Chinese Economics(Econ 4317)

The economy has an overlapping generations demographic structure. Each individual lives up to two periods. At period 1, the individual understands that with a probability of p, she can survive at period 2. In other words, p is the fraction of individuals who can survive for two periods. If the individual dies, the utility she earns is normalized to 0. At period 1, the young household consumes 61, saves 51, and works for wage to. In the second period, conditional on survival, the old household retires, consumes 2, and receives returns from savings. The interest rate is xed at r. The household derives the utility from a standard natural logarithm utility function, and discounts the future at the rate of ti. [> (a) Set up the household's maximization problem. Write down period-by-period budget constraint and inter-temporal budget constraint. [> (b) Solve the optimal consumption and saving decisions of the household. [> (c) What is the savings rate implied by the optimal decision? Now we incorporate a pay-as-you-go pension system into the economy. "the income tax rate levied on a young household's wage income is T, and the amount of pension paid to an old household is 17. Also assume that the number of newborns is fixed at N. [> (d) [f the government balances its budget every period, what is the expression of the pension payment b? [> (e) Rewrite the period-byperiod budget constraints and the inter-temporal budget constraint of the household- [> (f) Compare the present value of lifetime earnings for a household (who survives at period 2) living with and without the pension system- Under what condition she prefers the economy with the PAYG pension? [> (g) Resolve the optimal consumption and saving decisions of the household. [> (h) What is the savings rate when pension is available? Show that the availability of pension reduces the savings rate of the household. [> (i) Suppose China did not have a public pension system at all before. In order to provide necessary supports for current aged people, now the government plans to build a public pension fund. Which system (PAYG or FF) is more suitable in this case? D (j) Economists are debating on whether it is welfare-improving to replace the current PAYG system with a PP pension system. Discuss the reason why young workers are strongly opposing this policy proposal