Kindly help me with this microeconomics questions

.1 The staff of a large company is maintained as a stationary population by 500 new entrants each year at exact age 20. One third of those reaching age 30 leave immediately. Of the remainder, : of those attaining age 60 retire immediately and the survivors retire at age 65. The only other decrement is death. Calculate (i) the number of staff, (ii) the number of deaths in service each year. Basis: English Life Table No. 12 - Males .2 A certain country's school system provides education for all children between the ages of 5 and 16 exactly. The country's population is stationary, there being 100,000 births per year. uniformly distributed over the year. The population of the country is subject to the mortality of English Life Table No. 12 - Males. (i) Find the number of pupils at any given time. (ii) The country's teacher training colleges are such that a constant flow of new entrants to the profession is maintained. Teachers are recruited uniformly over the year, and the ratio of pupils to teachers is 20 to 1. All teachers enter the profession at age 21 and retire at age 60. there being no withdrawals. Find the annual number of new teachers recruited. 1.3 For many years a company has recruited, uniformly over each year, 200 employees on their 20th birthdays and a fixed number of additional employees on their 25th birthdays. Mor- tality has followed English Life Table No. 12 - Males. Employees may retire on their 60th or 65th birthdays, and one third of employees reaching their 60th birthdays retire on that date. Employees leave the company only through death or retirement, and the total number of employees is 10,000. Find the total number of new recruits each year. 1.4 The male population of a certain country has been stationary for many years, there being 100,000 male births per annum, spread uniformly over the year; the mortality of males follows English Life Table No.12 - Males, and migration may be ignored. (a) Calculate the size of the country's male population at any time. (b) The government of the country has decided to introduce a social security plan, under which all employed men between ages 15 and 65 must contribute a fixed sum every week, the same sum being also payable by their employers. Men over age 65 will receive a pension of 100 units of currency per week, and those sick or unemployed between ages 15 and 65 also receive this amount. If it may be assumed that at any time 95% of men between ages 15 and 65 are employed, while the remaining 5% are sick or unemployed, calculate the weekly contribution payable by each employed worker. The scheme is to be financed on a pay-as-you-go basis (no fund is built up) and administrative costs are to be ignored 1.5 A large manufacturing company has for many years staffed one of its divisions by the recruit- ment, uniformly over each year, of 1.000 staff at exact age 20. At the end of one year in the job, new staff are examined for suitability, and 20% are dismissed. All employees are assessed at age 35, and 50% are immediately moved out of the division. At age 40, all remaining em- ployees are moved out of the division. Death is the only other reason for leaving the division. Staff experience mortality according to English Life Table No. 12 - Males. Calculate the number of staff in the division..6 In a certain country, all civil servants are recruited on their 25th birthdays. (Birthdays are assumed to occur uniformly over the calendar year). Of those who reach exact age 40, 10% obtain employment in private companies and leave the civil service immediately. All remaining civil servants retire when they reach age 60 or die in service before this age. Civil servants have for many years experienced the mortality of English Life Table No. 12 - Makes, and will do so for the indefinite future. The population of civil servants has been stationary for many years, and civil servants are recruited at the rate of 3.000 each year. (i) How many civil servants are in service at any given date? (ii) The government of the country has just decided to reduce the size of the civil service by 10%. This is to be done by immediately lowering the retirement age of civil servants. Find the new retirement age (to the nearest month), assuming that there are no other changes. .7 In a mortality table with a one-year select period, the following relationships apply at age r: (0