scholarly journals Market equilibria and money

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sjur Didrik Flåm
Keyword(s):  
Fixed Point ◽  
Steady State ◽  
Value Added ◽  
Pareto Optimal ◽  
Generalized Gradients ◽  
Market Mechanisms ◽  
Mathematical Arguments ◽  
Second Welfare Theorem ◽  
Market Equilibria ◽  
Welfare Theorem

AbstractBy the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system.Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only.Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.

scholarly journals A formula on the subdifferential of the deconvolution of convex functions

1993 ◽  
Vol 47 (2) ◽  
pp. 333-340 ◽  
Author(s):  
M. Volle
Keyword(s):  
Convex Functions ◽  
Infimal Convolution ◽  
Parallel Sum ◽  
Similar Formula

It is known that, under suitable assumptions, the subdifferential ∂(f □ g) of the infimal convolution of two convex functions f and g coincides with the parallel sum of ∂ f and ∂ g. We prove that a similar formula holds for the subdifferential of the deconvolution of two convex functions: under appropriate hypothesis it coincides with the parallel star-difference of the sub-differentials of the functions.

On parallel sum of operators

2020 ◽  
Vol 603 ◽  
pp. 57-83
Author(s):  
Xiaoyi Tian ◽  
Shuaijie Wang ◽  
Chunyuan Deng
Keyword(s):  
Parallel Sum

Parallel sum of positive adjointable operators on Hilbert $$C^{*}$$ C ∗ -modules

2018 ◽  
Vol 29 (7-8) ◽  
pp. 1081-1090
Author(s):  
M. Eshaghi Gordji ◽  
H. Fathi ◽  
S. A. R. Hosseinioun
Keyword(s):  
Parallel Sum

Generalized gradients of monotone type

2004 ◽  
Vol 56 (2) ◽  
pp. 201-212
Author(s):  
Pandelis Dodos
Keyword(s):  
Generalized Gradients ◽  
Monotone Type
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