Hello it's a microeconomics questions

15.1 Let on, ag be the modes of decrement in a double-decrement table. Suppose that on is uniformly distributed over the year of age from a to r + 1 in its associated single- decrement table, and pitt 1, =chor Oct1. Find formulae for (ag)as and (ages in terms of of and qaz. 15.2 For a certain group of married women, for whom remarriage is not permitted, the dependent q- type rate of widowhood at each integer age i from 70 to 72 inclusive is twice the corresponding dependent q-type rate of mortality. The independent rates of mortality of wives follow a(55) ultimate (females). (i) Using a radix of 100,000 and assuming a uniform distribution of each mode of decrement in its associated single-decrement table, construct a double-decrement table for married women from age 70 to age 72 inclusive, giving also the value of (al)ra, the number of wives at age 73. (ii) Find the probabilities that a wife now aged 70 will (a) be alive and married at age 73; and (b) be widowed within 3 years. 15.3 In a certain country, widowed and divorced men are subject to the following independent g-type rates of decrement: mortality: English Life Table No. 12 - Males remarriage: rates depend on the age at, and the duration since, the end of former marriage; the following table is an extract from these rates: exact age at end duration duration of former marriage year Year 50 0.050 0.025 51 0.045 0.023 52 0.042 0.020 Calculate the probability that a man aged exactly 50 whose marriage has just ended will remarry within 2 years. 15.4 A large industrial company recruits a constant number of school leavers aged exactly 18 years on 1 July each year. Upon joining, workers undergo training for one year. Of those who complete this period of training, ten per cent fail a final test of competence and are dismissed. Employees may also leave service voluntarily at any time. The central rate of voluntary withdrawal from service is 0.15 for trainees and 0.10 at each age for fully trained employees. The occupation is hazardous and all workers, including trainees, are exposed to the risk of injury. The independent q-type rate of injury is 0.051219 at age 18 and 0.050030 at ages 19 and above. An employee who is injured is transferred to alternative work with a subsidiary company, at a relocation cost of 21,000. The mortality of all employees follows English Life Tables No.12 - Males. The number of employees attaining age 21 each year is 500. (i) Construct a service table covering the first 3 years of employment with the original com- pany, distinguishing between those about to take the final test of competence and those who pass it. [Regard failing the test as a special mode of decrement ] (ii) How many people are recruited on each 1" July