Considering credit market imperfections and social security in the two period model.

Suppose a PAYG social security system is established where social security is funded by a proportional tax on the consumption of the young. That is, the tax collected by the government issc, where s is the tax rate and c is consumption of the young. Retirement benefits are given out as a fixed amount b to each old consumer. Can social security work to improve welfare for everyone under these conditions? Use diagrams to answer this question.