The labour supply can be understood using the Consumer Theory. For a typical person, the opposite of labour is leisure. Therefore wages are the opportunity cost of leisure, or the price of leisure. We are assuming that leisure is consumed just like any other goods, and people would want more of it.
With this understanding, a budget constraint line can actually be plotted. The budget constraint of a person is 24 hours per day, and the person can choose to spend it on consuming leisure or on obtaining wages, which in other words is to supply labour.
Substitution and Income Effects of Wages
When wage increases, substitution effect will cause the person to reduce his consumption of leisure, because the opportunity cost of leisure had increase. However, the income effect also plays a part, because since the person had gained more income, he can afford to consume more leisure (assuming leisure is a normal good). This may also be due to achieving an income target or threshold, and any additional income may not yield as much utility as increasing the consumption of leisure.
Therefore, the characteristics of labour supply depends very much on these two effects. For people who have no other avenues to spend their leisure time, the substitution effect may be diminished. Similarly, for someone who is very deeply involved in the labour market, the income effect will be very significant, as compared to a freelancer with numerous other commitments.
It is theoretically possible that if income effect greatly dominates substitution effect, labour supply curve may become downward slopping, meaning an increase in wages actually decreases labour supplied.
Case Study regarding Child Labour
An argument against free trade is that the increase in global demand for goods from less developed region is worsening child labour as more children joined the labour force to meet the market demand. This creates a vicious cycle as children who did not receive education are forgoing higher wage opportunities in the future.
This argument ignores the income and substitution effect in the child labour market. Free trade had cause the price for the exported goods to increase, and for the producers in developing region, they receive more income. The income effect will make the producers choose to send their children to school for education instead of letting them join the labour market. Of course, the substitution effect would tempt some children to give up education to earn higher wages. However, if income effect greatly dominates substitution effect, we will actually see a decrease in child labour. Therefore, more data and statistics is actually required to reach a conclusion.
(Reference: MIT OCW Principles of Microeconomics)