Backward bending supply curve of labour
In economics, a backward-bending supply curve of labour or backward-bending labour supply curve is a graphical device showing a situation in which, as "real" or inflation-corrected wages increase beyond a certain level, people will substitute leisure (non-paid time) for paid work-time and thus higher wages lead to less labor-time being offered for sale.
The "labor-leisure" tradeoff is the tradeoff faced by wage-earning human beings between the amount of time spent engaged in wage-paying work (assumed to be unpleasant) and satisfaction-generating non-paid time that allows (1) participation in "leisure" activities and (2) use of time to do necessary self-maintenance, such as sleep. The key to this tradeoff is a comparison between the wage received from each hour of working and the amount of satisfaction generated by use of non-paid time. Such a comparison generally means that a higher wage entices people to spend more time working for pay; this "substitution effect" implies a positively sloped labor supply curve. However, the backward-bending labor supply curve results when an even higher wage actually entices people to work less and to "consume" more leisure or non-paid time. 
As wages increase above the subsistence level (discussed below), there are two considerations affecting a worker's choice of how many hours to work per unit of time (usually day, week, or month). The first is the substitution or incentive effect. With wages rising, this says that the trade-off between working an additional hour for pay and taking one extra hour of non-paid time changes in favour of working. Thus, more hours of labor-time will be offered at the higher wage than the lower one. The second and countervailing effect is that the hours worked at the old wage rate now all gain more income than before, creating an income effect that encourages more leisure to be chosen because it is more affordable. Most economists assume that non-paid time (or "leisure") is a "normal" good which means that people want more of it as their incomes (or wealth) rise. Since a rising wage rate raises incomes, all else constant, the attraction of non-paid time rises, eventually cancelling out the substitution effect and implying the backward bend.
Referring to the graph, if real wages were to increase from W1 to W2 then for an individual worker the substitution effect outweighs the income effect; therefore, they would be willing to increase their hours worked for pay from L1 to L2. However, if the real wage increased from W2 to W3, then the number of hours offered to work for pay would fall from L2 to L3. This is because the strength of the income effect now exceeds that of the substitution effect: the utility to be gained from an extra hour of non-paid time is now greater than the utility to be gained from extra income that could be earned by working the extra hour.
The above only examines the effect of changing wage rates on workers already subject to those rates — that is, only these individuals' labour supply response was considered. It did not consider the additional labour supplied by workers working in other sectors (or unemployed), who are now more attracted to the jobs in the sector paying higher wages. Thus, for a given market, the wage at which the labour supply curve bends backward may be higher than the wage at which a given worker's curve bends back.
On the other hand, for the aggregate labor market, that is, a labor market without "other sectors" for workers to come from, the original story of the backward-bending labor-supply curve applies, except to the extent that some workers suffer from involuntary unemployment.
- Workers choose their hours.
- There are no contractual obligations to work a certain number of hours.
- Workers are utility maximising agents.
- Work provides disutility that must be compensated for by paying wages.
- Non-paid time is a "normal" good.
Higher pay for overtime hours can reduce or negate the effect of a backward bending labour supply curve, by increasing wages only for hours worked beyond a certain amount. Overtime maintains the substitution effect at high labour supply, but the income effect from wages increasing on all previous hours worked is eliminated. Thus higher hourly overtime pay can cause workers to work more hours than they would if the higher rate was paid on all hours.
Inverted S shaped supply curve
At very low wage levels — that is, near the subsistence level — the supply curve may also be curved backwards for a completely different reason. This effect creates an "inverted S" or "backward S" shape:a tail is added at the bottom of the labor-supply curve shown in the graph above with the quantity of labor-time supplied falling as wages rise. In this case, because families face some minimum level of income needed to meet their subsistence requirements, lowering wages increases the amount of labor-time offered for sale. Similarly, a rise in wages can cause a decrease in the amount of labor-time offered for sale: individuals take advantage of the higher wage to spend time on needed self- or family-maintenance activities.  
- Friedman, Jack P. (2000-05-01). Dictionary of Business Terms. Barron's Educational Series. ISBN 978-0-7641-1200-3.
- Dasgupta, Purnamita and Goldar, Bishwanath (2006). "Female Labour Supply in Rural India: An Econometric Analysis" Indian Journal of Labor Economics, 49(2), 293-310.
- Sharif, Mohammed (2000) "Inverted 'S' – The Complete Neoclassical Labour-Supply Function." International Labour Review, 139(4): 409-35; plus Dessing, Maryke (2002) "Labor supply, the family and poverty: the S-Shaped Labor Supply Curve," Journal of Economic Behavior & Organization, 49(4) December: 433–458; and (2008) "The S-Shaped Labor Supply Schedule: Evidence from Industrialized Countries," Journal of Economic Studies, 35(5-6): 444-85; and Bendewald, Jennifer. Subsistence Theory in the U.S. Context: A CrossSectional Labor Supply Estimate.