Related Experiment Video
Updated: Apr 28, 2026
05:39
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
4.7K
On Ramsey's conjecture
1Department of Economics, Cornell University, Ithaca NY, USA.
Journal of Economic Theory
|June 14, 2014
Summary
In the long run, Ramsey
Area of Science:
- Economics
- Mathematical Economics
- General Equilibrium Theory
Background:
- The Frank P. Ramsey model analyzes optimal economic growth.
- Heterogeneous households and no-borrowing constraints are key features.
- Previous studies in discrete-time models yielded different conclusions.
Purpose of the Study:
- To confirm Frank P. Ramsey's conjecture on long-run wealth distribution.
- To analyze the stability and efficiency of economic equilibria under specific constraints.
- To compare continuous-time model results with discrete-time findings.
Main Methods:
- Analysis of a one-sector economic model with finitely many heterogeneous households.
- Inclusion of no-borrowing constraints for all households.
- Derivation of results using the continuous-time formulation of Ramsey's model.
Main Results:
- Confirmation of Ramsey's conjecture: society divides into patient capital owners and impatient non-owners.
- Existence of a unique, globally asymptotically stable steady-state equilibrium.
- The most patient household accumulates all capital in finite time under any equilibrium.
- All equilibria are proven to be efficient, despite no-borrowing constraints.
Conclusions:
- The continuous-time Ramsey model supports long-run wealth polarization.
- Economic efficiency is maintained even with borrowing restrictions.
- Results contrast sharply with prior discrete-time model findings, highlighting the importance of model formulation.
Related Concept Videos
01:18Parseval's Theorem
1.4K
Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...
1.4K
01:30Fundamental Theorem of Algebra
499
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as: with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
499
01:09Rolle’s Theorem
222
Rolle’s Theorem states that if a real-valued function is continuous on a closed interval, differentiable on the open interval, and takes equal values at both endpoints, then there is at least one point within the open interval where the derivative of the function is zero.Rolle’s Theorem describes an important property of differentiable functions, this theorem applies to a real-valued function defined on a closed interval, provided three specific conditions are met. First, the...
222
01:14Norton's Theorem
2.0K
Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the one...
2.0K
01:18Castigliano's Theorem
1.4K
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
1.4K
01:15Thevinin's Theorem
2.2K
Thévenin's theorem plays a pivotal role in electrical circuit analysis, offering a solution to the challenges posed by variable loads within a circuit. In practical applications, it is common to encounter circuits where certain elements remain fixed while others fluctuate, often referred to as the "load." A typical household electrical outlet serves as a prime example of a variable load, as it can be connected to a variety of appliances, each with its own unique electrical characteristics.
2.2K