How a rise in the wage can reduce the amount a person wants to work

Short answer. A higher wage has two opposing effects on hours of work. The substitution effect pushes hours up, and the income effect pushes them down, provided leisure is a normal good. If the income effect is the stronger of the two, the person chooses to work less at the higher wage.

The choice between work and leisure. A person's time is limited, so time spent at leisure has other possible uses, and working is one of them; deciding how much labour to supply is a choice between income and leisure. We apply the consumer's choice between two goods, with leisure as one good and the goods bought with earnings as the other. Each hour of leisure costs the wage that could have been earned in that hour, so the wage is the price of leisure. A rise in the wage is therefore a rise in the price of leisure. Like any price change, it can be split into a substitution effect and an income effect.

Substitution effect. Leisure is now dearer relative to goods: each hour off costs more of them. Keeping her satisfaction unchanged, the person substitutes away from the good that has become relatively dearer. She takes less leisure and works more. This effect always favours more work.

Income effect. At the higher wage, the same hours of work earn more, so she is better off. How she responds depends on the kind of good. Demand for a normal good rises with income, and demand for an inferior good falls. For most people leisure is normal, so being better off leads her to want more leisure, and so less work.

When the wage rise reduces work. The two effects pull in opposite directions, so the net result depends on their relative strength, just as with any good whose substitution and income effects oppose each other.

The income effect is more likely to win at high wages, when the person already earns a large income and values extra free time more than extra earnings. Her labour supply curve then bends backwards: hours rise with the wage up to a point and fall beyond it, because at low wages the substitution effect dominates and at high wages the income effect does.

Example. Our own figures. A freelance designer in Bengaluru earns ₹500 an hour and works 10 hours a day, making ₹5,000. Her rate rises to ₹1,000 an hour. She could keep 10 hours and earn ₹10,000, but she chooses 8 hours: she still earns ₹8,000, which is more than before, and she has two more hours free. For her, the income effect has outweighed the substitution effect.

Assumptions. Her tastes and non-wage income stay the same, and prices of goods are unchanged. She is free to choose her hours. Leisure is a normal good for her: if it were inferior, both effects would push towards more work.

Conclusion. A rise in the wage makes leisure dearer, which encourages work, but also makes the person richer, which encourages more leisure. If the income effect dominates, she wants to work less at the higher wage.