In this paper we derive the correct solution of optimal closure of the state sector studied in Section 6.4 of Aghion and Blanchard (1994). Aghion and Blanchard only present an 'approximate' solution which entails a constant unemployment rate in what they call a turnpike approximation. We show that optimal unemployment paths have two features. First, unemployment is increasing up to a certain point in time, when, second, the remaining inefficient state sector is closed down. At that point in time, which we may define as the end of transition, unemployment is discontinuous. The approximate solution presented by Aghion and Blanchard is thus found to lead to welfare losses compared to the optimal policy. In particular, the unemployment rate corresponding to the solution presented in Aghion and Blanchard is too low. Our solution is formally based on transforming the dynamic optimization problem to a scrap value problem with free terminal time.