2. Suppose there is a pay-as-you-go social semi-y system where social security is funded by a proportional tax on the consumption of the young. That is, the tax collected by the govemment is vc, where v is the tax rate and c is consumption of the young. Retirement benefits are given nut as a xed amount b to each old consumer. Assume the population grows at rate r: and the real rate of interest on borrowing and lending is r. 1Write 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 for the following two cases: when r r. n or when r s: it 1' Use diagrams to answer this