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1 - makes it the logical starting point The agent’s...

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1 Dynamic Optimization Problems 1.1 Deriving first-order conditions: Certainty case We start with an optimizing problem for an economic agent who has to decide each period how to allocate his resources between consumption commodities, which provide instantaneous utility, and capital commodities, which provide production in the next period. At this point we assume that this agent doesn’t interact with anybody else in the economy. This might seem strange since the goal is to describe the behavior of macroeconomic variables. There are environments, however, in which the behavior of an economy with a large number of different agents can be described by the optimization problem of a representative agent. The assumptions to justify such a representative-agent approach are strong but the relative simplicity
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Unformatted text preview: makes it the logical starting point. The agent’s current period utility function, u(c t ), is assumed to depend only consumption, c t . The technology that turns capital, k t , into production is described by the production function f (k t ). Here k t measures the existing capital stock chosen during t − 1 and productive at the beginning of period t. Because of depreciation during production, only (1 − δ) will be available during period t. Typically the utility function and the production function are assumed to be continuous, differentiable, strictly increasing and concave in its argument and to satisfy the Inada conditions. A function g (x) satisfies the Inada conditions if lim x→0 ∂g(x) ∂x = ∞ and lim x→∞ ∂g(x) ∂x = 0....
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