# Derivation of a Stochastic Labour Market Model from a Semi – Markov Model

### Abstract

The labour Market which is a major component of any economy refers to the supply and demand for labour. The two possible labour market states are unemployment and employment, and the transitions between these states are described by Markov processes. This paper is aimed at deriving a two – state stochastic model from the interval transition probability of a Semi – Markov Model that can be used to study the transition rate between the two labour market states. A stochastic model of four equations is derived using the probable movement between the two labour market states. The solution of the model exist and it is unique.The derived model equations are solved analytically and matlab programmes are written to help in the computation of the probable transition probabilities. The results of applying this model to the Nigeria’s labour market shows that the rate at which individuals are moving from unemployment state to employment state is very small compared to the rate at which individuals are remaining unemployed: about 559,948 persons (0.69%) are likely to enter the employment state from the unemployment state in 2035 while about 80,445,864 (99.13%) persons are likely to remain unemployed in that same year (2035). Also, the rate at which individuals are moving from employment state to unemployment state is very small compared to the rate at which individuals are remaining employed: about 4,604,040 (6.80%) persons are likely to enter the unemployment state from the employment state in 2035 while about 55,532,851 (82.02%) persons are likely to remain employed in that same year (2035) thereby increasing the number of unemployed. The result also indicates that this model can only measure effectively short term movements between the two labour market states.

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*International Journal of Mathematical Analysis and Optimization: Theory and Applications*,

*2019*(2), 610 - 630. Retrieved from http://jmtcs.unilag.edu.ng/index.php/ijmao/article/view/568