If an individual earns an overtime pay for over 8 hours of work, then how can this be depicted in the standard income-leisure model? In case of higher wages for overtime work is the theory of backward bending labor supply curve always violated? Assume flexibility of preferences

The Backward Bending Supply Curve:

The concept of the backward bending supply curve is associated with labor markets that represent a situation where after a certain point, a higher level of wages can lead to a decline in labor supply and thus the output. This is due to the increased leisure time of the workers that encourage workers to work less.

The standard income-leisure model: From an individual worker's perspective, an increased level of wages also increases the opportunity cost of leisure time. The trade-off between income (wage) and leisure specifies the sacrifice of leisure time for higher wages. If an individual earns an overtime amount for working over more than 8 hours, then according to this model, getting higher wages by the worker might result in the high opportunity cost of leisure that also influenced the output at the same time. For example- the higher is the working time contributed by the worker, the higher would be the wage and the less would be the leisure-time period.

In the context of a backward bending supply curve, overtime in industries by workers leads to low productivity and output.

In the case of higher wages for overtime work, is the theory of backward bending labor supply curve always violated?

The concept of a higher wage rate for doing overtime in industries can reduce the impact of a backward bending labor supply curve effectively, by increasing wages only for hours worked beyond a certain amount to increase productivity. Thus, higher hourly overtime pay can cause workers to work and produce after working for more hours than if the higher rate is paid on all hours.

If there is the flexibility of preferences in the labor market, the concept of overtime does not influence the work and productivity both at the time when salaried employees take advantage of fixed incomes and flexible conditions regarding the worker's ability to influence working hours. However, flexible working can improve work intensity through enabled intensification.