Suppose Paul\'s utility depends on the amount of time spent playing on the Inter

Question

Suppose Paul's utility depends on the amount of time spent playing on the Internet (x) and the amount of time playing video games (y), and his utility function is U(x,y)= 3x0.2y0.8e has 15 hours of free time to spend on these two activities each week, and his goal is to maximize his utility. The price he pays for each activity is one. Draw the graphical constrained maximization problem if Paul considers Internet and Video games as imperfect substitutes. Set up the Lagrangian for this constrained maximization problem. What are the necessary conditions for the optimum from the Lagrangian? What is the optimal amount of time spent surfing the Internet and playing video games each week?

Explanation / Answer

a) U(x,y) s.t. x+y=15

b)Lagrangian :L= U(x,y) - (x+y-15)

c) dL/dx =0

dL/dy = 0

x+y =15

d) 0.6x-0.8y0.8 -1 =0 y/x =(5/3)4/5

2.4x0.2y-0.2= 1

x+y =15

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