Question 3 (15 points] Assume that the world has only 2 time periods. Workers are born and work in period 1 when they earn wages and retire and die in period 2 during which they receive social retirement benefits. They pay a 10% payroll tax to fund social security (pensions). The system is pay as you go (unfunded). Whatever is collected in payroll taxes from workers in the current period is paid out to retirees by evenly dividing collections of payroll taxes during the year among retirees in that period. In period 1 (before the social security system was set up there were 10 workers earning $30000 per annum. Assume that population of workers and wages of workers both grow at 5% per period - use a compounded growth rate for both. Ignore discounting issues and the time value of money. Define the rate of return per worker to any generation of workers/retirees as (total retirement benefits received per worker in that generation - total taxes paid per worker by that generation) / total taxes paid per worker by that generation. (a) [9 points] Complete the following table of workers, retirees, incomes, taxes, retirement benefits, and rate of returns (ROR) for this scenario. You can use a spreadsheet to complete the calculations. tax paid per earnings per # of worker workers ($) 10.0 30000.0 tax paid per worker (5) 0.0 benefits received per retiree ($) NA retiree total tax collected #of retirees 0.0 NA (benefits - tax) per retiree ($) NA ROR per worker/retiree (%) Period t (S) (5) t=1 NA NA tes t = 6 (last generation is retired) (b) [4 points) According to the table, is there a redistribution from young to old and/or legacy debt? Explain your answers. Question 3 (15 points] Assume that the world has only 2 time periods. Workers are born and work in period 1 when they earn wages and retire and die in period 2 during which they receive social retirement benefits. They pay a 10% payroll tax to fund social security (pensions). The system is pay as you go (unfunded). Whatever is collected in payroll taxes from workers in the current period is paid out to retirees by evenly dividing collections of payroll taxes during the year among retirees in that period. In period 1 (before the social security system was set up there were 10 workers earning $30000 per annum. Assume that population of workers and wages of workers both grow at 5% per period - use a compounded growth rate for both. Ignore discounting issues and the time value of money. Define the rate of return per worker to any generation of workers/retirees as (total retirement benefits received per worker in that generation - total taxes paid per worker by that generation) / total taxes paid per worker by that generation. (a) [9 points] Complete the following table of workers, retirees, incomes, taxes, retirement benefits, and rate of returns (ROR) for this scenario. You can use a spreadsheet to complete the calculations. tax paid per earnings per # of worker workers ($) 10.0 30000.0 tax paid per worker (5) 0.0 benefits received per retiree ($) NA retiree total tax collected #of retirees 0.0 NA (benefits - tax) per retiree ($) NA ROR per worker/retiree (%) Period t (S) (5) t=1 NA NA tes t = 6 (last generation is retired) (b) [4 points) According to the table, is there a redistribution from young to old and/or legacy debt? Explain your answers