Having a hard time connecting the two picture, why is the supply of good 1 decreasing after a certain point of p1?
1 Answer
Raising your wage means that you can consume more. It also means (if you want to) that you can afford to consume more leisure. However, because you have to forgo more consumption per hour of leisure than you did at the old wage, this causes you to substitute away from leisure and towards consumption (more consumption, less leisure) which causes you to supply more labor.
However, with a high enough wage, the marginal utility of consumption is very low while labor supply has gone so high that the marginal utility of leisure is very high. Eventually the wage is so high that the same wealth effect that made you work more makes you consume so much that consuming more looks less attractive than working less. This causes labor supply to drop and the supply curve to bend back.
All of this depends on the household utility function. There are some utility functions where the backward bending never occurs. For example, linear utility.