Backward bending supply curve of labour

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This supply curve shows how the change in real wage rates affects the amount of hours worked by employees.

Referring to the graph, if real wages were to increase from W1 to W2 then the worker will obtain a greater utility, due to their higher income. Therefore, they would be willing to increase their hours worked from L1 to L2. Note that this may be hours worked per day, month, year or even lifetime. Over this section of the curve the substitution effect is positive while the income effect is negative. However, the substitution effect is greater than the income effect. Therefore, the increase in the real wage rate will cause an increase in the number of hours worked.

However, if the real wage increased from W2 to W3, then the number of hours worked per year would fall from L2 to L3. This is because the income effect has now become greater than the substitution effect. This is because utility gained from an extra hour of leisure is greater than the utility gained from the income earned working. Basically, beyond the wage of W2 we see that the worker is being paid enough to sustain their current lifestyle without having to work more hours, therefore creating the backwards bend in the curve.

The above only examines the effect of changing wage rates on workers already subject to those rates. It does not consider the additional labour supplied by workers previously in lower-paid sectors, who are attracted to the jobs where the individual supply curve has passed its peak. This may be substantially delayed due to the time necessary for those new entrants to gain the requisite skills in the higher-paying field.

[edit] Assumptions

Workers choose their hours.
Workers are homogeneous.
There are no contractual obligations.
Workers are utility maximising agents.

So as we can see from these assumptions, this condition is rare in aggregate under real world conditions, though at any time individual workers may have a personally backwards bending labour supply curve. Early retirement can sometimes be considered an example of the phenomenon over an entire lifetime. Overtime can reduce or negate the effect of a backward bending labour supply curve, by increasing wages only for hours worked beyond a certain amount. This increases the substitution effect at high labour supply but does not increase the countervailing income effect by as much as a higher flat wage rate would. This can cause workers to work more hours than they would under any flat wage rate, high or low.