Introduction to Dynamic Optimization: The Calculus of Variations

Static models aim to find values of the independent variables that maximize particular functions. Such optimization problems seek the value or values of an argument that optimize a given function at a particular point. Dynamic models aim to find not just the maximum value of some function, but rather, the actual function that provides a time path for the values of the economic variables so that some value function is maximized or minimized over a given interval of time.