Answer the the following microeconomics questions
.1 Let d1, or: be the modes of decrement in a double-decrement table. Suppose that d1 is uniformly distributed over the year of age from a: to a: + 1 in its associated single- decrement table, and p.31, = cfor [1 it E 1. Find formulae for {my}? and {my}? in terms of q:1 and 43:2. .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 a: from 'F to 'F2 inclusive is twice the corresponding dependent o-type rate of mortality. The independent rates of mortality of wives follow o[55} ultimate {females}. [i]- Using a radix of 1m,[l 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 'l' to age T2 inclusive, giving also the value of [Hf}f3, the number of wives at age 1'3. {ii} Find the probabilities that a wife now aged T will {a} be alive and married at age T3; and {b} be widowed within 3 years. .3 in a certain country, widowed and divorced men are subject to the following independent q-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 cf former 1 marriage year year 5i] {11125 51 d {11123 52 {11142 i' Calculate the probability that a man aged exactly 5i] whose marriage has just ended will remarry within 2 years. .4 A large industrial company recruits a constant number of school leavers aged exactly 13 years on 1 July each year. Upon joining, Iw'ilznrkers undergo training for one year. Of those who complete this period of training, ten per cent fail a nal test of competence and are dismissed. Employees may also leave service voluntarily at any time. The central rate of voluntary withdrawal from service is {1.15 for trainees and (1.111] 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 .51219 at age 13 and at ages 19 and above. An employee who is injured is transferred to alternative work with a subsidiary company, at a relocation cost of J3 1,1300. The mortality of all employees follows English Life Tables No.12 - Males. The number of employees attaining age 21 each year is . {i} Construct a service table covering the rst 3 years of employment with the original com- pany, distinguishing between those about to take the nal test of competence and those who pass it. [Regard failing the test as a special mode of decrement ] l'ii]I How manv people are recruited on each 1at Julv
