Ramsey-Cass-Koopmans Model
Solow with optimizing households: the saving rate chosen by intertemporal utility maximization.
Definition
The optimal-growth model: Solow with the saving rate chosen by an infinitely-lived household maximizing discounted utility, solved with an Euler equation and a saddle-path phase diagram.
Key equation
Euler: Ċ/C = (1/σ)(f′(k) − δ − ρ)
The intuition
Consume now or invest for more later? The household balances impatience (ρ) against the return on capital: consumption grows exactly when the interest rate beats the discount rate. The economy rides a razor-thin saddle path to a steady statesteady stateThe resting point of a growth model, where capital per worker stops changing because investment exactly covers depreciation and dilution. where f′(k) = δ + ρ.
Exam tip
The Ramsey steady statesteady stateThe resting point of a growth model, where capital per worker stops changing because investment exactly covers depreciation and dilution. has LESS capital than the golden rule, impatience makes over-saving suboptimal, never optimal.
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