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In mainstream economic theories, the aggregate supply of labour is the sum of the labour supplied by everyone in the economy at a given real wage rate. Individuals decide how much to work by weighing the benefits against the costs of working. To make themselves as well off as possible, individuals should choose to supply labour up to the point at which the income obtained from working an extra hour just makes up for the extra hour of leisure they have to forgo.

In reality, labour supply is a function of variables in an economy. Labour supply curve is derived from the labour-leisure trade-off. As a result, there are two effects on the amount of desired labour supplied due to a change in real wage, namely the substitution effect and the income effect. From a Marxist view a labor supply is a core requirement in a capitalist society. In order to avoid labor shortage and ensure a labor supply, a large portion of the population must not possess sources of self-provisioning, which would allow them to be independent, and they must instead be compelled, in order to survive, to sell their labor for a subsistence wage. This Marx calls the "reserve army" of the capitalist system. In addition, Marx believe that within a capitalist system, labour is not augmented by technology instead it is replaced my technology.

The Labour-Leisure Trade-off

The trade-off is due to the fact that for each individual, there is a limited amount of time available to him or her. In microeconomic theory, individuals are assumed to be rational and seek to maximise their utility function. In labour market, their utility function is determined by choice between leisure and labour and constrained by the amount of waking hour available to them.

Mathematically, let w denote hourly wage, k denote total waking hours, L denote working hours,π denote other incomes or benefits and A denote leisure hours.The utility function and budget constraint can be expressed as following: max U(w L + π, A) such that L + A ≤ k.

This can be solved by using substitution or Lagrangian multiplier.

Real Wages and Labour Supply

Generally, an increase in the real wage affects households' decision of labour supply in two ways. First, an increase in the real wage increases the benefit of working an additional hour and thus increases the incentive for households to supply more labour. This effect is called the substitution effect. Secondly, an increase in the real wage increases households' wealth. Wealthier households can afford additional leisure and thus will supply less labour. This effect is called the income effect. These two effects operate in opposite directions.

Pure income effect

Consider what will happen to an individual's labour supply decision if he won the lottery. The lottery prize has made him wealthier, thus he reduces his labour supply. In the meantime, the lottery prize does not affect the current reward for giving up an hour of leisure, i.e. the real wage remains the same, there is no substitution effect. An increase in the expected future real wage is also an example of pure income effect.

Pure substitution effect

Consider a one-day rise in the real wage. Households' wealth is not substantially increased and can thus be treated as being constant. Therefore, the income effect of the one-day wage increase is negligible. There is only substitution effect. Households that are rational will only increase their labour supply for one day and resume to their normal labour supply once the real wage goes back to normal.

Income effect and substitution effect together

Consider a long-term increase in the real wage. An individual would be willing to work more as reward for working is greater, this is the substitution effect in play. On the other hand, at this higher wage, he can afford things by working only three or four days a week and spend the rest time on leisure. In this sense, he is tempted to work less and this is the income effect.

The longer the higher wage is expected to last, the larger its impact on his lifetime resources is and the stronger the income effect is. Thus, the household is more likely to reduce the amount of time he works. On the other hand, if he expects the higher wage will not last very long, the income effect is week and he may choose to work more now to take advantage of the higher wage. Therefore, the longer an increase in the real wage is expected to last, the stronger the income effect and the more likely the quantity of labour supplied will be reduced.

Labour Supply Curve

The labour supply curve of an individual relates the amount of labour supplied to the current real wage, all other things being constant. If the current real wage is measured on the vertial axis and the amount of labour supplied is measured on the horizontal axis, the labour supply curve slops upward because an increase in the current real wage leads to an increase in the amount of labour supplied.

Factors shifting the labour supply curve

Any factor that changes the amount of labour supplied at a given level of the current real wage shifts the labour supply curve. Increase in wealth shifts the labour supply curve to the left. An increase in the expected future real wage shifts the labour supply curve to the left.

Aggregate Labour Supply

The aggregate supply of labor is the total amount of labour supplied by everyone in the economy. The aggregate quantity of labour supplied increases when the economy-wide real wage rises. First, when the real wage rises, people who are already working may supply even more hours by offering to work overtime, by changing from part-time to full-time work, or by taking a second job. Second, a higher real wage may attract some people to join the labour force. For these two reasons, the aggregate labor supply curve slopes upward.

Factors that shift the aggregate labour supply curve

Increase in wealth casues the labour supply curve to shift to the left as it increases the amount of leisure workers can afford.
Increase in expected future real wage causes the labour supply curve to shift to the left
An increase in working-age population shifts the labour supply curve to the right
An increase in participation rate shifts the labour supply curve to the right.