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[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...

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

U (L,Y ) = LY + 2Y , 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).

  1. Assume that your hourly wage is 1. Write down your budget constraint.
  2. How many hours of labour would you supply when your hourly wage is 1? You can use any method you want.
  3. Now suppose that your hourly wage increases to 2. How many hours of labour would you supply now?
  4. 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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