社会保险习题 答案

1 (A life-eyele model with social security) In society there are individuals who work in the first period and retire in the second period. The population grows atrate at m per period, Luis the labor force at time tand Alis the retiree at time t Population growth rate nimplies that 太一(+站1 and太一(+月4 Each worker at time eams a wage of W， Each aged retiree receives benefits of b Now the society implements the pay-as-you-go social security system, so the govemment collects tax mate of to balance the revenue and cost which implies the total tax 五= WE =为=有4， Suppose each individual has the unique utility function HL+计1，where the argument of the u function is firstperiod consumption and the argument of the v function is consumption during retirement u and v have the same function form. The retum rate of savingisp 1D Assume each individual is completely myopiateach individual has no incentive to savej)，Solve the equilibrium when individuals are toually myopia and the pay-as-you-go social security system does not exist- When saeh individual ii compleely mopia each individual will consume the eneiin he stperiod 人 Assume each individual is completely myopia and the pay-as-you-go social Security system implemented. Solve the optimal tax rate 6 that maximize the social welfare (Weights of workers and retiree are indifference) 下payraryoutrgo socil secuig wsen has been implemented govemments wil ee eene ad et Fan ao rt artog ov 60 Thesocialweltore hnetion an be writen as  3) Assume individuals are partly myopia(A is mhe fraction of myopes and -AL is the fiaction of life-cyclers, Life-cyclers have the ability to smooth the consumption to maximize their utility and have no difference between the first period and the second period)