**Definition: **

A value function is often denoted v() or V(). Its value is the present discounted value, in consumption or utility terms, of the choice represented by its arguments.

The classic example, from Stokey and Lucas, is:

v(k) = max_{k'} { u(k, k') + bv(k') }

where k is current capital,

k' is the choice of capital for the next (discrete time) period,

u(k, k') is the utility from the consumption implied by k and k',

b is the period-to-period discount factor,

and the agent is presumed to have a time-separable function, in a discrete time environment, and to make the choice of k' that maximizes the given function.

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