A linear model to determine the optimal policy for investment in social infrastructure is formulated and its solution is obtained using the Maximum Principle. The unique solution is characterized by a-bang-bang control, with only one interval of investment in social capital, and the endpoints of this interval can be numerically determined, given values for the parameters of the model. A generalization of the model which allows instantaneous jumps in the level of social capital is also analyzed,

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... and the solution to the modified problem is shown to be a uniquely determined impulse control. The final extension of the model allows us to determine an upper bound for the optimal time horizon.