Fully Funded social security. Suppose the government taxes each young person an amount (cid:28) and uses the proceeds to purchase capital. Individuals born at t therefore receive (1 + rt+1)(cid:28) when they are old. (b-i) Write down the individuals utility maximization problem, derive the rst order condition and solve for st . Find @st @(cid:28) and explain the eect of (cid:28) on private saving. (b-ii) Express kt+1 as a function of kt . How does k dier from the old value of k when the social security is absent? And why? (b-iii) Can the government use Fully Funded social security to improve on a decentralized equilibrium?.