4. [25 points] Suppose that you have the following utility function:

*U *(*L*,*Y *) = *LY *+ 2*Y *, where *L *is hours of leisure and *Y *is other goods. The price

of *Y *is 1. For now suppose that wages are your only source of income. **You **

**allocate 18 hours a day between work and leisure (and sleep during the remaining 6 hours). **

- Assume that your hourly wage is 1. Write down your budget constraint.
- How many hours of labour would you supply when your hourly wage is 1? You can use any method you want.
- Now suppose that your hourly wage increases to 2. How many hours of labour would you supply now?
- Finally, imagine that you have received an inheritance which always pays you 8 dollars per day. The hourly wage is still 2. How many hours of labour will you supply?

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