Part 2 OLG model and pension reform The economy is populated by two generations of households. An individual household lives for two periods, has a natural logarithm utility function, and discounts the future at the rate of B. In period 1, the young household consumes C1, saves Si, and works for wage w. A proportional labor income tax is applied on the first-period income, and the tax rate is t. In period 2, the old household retires, consumes C2, and receives gross returns from savings, and pension benefit b. The interest rate is r. The number of newborns is growing at the rate of g (can be positive or negative). (a) If the government balances its budget every period, express the pension payment b in terms of known parameters or variables. (1pt) (b) Briefly discuss the recent demographic change in China and its effect on future pension benefit. List two policies that can mitigate this effect. (2pts) (c) Set up the maximization problem of the household described above. (1pt) (d) Solve the household problem and express the savings rate of the household in terms of known parameters or variables. (2pts) (e) If the government replaces the existing Pay-As-You-Go pension system with a Fully Funded pension system, what are the advantages and disadvantages associated with the reform. (2pts) Part 2 OLG model and pension reform The economy is populated by two generations of households. An individual household lives for two periods, has a natural logarithm utility function, and discounts the future at the rate of B. In period 1, the young household consumes C1, saves Si, and works for wage w. A proportional labor income tax is applied on the first-period income, and the tax rate is t. In period 2, the old household retires, consumes C2, and receives gross returns from savings, and pension benefit b. The interest rate is r. The number of newborns is growing at the rate of g (can be positive or negative). (a) If the government balances its budget every period, express the pension payment b in terms of known parameters or variables. (1pt) (b) Briefly discuss the recent demographic change in China and its effect on future pension benefit. List two policies that can mitigate this effect. (2pts) (c) Set up the maximization problem of the household described above. (1pt) (d) Solve the household problem and express the savings rate of the household in terms of known parameters or variables. (2pts) (e) If the government replaces the existing Pay-As-You-Go pension system with a Fully Funded pension system, what are the advantages and disadvantages associated with the reform. (2pts)