Question 1: Social Security in an OLG Model. (40 points) Consider an OLG economy where Y = K(AN)1- and the growth rate of A and N are zero and n, respectively. Households' instantaneous utility function is given by U = In(C). Pay-as-you-go social security. Suppose the government taxes the young individuals' labor income at rate r and redistribute the benefits to old individuals.(10 points) Suppose that the economy is dynamically inefficient. Prove that the proposed tax policy is a Pareto improvement