In the labour market, we can think of an individual at any point in time as occupying one of the three distinct states; he/she is either employed (state E), unemployed (state U) or not in the labour force (state N). During each period an individual may change from one state to another with some defined probability or remain in the current state. The transition probability matrix contains the average probability of remaining employed [Pr(E,E)], the average probability of an employed person becomes unemployed after one period Pr(U,E)] and other transition probabilities. Suppose that the transition probability matrix in a given labour market is given by and the initial distribution of individuals (in millions) is given by x0=[201050]⊤ What is the distribution of the labour force after ONE period? Hint: Use Matrix Multiplication Describe the approach you will adopt to find the distribution of the labour force after 3 periods.
