On an “Important Principle” of Arrow and Debreu

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnis Vilks
Keyword(s):  
Simple Model ◽  
Technological Progress ◽  
Competitive Equilibrium ◽  
Private Ownership ◽  
Existence Of Equilibrium ◽  
Important Principle

Abstract In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.

SIMPLE PROOF OF EXISTENCE OF EQUILIBRIUM IN A ONE-SECTOR GROWTH MODEL WITH BOUNDED OR UNBOUNDED RETURNS FROM BELOW

2003 ◽  
Vol 7 (3) ◽  
pp. 317-332 ◽  
Author(s):  
Jorge Durán ◽  
Cuong Le Van
Keyword(s):  
Growth Model ◽  
Simple Proof ◽  
Competitive Equilibrium ◽  
Direct Approach ◽  
Standard Approach ◽  
Existence Of Equilibrium ◽  
Competitive Equilibria

We analyze a Ramsey economy in which gross investment is constrained to be nonnegative. We prove the existence of a competitive equilibrium for the case in which utility need not be bounded from below and the Inada-type conditions need not hold. The analysis is carried out by means of a direct and technically standard approach. This direct approach allows us to obtain detailed results concerning properties of competitive equilibria, and is easily adapted for the analysis of analogous models often found in macroeconomics.

Dynamics in a Non-Scale R&D Endogenous Economic Growth for Chinese Development

2012 ◽  
pp. 933-946
Author(s):  
Qiong He
Keyword(s):  
Economic Growth ◽  
Human Capital ◽  
Economic Development ◽  
Technological Progress ◽  
Equilibrium Solution ◽  
Competitive Equilibrium ◽  
Labor Movements ◽  
Technology Spillover ◽  
Technology Gap ◽  
State Growth

By introducing nonlinear technology gap into Jones (1995b), this chapter constructs an R&D non-scale growth model that includes endogenous human capital and technological progress. The goal is to take the model’s implications to the data to explaining the Chinese economic development experiences at period 1979-2004. Our model suggests that the technology gap has the block neck effect on the economic development. The market competitive equilibrium solution shows that R&D and technology spillover can enhance the steady state growth rate. The mode’s transitional dynamics is also analyzed on the effects of human capital, capital, technological progress and intersectional labor movements on economic growth, technological progress has the most effect on the economic development, and more human capital shift into R&D sector from final goods sector.

scholarly journals Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
I. Benedetti ◽  
M. B. Donato ◽  
M. Milasi
Keyword(s):  
Variational Inequality ◽  
Equilibrium Model ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Quasivariational Inequalities ◽  
Existence Of Equilibrium ◽  
Upper Semicontinuous ◽  
Generalized Quasivariational Inequalities ◽  
Quasi Variational Inequality

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach.

Dynamics in a Non-Scale R&D Endogenous Economic Growth for Chinese Development

2011 ◽  
pp. 124-138
Author(s):  
Qiong He
Keyword(s):  
Economic Growth ◽  
Human Capital ◽  
Economic Development ◽  
Technological Progress ◽  
Equilibrium Solution ◽  
Competitive Equilibrium ◽  
Labor Movements ◽  
Technology Spillover ◽  
Technology Gap ◽  
State Growth

By introducing nonlinear technology gap into Jones (1995b), this chapter constructs an R&D non-scale growth model that includes endogenous human capital and technological progress. The goal is to take the model’s implications to the data to explaining the Chinese economic development experiences at period 1979-2004. Our model suggests that the technology gap has the block neck effect on the economic development. The market competitive equilibrium solution shows that R&D and technology spillover can enhance the steady state growth rate. The mode’s transitional dynamics is also analyzed on the effects of human capital, capital, technological progress and intersectional labor movements on economic growth, technological progress has the most effect on the economic development, and more human capital shift into R&D sector from final goods sector.

scholarly journals Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 867-932 ◽  
Author(s):  
Elizabeth Baldwin ◽  
Paul Klemperer
Keyword(s):  
Coalition Formation ◽  
Competitive Equilibrium ◽  
Equivalence Theorem ◽  
Equilibrium Existence ◽  
Existence Of Equilibrium ◽  
New Methods ◽  
Geometric Objects ◽  
Bank Of England ◽  
Intersection Points

An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into “Demand Types” incorporates existing definitions (substitutes, complements, “strong substitutes,” etc.) and permits new ones. Our Unimodularity Theorem generalizes previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a “demand type.” Contrary to popular belief, equilibrium is guaranteed for more classes of purely‐complements than of purely‐substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition‐formation, and the “Product‐Mix Auction” introduced by the Bank of England in response to the financial crisis.

Chaos and secular cycles in a structurally simple model society

2012 ◽  
Author(s):  
Alexander Medvinsky ◽  
Alexey Rusakov
Keyword(s):  
Simple Model

A Simple Model of Changes in Lumbar Intervertebral Angles During Sagittal Torso Flexion

2011 ◽  
Author(s):  
Riley E. Splittstoesser ◽  
Greg G. Knapik ◽  
William S. Marras
Keyword(s):  
Simple Model

Discussion of the band structure effects on thermoemission as deduced from a simple model

1976 ◽  
Vol 37 (2) ◽  
pp. 149-158 ◽  
Author(s):  
A.K. Bhattacharjee ◽  
B. Caroli ◽  
D. Saint-James
Keyword(s):  
Simple Model ◽  
Band Structure
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