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Fully Funded social security. Suppose the government taxes each young person an amount and
uses the proceeds to purchase capital. Individuals born at t therefore receive (1 + rt+1) when they
are old. (b-i) Write down the individuals utility maximization problem, derive the rst order
condition and solve for st . Find @st @ and explain the eect of 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?

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