1,288 research outputs found
Linearity, Slutsky symmetry, and a conjecture of Hicks
No full textHicks (1956) conjectured that Slutsky symmetry should hold for discrete as well as infinitesimal price changes if demand functions are globally linear. This paper proves this conjecture using the LES utility function and the Slutsky compensation for price changes. More importantly, in sharp contrast to previous doubts expressed by Hicks, Samuelson and others, this paper provides the first formal demonstration that compensated cross price effects can indeed be symmetric for discrete changes in prices.
Using the compensating and equivalent variations to define the Slutsky Equation under a discrete price change
No full textIn our experience, all textbook presentations of the Slutsky Equation under a discrete price change use a compensation scheme based on the compensating variation. Our students have sensed this convention is arbitrary in that they have asked, why consider this compensation scheme, and not one based on the equivalent variation? The present paper outlines how one might address this matter analytically, and then discusses how our findings provide a new insight into the Giffen Paradox.Compensating Variation
Real income growth and revealed preference inconsistency
No full textIf a smooth demand function violates the strong axiom of revealed preference, the income and prices can follow a cycle and returm to their starting values even though real income is always rising. We show how real income growth along the "worst" revealed preference cycle depends on the range of price variation and on violations of the Slutsky conditions. We relate this result to proposed reforms of the consumer price index and use it to justify a new index of local demand inconsistency. We also use the Slutsky matrix to determine an upper bound on the number of observations required to detect revealed preference inconsistency
Real income growth and revealed preference inconsistency.
No full textIf a smooth demand function violates the strong axiom of revealed preference, the income and prices can follow a cycle and returm to their starting values even though real income is always rising. We show how real income growth along the "worst" revealed preference cycle depends on the range of price variation and on violations of the Slutsky conditions. We relate this result to proposed reforms of the consumer price index and use it to justify a new index of local demand inconsistency. We also use the Slutsky matrix to determine an upper bound on the number of observations required to detect revealed preference inconsistency.
Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness
No full textThis paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infinite dimensional unobservable. To analyze the economic restriction, we employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may test the economic restriction by considering quantiles of linear combinations of the dependent variable. For this hypothesis we develop a new empirical process based test that applies kernel quantile estimators, and derive its large sample behavior. We investigate the performance of the test in a simulation study. Finally, we apply all concepts to Canadian individual data, and show that rationality is an acceptable description of actual individual behavior.
Did Pareto discover income and substitution effects? On an interpretation suggested by Hutchison
No full textTerence Hutchison (1953) has argued that in his Manual of Political Economy Vilfredo Pareto provided a verbal, non-mathematical description of income and substitution effects. Hutchison's claim on Pareto''s behalf is important since it would move the date of the discovery of the concept (if not the mathematical proof) of separate income and substitution effects back from 1915 to the 1906 publication of the original Italian language version of the Manual, and would reassign priority for the discovery from Slutsky to Pareto. This note reexamines this claim of Hutchison''s, and shows that in fact it is mistaken. Pareto did not actually discuss income and substitution effects as they are now understood. Rather, in the passage which Hutchison cites, Pareto was discussing the impact of a change in income, not prices, on quantities demand.
Household Nash equilibrium with voluntarily contributed public goods
No full textWe study noncooperative models with two agents and several voluntarily contributed public goods. We focus on interior equilibria in which neither agent is bound by non negativity constraints, establishing the conditions for existence and uniqueness of the equilibrium. While adding-up and homogeneity hold, negativity and symmetry properties are generally violated. We derive the counterpart to the Slutsky matrix, and show that it can be decomposed into the sum of a symmetric and negative semidefinite matrix and another the rank of which never exceeds the number of public goods plus one. Under separability of the public goods the deviation from symmetry is at most rank two.Nash equilibrium, Intra-household allocation, Slutsky
In Quest of the Slutsky Diamond.
No full textThe Slutsky equation can be constructed as a parallelogram (a diamond), the area of which is proportional to the elasticity of substitution. This construction permits to show immediately that demand functions become concave on an interval if the elasticity of substitution increases sufficiently. Also, the diamond sheds light on the fact that the production level increases with the elasticity of substitution. As an application, the author shows that the elasticity of substitution has a direct bearing not only on the rate of growth of an economy, but also on the very existence of sustained growth. Copyright 1989 by American Economic Association.
Drevin and Slutsky: The Context of One Poem
No full textThe study presents one of the analytical fragments of the Armenian text of Russian poetry. The corpus of “Armenian” texts includes the poem “The Builder of Paradise, the painter Drevin” by Boris Slutsky, which is outwardly unrelated to Armenia. The purpose of the article is to analyze the semantics of the poem’s context, in particular, its indirect connection with Armenia. The author solves a number of problems: characterizing the artistic work of Alexander Drevin and the role of Armenia in it, including writing an essay about the tragic biography of the artist; designation of Armenia’s place on the scale of values in the poetry of Boris Slutsky; characteristics of the Soviet image of paradise and its embodiment in art and literature. Using historical, cultural and biographical methods, the study reveals the Armenian subtext in the “non-Armenian” poem “The Builder of Paradise, the painter Drevin” based on the poems of Boris Slutsky and the archival file on charges of counter-revolutionary activities against Alexander Drevin (GA RF)
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