To think of the social security problem, assume the economy is populated by two overlapping generation populations, the young and the old. Population follows the growth rate n. Each person lives two period, young (t = 1) and old (t = 2) The utility function is given by U(C1, C2) = ln c + ln cz. When he is young, he receives wage w. At old period, he receives social security s. The life time budget constraint is C2 Ci + 1+r =w(1-7)+ 5 1+r where t is income tax. 1+r is the interest rate. To balance the social security payment. The following condition must hold (1 +n)=S where the wt (1+ n) if the tax revenue received from the young and s is the expenditure transferred to the old. 1+n is the population growth rate. Therefore, when is decided, the tax rate t = w(1+n) 1. Show a person's efficiency condition is choosing c and c2. Explain the intuition. 2. Solve ci, ca and explain how would this being affected by s, r and n 3. Now suppose we change the tax from income tax to lump sum tax T. That is, a person's budget constraint becomes C2 Ci + = w- T + 1 +r 1+r For the government, to balance the budget, what is the lump-sum tax T? 4. Are people happier in the new tax regime? (show the proof) To think of the social security problem, assume the economy is populated by two overlapping generation populations, the young and the old. Population follows the growth rate n. Each person lives two period, young (t = 1) and old (t = 2) The utility function is given by U(C1, C2) = ln c + ln cz. When he is young, he receives wage w. At old period, he receives social security s. The life time budget constraint is C2 Ci + 1+r =w(1-7)+ 5 1+r where t is income tax. 1+r is the interest rate. To balance the social security payment. The following condition must hold (1 +n)=S where the wt (1+ n) if the tax revenue received from the young and s is the expenditure transferred to the old. 1+n is the population growth rate. Therefore, when is decided, the tax rate t = w(1+n) 1. Show a person's efficiency condition is choosing c and c2. Explain the intuition. 2. Solve ci, ca and explain how would this being affected by s, r and n 3. Now suppose we change the tax from income tax to lump sum tax T. That is, a person's budget constraint becomes C2 Ci + = w- T + 1 +r 1+r For the government, to balance the budget, what is the lump-sum tax T? 4. Are people happier in the new tax regime? (show the proof)