Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1511.00065

A New Class of Problems in the Calculus of Variations

Ivar Ekeland·Yiming Long·Qinglong Zhou
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper investigates an infinite-horizon problems in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern for the well-being of future generations. We show that there are no optimal solutions, but that there are equilibrium strateges, i.e. Nash equilibria of the leader-follower game between successive generations. To solve the problem, we approximate the Chichilnisky criterion by a biexponential criterion, we characterize its equilibria by a pair of coupled differential equations of HJB type, and we go to the limit. We find all the equilibrium strategies for the Chichilnisky criterion. The mathematical analysis is difficult because one has to solve an implicit differential equation in the sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak. It is shown that optimal solutions a class of problems raising from time inconsistency problems in the framework of the neoclassical one-sector model of economic growth, and contains new results in environment economics. Without exogenous commitment mechanism, a notion of the equilibrium strategies instead of the optimal strategies is introduced. We characterized the equilibrium strategies by an integro-differential equation system. For two special criteria, the bi-exponential criteria and the Chichilnisky criteria, we established the existence of the equilibrium strategies.

Explore related subjects

econ.GNmath.OCq-fin.EC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ivar Ekeland, Yiming Long, Qinglong Zhou. 2015-10-31. A New Class of Problems in the Calculus of Variations. https://doi.org/10.1134/s1560354713060026

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Local Media and the Shaping of Social Norms: Evidence from the Ebola outbreak

Media's influence on norms and behavior is widely recognized. Less is known about the role played by media being local. I examine this in a high-stakes context, the Ebola outbreak in Guinea. I exploit quasi-random variation in access to radio and the timing of a public-health campaign aired on community radio. I find that 12-17% of Ebola cases could have been prevented if places with access to a neighboring community radio station had instead had their own. Impacts are driven by radio being local rather than by ethno-linguistic belonging. Local media facilitates coordination in behaviors observed and sanctioned locally.

econ.GN↗
arXiv2026

Productivity Shocks and Input Misallocation: A Decomposition

This paper asks how much input misallocation productivity uncertainty generates and at which stage of input decisions it arises. I separate revenue productivity by when each component is revealed and trace each into the gap between an input's marginal revenue product and its price. In six European countries, shocks revealed after an input is committed account for 20 percent of capital gap dispersion and 5 percent of labor gap dispersion. An unanticipated one percent rise in productivity raises the capital gap by 0.92 percent and the labor gap by 0.19 percent, because most of the shock passes into the wage.

econ.GN↗
arXiv2026

When Do Type-Specific Wages Buffer Distributional Incidence in TANK?

When do relative wages buffer the unequal incidence of aggregate shocks? I derive a consumption-gap decomposition and a present-value condition for partial offset in a TANK model. An extension separates wage-setting demand elasticity from substitution between labor segments and allows each segment to contain both financial types. With a zero inherited wage gap and a same-sign discounted wedge, substitution above one gives offsetting earnings reallocation; substitution below one gives amplification. The channel disappears when financial types have identical segment exposure. Numerical experiments assess these mechanisms, shock persistence, policy feedback, and aggregate-IRF matching. In the nested perfect-alignment monetary benchmark, the peak consumption gap is about two-fifths smaller under type-specific wages than under the common-wage closure. These are conditional model comparisons, not empirical effect estimates or welfare rankings.

econ.GN↗