Set up the following problem as a control problem.

A government has an objective function that indicates it wants to maximise votes, v, by pursing policies towards unemployment, u, and inflation π. The party is constrained in its behaviour by the existence of an augmented Phillips curve of the form

π = −α(u − un) + πe α > 0 and expectations take the form of adaptive expectations, i.e.

π˙ e = β(π − πe

) β > 0 The government has just won the election at t = 0 and the next election is in 5 years’ time. It assumes that voters have poor memories, and weight more heavily the economic situation the closer it is to the election. It accordingly assumes a weighting factor of e0.05t

.