# Income and Substition Effect: Assumptions: Normality vs. Inferiority of Goods

A question concerning the income and substitution effect when the wage changes

Let us assume that the substitution effect leads to more less leisure as the relative price of leasure increases, and more labor supply.

Let us also assume that the income effect works in the opposite direction. So, the individual will decide for more leisure and less labor (income effect).

Now, here is the question:

This income effect can only work in the opposite direction (more leisure, less labor) if we have the underlying assumption that leisure is a normal good, right? Such that, if income increases, I want to have more of the normal good (leisure) and less of the alternative good (labor).

An additional, necessary assumption would be that labor is an inferior good, not? Otherwise the income effect would lead in the same direction as the substitution effect.

This income effect can only work in the opposite direction (more leisure, less labor) if we have the underlying assumption that leisure is a normal good, right?

If you only talk about positive income effect then yes leisure would have to be a normal good.

An additional, necessary assumption would be that labor is an inferior good, not? Otherwise the income effect would lead in the same direction as the substitution effect.

No, labor is not a good/service for an individual. An individual is not consuming labor. Since it is not a good/service to begin with we can't say its inferior or normal good.

The reason why you have substitution between labor and leisure is not because you can consume either labor or leisure but because labor and leisure are considered mutually exclusive. That is $$l = 1- \ell$$ where $$l$$ is labor supply, $$\ell$$ leisure and the 1 is there because we normalize the daily/weekly/monthly/etc time endowment to 1.

Its impossible to have $$l=0.6$$ and $$\ell =0.5$$ or $$l=0.3$$ and $$\ell =0.4$$. Since any time not working is by definition leisure and any time working by definition cannot be leisure you will always have $$l = 1- \ell$$.

Hence it is simply impossible to increase both consumption of leisure and supply of labor at the same time. This has nothing to do with assumptions on whether leisure is normal or inferior good, its simply implied from way how we commonly define leisure and labor. An increase in use of leisure means automatic drop in supply of labor and vice versa.

• Thanks a lot! Very helpful explanation. I will get back to you presently, if I got another question Dec 31, 2022 at 10:57
• One question: Do we also assume that all the wage that the HH (household) earns will be consumed? If we do not have access to capital markets (no bond holdings in the model) than this would be the case, right? Dec 31, 2022 at 10:59
• @Tenetet that depends on the model, in some models there are no savings in some you can save.
– 1muflon1
Dec 31, 2022 at 11:01
• @Tenetet no you can possibly have model with no capital markets and still saving between periods. Then the individual just does not get any interest on saving so implicitly nominal interest on saving is zero
– 1muflon1
Dec 31, 2022 at 11:02
• Ok, I see. Makes sense. Regarding income effect, let us assume both consumption as well as leisure are normal goods. If the wage increases, then my total wealth (income) increases. If my total wealth increases, then I want to have more of both (cons.+leisure) as they are normal goods. So it could also be that I want the good "consumption" so much more that because it is more important to me than leisure that I also supply more labor in the income supply? Would this theoretically be possible? Because normally one assumes that income effect only means that I take more leisure and that's it. Dec 31, 2022 at 11:05