Problem 2. (15 Points) A regular survey of the workforce at the end of each year

Question

Problem 2. (15 Points) A regular survey of the workforce at the end of each year reveals that 1/5 are unemployed (State U), and this fraction does not change from year to year. In addition, in any given year 40% of the unemployed at the end of the previous year will find a job (State E). What percentage of the employed at the end of the previous yearws be employed at the end of the given year? You need to assume that each person in the workforce survives every year and that the Markov property holds for the corresponding process (which indicates whether a person is employed).

Explanation / Answer

At the end of every year, 20% of the workforce are unemployed, so 80% are employed.

At the end of the next year, 40% of the unemployed at the end of the previous year find a job. This is 40% of 20% = 8% of the total workforce.

So 8% of the total workforce switch from unemployment to employment. So, equal proportion of the workforce switch from empployment to unemployment.

8% is 10% of 80% (8*100/80).

So, 90% of the employed at the end of the previous year will still be employed at the end of the given year.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.