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Keynes–Ramsey rule — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Keynes%E2%80%93Ramsey_rule
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T16:43:29.968Z
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Keynes–Ramsey rule — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Keynes%E2%80%93Ramsey_rule (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_cf36ced4f9ee (Metraipolis archive dc_cf36ced4f9ee, sha256 70d414051fbc315f9c584e6f3378f2caf678bc479459c6dd100e5c7a2659e2a1)

BibTeX

@misc{dccf36ced4f9ee,
  title = {Keynes–Ramsey rule — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Keynes%E2%80%93Ramsey_rule},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_cf36ced4f9ee; sha256 70d414051fbc315f9c584e6f3378f2caf678bc479459c6dd100e5c7a2659e2a1},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Keynes%E2%80%93Ramsey_rule. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is expressed as a differential equation relating the rate of change of consumption with interest rates, time preference, and (intertemporal) elasticity of substitution. If derived from a basic Ramsey–Cass–Koopmans model, the Keynes–Ramsey rule may look like c ˙ ( t ) = σ ⋅ ( r − ρ ) ⋅ c ( t ) {\displaystyle {\dot {c}}(t)=\sigma \cdot (r-\rho )\cdot c(t)} where c ( t ) {\displaystyle c(t)} is consumption and c ˙ ( t ) {\displaystyle {\dot {c}}(t)} its change over time (in Newton notation), ρ ∈ ( 0 , 1 ) {\displaystyle \rho \in (0,1)} is the discount rate, r ∈ ( 0 , 1 ) {\displaystyle r\in (0,1)} is the real interest rate, and σ > 0 {\displaystyle \sigma >0} is the (intertemporal) elasticity of substitution. The Keynes–Ramsey rule is named after Frank P. Ramsey, who derived it in 1928, and his mentor John Maynard Keynes, who provided an economic interpretation. Mathematically, the Keynes–Ramsey rule is a necessary first-order condition for an optimal control problem, also known as an Euler–Lagrange equation.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Mathematical optimization»).
Fonte: Wikipedia in inglese, voce «Keynes–Ramsey rule» — https://en.wikipedia.org/wiki/Keynes%E2%80%93Ramsey_rule
Wikidata Q19287889 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q19287889
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Keynes%E2%80%93Ramsey_rule?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1360336835, consultata il 2026-10-06T15:18:45.057Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 1ba3431c5106e83d975473284abf10ca17a730f596949fffa03ba97d42910c06