In a given day, once you subtract 8 hours for sleep, you effectively have 16 hou

Question

In a given day, once you subtract 8 hours for sleep, you effectively have 16 hours from which you can choose to work or enjoy leisure (that is to say, sleep doesn't count as leisure). You have a job that pays $20/hour and that is your only source of money. Assume you live in a world where the only good available for purchase is fudge bars, and they cost $2 each. Your utility function in fudge bars and leisure is given by U(F,R)=(F^.5)*(R^.5). If you are behaving optimally, how many fudge bars will you purchase in a week?

Explanation / Answer

There are only 16 practical hours in a day, and 7 days in a week, that gives us 112 hours in the week The Utility function is U(F,R)=(F0.5*R0.5) Therefore, maximum utility is derived when 0.5 of the utility is fudge bars, and 0.5 of the utility is leisure Since maximum utility is equal, you only need to find out the equation at which both hours worked and fudge bars are equal You make $20/hour, and fudge bars are $2, so your real wage is 10 fudge bars/hour So you need to work x hours, and have y hours of leasure to make that equal There are 112 hours for you to give your time to, so we know x+y=112 You also know that each hour of work is 10 fudge bars, and that fudge bars have to equal hours of leisure, so you have y=10x Sub that into the first equation, and you get 10x+x=112 11x=112 x=10.181818 So you should work 10.18 hours, which means you should buy 101 fudge bars

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