Question

Consider the situation of a mass layoff (i.e. a factory shuts down) where 1,200 people become unemployed and now begin a job search. In this case there are two states: employed (E) and unemployed (U) with an initial vector X' = (E U) (0 1,200) Suppose that in any given period an unemployed person will find a job with probability 0.7 and will therefore remain unemployed with a probability of 0.3. Additionally, persons who find themselves employed in any given period may lose their job with a probability of 0.1 (and will have a 0.9 probability of remaining employed) (a) Set up the Markov transition matrix for this problem (b) What will be the number of unemployed people after (i) 2 periods (ii) 3 periods (ii) 5 periods (iv) 10 periods? (c) What is the steady- state level of unemployment?

Answer 1

Mankov Hatrix 3 t . [o 2 120 0 ( 200 7 12 0 12 0 16 1921 v,1 2= 192 U2nunben T T.. 10 09 7 t58 4 [n.si 21. Q 91-0 150 3363 v) 23

150 00 C 4-191 212 Sin u te numlen in (onvinging 150