Consider a person who has to decide how spend their weekend. The person would li

Question

Consider a person who has to decide how spend their weekend. The person would like to `consume'
leisure, but would also like to consume goods over the weekend, which would require them to work.
They have access to a job that pays by the hour and where they can choose to work as many hours
as they wish. They are paid the same irrespective of whether they work on Saturday of Sunday.
Unfortunately, they also have a homework assignment to complete over the weekend, which will take
them exactly four hours in total and must be done. Completing homework has no eect on the
person's well-being.
(a) Assuming that leisure/consumption/homework are regarded as the same thing irrespective of
whether they occur on Saturday or Sunday, set out the maximization problem and derive the
rst order conditions for an optimal solution. Describe each part of your model and the outcome
carefully. You may assume that there is only a single consumption good with a price of $1.

Explanation / Answer

You have an edowment of time of 48 hours 4 hours must be spent doing hwk, so simply discard them they will have no effect on the problem decide on a wage say w then the utility max problem is simple to up max (l,c) U(c,l) s.t. c=(44-l)w substitute, take derivative, and set it =0 thats it substitution makes this a single variable problem

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