Joanne Sleeps Exactly 8 Hours Per Day, and She Devotes

Essay

Joanne sleeps exactly 8 hours per day, and she devotes the remaining 16 hours to
work (H), golf (x₁)and computer games (x₂). She can work as many hours as she wants at a wage rate of $w per hour. The money price of a round of golf is p1 and the time price is 4 hours. Each computer game takes 2 hours to play and Joanne downloads the game from the internet for free (p₂ = 0). Her utility function is
U(x₁,x₂)= x₁x₂
i)Find the utility maximizing values of x₁ and x₂ as functions of w and p₁.
ii)When w = $10 per hour and p₁ = $40 how many rounds of golf is Joanne going to play? How many computer games? How many hours is she going to work?