Labor economics;

Institutions: A government has to meet an erogenous spending stream, gf per young person. It can raise taxes 74 per person in life period i and issue bonds, by per young person to cover expenditures. Markets in bonds and consumption goods (ignore inside money). (a) Write down the problem for an individual born in period t and derive the equation that (implicitly) gives savings as a function of the parameters of the individual's problem. (b) What is the government budget constraint in period ? (Assume govern- ment Ponzi-games are ruled out) (c) Define and characterize the competitive equilibrium. (d) To what extent can you change the paths of by, Ty and T2, subject to the government budget constraint, so that the allocation does not change? Comment on the answer. (e) Write down the Planner's problem and characterize his optimal alloca- tion. (f) Under what circumstances might government policy be Pareto improv- ing? Now suppose u(c) = In(c), 8 = 1, e1 = ez = e and ge = g for all time. (g) If the government in the decentralized economy cannot run a deficit (i.e. be = 0 for all t) and taxes are non-negative, what is the minimum size of g required for the government to achieve the optimal allocation. Explain the answer. (h) Suppose instead that the government cannot be ageist so that The = To = T. As long as taxes cover the immediate government spending (i.e. (2 + n)T/(1 + n) = g) solve for the optimal level of (constant) government debt, b* in terms of n, e and T