Suppose there is a pay-as-you-go social security system where social security is funded by a proportional tax on the consumption of the young. That is, the tax collected by the government is vc, where v 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. Assume the population grows at rate n and the real rate of interest on borrowing and lending is r. Write down an expression for the intertemporal budget constraint that considers the information given above. Can social security work to improve welfare for everyone under these conditions? Use diagrams to answer this question.