Artificial intelligence and associated technological advances have progressively diffused from routine tasks to non-routine tasks, causing disruptions in the labour market. In this work, we study the effect of automation on the labour market outcomes for low-skill and high-skill workers. We use the agent-based modelling approach to model firms and workers as rational agents with defined objective functions, endowments, and interactions. Using extensive simulations, we analyse the emergent phenomena of employment levels and wage inequality in the labour market under varying scenarios. The key findings of our simulations indicate that routine task automation decreases demand for low-skill workers, increases demand for high-skill workers, and increases wage inequality. Cross-skilling low-skill workers to perform non-routine tasks increases the demand for both low-skill and high-skill workers while curbing the growth in wage inequality. Further, the results indicate that non-routine task automation increases the demand for low-skill workers, decreases the demand for high-skill workers, and reduces wage inequality as the high-skill workers lose their wage premium advantage. The findings also suggest that cross-skilling of displaced high-skill workers in routine tasks fulfils increased labour demand and provides them with employment opportunities. This study suggests that if the objective is to reduce wage inequality between the different classes of workers, the automation of non-routine tasks is preferable. However, if the objective is to increase the demand for both low-skill and high-skill workers, then automation of routine tasks is preferable, with no restrictions on different classes of workers competing amongst themselves to get the job. Based on our results, we propose policy prescriptions regarding the job categories in which automation can be introduced for societal benefits, the skill enhancement programmes needed for the workers, and guidelines on the redeployment of labour displaced through automation.