Dynamic Optimization Basics
Choosing over time: Bellman thinking, Euler equations, and the tools behind Ramsey and RBC.
Definition
Choosing over time: Bellman equations (value today = best of reward now plus discounted value tomorrow) and Hamiltonians for continuous time, the machinery under Ramsey, RBC, and asset pricing.
Key equation
V(k) = max_c { u(c) + βV(k′) }; Euler: u′(c_t) = β(1+r)u′(c_{t+1})
The intuition
The Euler equation is the universal intertemporal deal: give up a crumb today, invest it, consume the grown crumb tomorrow, at an optimum you're indifferent. Every consumption-saving, investment, and search model repeats this one idea.
Exam tip
Whatever the model, derive and INTERPRET the Euler equation, it's the expected step in any dynamic question.
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