and of the developments that preceded it, for these matters have recently been discussed in the scholarly article by Stigler [13]. It should be enough to note that Engel was mainly influenced by two of his older contemporaries. One was the French engineer Fred6ric Le Play, who had collected budgets from households all over Europe, mostly, it seems, from humanitarian interest. Engel had been Le Play's student at the Ecole des Mines in Paris. The other main influence was the Belgian statistician Qu6telet, who was a firm propoinent of the idea that human characteristics, at least in the average, were governed by laws as definiite as those which govern

COMPARATIVE dynamics is a relatively unworked but highly significant area of economic analysis. It is important to appreciate the implications of changes in the structure of a dynamic system and, thus, the extent to which the analytical results depend on the particular, restricted forms employed. These are the problems with which comparative dynamics deals in general 1 and with which this paper is centrally concerned, with particular respect to the stability of difference-equation models of income determination. Dynamic difference-equation models of economic fluctuations have been useful tools for the economist. Though not intended to provide, in themselves, a complete description of aggregate economic activity, such models have led to a better appreciation of cycle-producing forces and the character of cyclical movements. These models have been developed in a variety of forms based on different assumptions about time sequences and using different types of expenditure functions as components. Inevitably, however, each of the models represents a special case whose analysis provides conclusions of only limited applicability. There has not, I believe, been adequate recognition of the important qualifications which must as a result be applied to many of the existing dynamic models of economic fluctuations. In this paper greater generality will be sought in two ways: first, by the construction of a number of alternative systems based on different assumptions about the lag sequences involved; second, by detailing somewhat more than has been done the expenditure functions which are the components of the models. I believe that it will be possible in this way to provide further insights which are important in themselves and in qualifying previous dynamic analyses. The variety of results which can be obtained will be illustrated rather than treated exhaustively. The procedure of this paper will be to construct and compare a series of alternative models. In section I the general method of analysis will be illustrated in presenting models based on the Robertsonian lag of expenditures behind the receipt of income.2 Section II will begin to break new ground in the analysis of models which use the Lundberg lag of output behind sales.3 Finally, in section III models will be developed using both types of lag. The investigation is confined to models of effective demand in a closed economy. The expenditure functions used are, in general, adaptations of a simple consumption function and the acceleration principle -admittedly gross, but useful, simplifications of reality. Even though thus confined to simple lag relations and spending functions, the analysis becomes quite complicated. After constructing each model, the types of movements which it may generate and the conditions which it must satisfy for stability will be investigated.4 The systems constructed will be subject to the well-known limitations of linear models. It would not be difficult, however, to apply simple types of nonlinear restraints to the systems, and the effects of such restraints will be noted at several places. The mathematical techniques of stability analysis which are the basis of this paper have been introduced into economics by Professor P. A. Samuelson. Their usefulness has, perhaps, not been fully appreciated, and this paper provides an example of their application. A general comment on the use of stability conditions may be in order here. We want to investigate the economic implications of a number of alternative dynamic systems; we know that such systems are able to produce a variety of motions consisting of monotonic and