A feedback policy for a modified Samuelson–Hicks model

Under the assumption that the income Yt follows a Samuelson–Hicks type of model, we calculate a policy variable Gt , in closed form, so that Yt satisfies an ideal law being an influence variable. The approach uses some recently developed tools of non-linear feedback design; it is fully parameterized and allows the dynamic change of the influence variable . From the control theory point of view, we solve a non-linear model matching problem and produce a policy instrument that shapes the income Yt within a desired family of behaviours.

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