Is labour supply curve upward-sloping?

   Demand curves are downward sloping. This is already a basic knowledge for everyone who has learned economics. Do we need to know why demand curves are downward sloping? Someone think that we do not need to if there is no any exception to this law (no upward sloping demand curve). In fact, high-school economics syllabus does not require students to understand the reason why. Meanwhile, some others think that even if there is no exception, we should still know the reason why. 

   As I have discussed in a past post, my viewpoint is that know-why is very important. I am not sure my arguments given in that post is convincing enough. Anyway, I think that more people will appreciate that know-why is important if we cannot explain an important phenomenon without a theory of know-why. This post is exactly concerned with this phenomenon - why labour supply curve is upward sloping but it can be, actually sometimes is, downward sloping? 

   Isn't labour supply about supply curve? Why is it related to demand curve? The reason is simple: if one does not work, one can enjoy the leisure time; if one works, one sacrifice the leisure time. Hence, labour supply and leisure demand are two sides of the same coin. When one demands more leisure time, one supplies a smaller amount of labour service. When one demands less leisure time, one supplies more labour service to the market. 

   OK, now the demand curve for leisure should be downward sloping if all demand curves are downward sloping. If leisure demand curve is downward sloping, then labour supply curve is upward sloping because labour supply is the opposite of leisure demand. Meanwhile, if labour supply curve may be downward sloping, leisure demand curve may be upward sloping. If this is true, we have an exception to the law of demand -- the demand curve for leisure is not downward sloping!

   Then, are there any labour supply curves downward sloping? Yes, there is plenty of empirical evidence showing that labour supply curves may sometimes be downward sloping. In particular, people find that the supply curve is backward bending -- when the price of labour service (wage) is not too high, the supply curve is upward sloping; but when wage is high enough, the curve becomes downward sloping. In economics, this phenomenon is not considered to be a surprising result. It is not controversial and can be easily explained! Why? Why do we consider demand curve should be downward sloping but don't consider backward bending labour supply as a surprising result?  

   The whole thing is related to the reason why demand curve is downward sloping and the explanation that I have already given in a past post - substitution effect and income effect. When the price of a good increases, it triggers people to replace the good by another good whose price is not changed. If both goods (e.g. apple and orange) can help you achieve the same goal, you will avoid the more expensive good (apple), and buy another good (orange) more, when price (of apple) rises. This is substitution effect. Meanwhile, a higher price of a good means that the same income cannot buy so many goods as before. This effect is like a reduction in your income (although your income is not actually reduced). If the good is a normal good, income reduction leads you to buy fewer of this good. This is income effect. Hence, taken together, demand curve is downward sloping. 

   Now, leisure is a normal good. When you are rich, you prefer enjoying more leisure. 

   When wage (the price of enjoying leisure time) is higher, you tend to enjoy less leisure time. Instead, you replace leisure by material consumption that can be increased by working more and earning more. This is substitution effect. When wage is higher, this effectively increases your income as you can earn more by working the same hours. The income effect for leisure is positive. This means you tend to enjoy more leisure time (and supply a smaller amount of labour service). Taken together, substitution effect and income effect work in opposite direction. As such, higher wage may not reduce leisure demand. It may increase leisure demand (leisure demand curve is upward sloping) if the income effect dominates the substitution effect. This also means labour supply curve may be downward sloping. 

   Now, you can see: the same framework of substitution-income effect can explain why normally demand curves are downward sloping and why labour supply curve may be backward bending. Demand curves are normally downward sloping because most goods are normal goods. Labour supply is backward bending because leisure is also a normal good but a higher price of leisure increases one's income. A higher price will not reduce income, unlike the cases for other goods, because one can sell leisure time for earning income. This example illustrates clearly why the framework of substitution and income effects is so important and useful. 

   There is one more thing requiring explanation. A backward-bending labour supply curve means that the curve is downward sloping only when the wage is high. When the wage is low, the curve is still upward sloping. Why income effect of leisure is relatively bigger and so will dominate substitution when wage is high enough? One suggestion is that people will begin to tire when working long hours. Hence, at some point, they would rather enjoy more leisure time than work more. In fact, the point is that poor people working long hours also tire. But when their wage is low, the income effect from wage rise is not strong enough. When wage is low, some increase will not enable the worker to earn much more. But this income effect should become more pronounced when wage is already high. So, evaluating the hardship of tiring and more income, workers may think that avoiding the hardship is more important. This explains why income effect is more pronounced when wage is already high.