Suppose Paul's utility depends on the amount of time spent ...

[casperchen82]

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) = 3x0.2 y0.8
  He has 15 hours of free time to spend on these two activities each week, and his goal is to maximize his utility.
  a. Set up the Lagrangian for this constrained maximization problem.
  b. What are the necessary conditions for the optimum from the Lagrangian?
  c. What is the optimal amount of time spent surfing the Internet and playing video games each week?

Question 2

How do the three basic economic questions relate to the firm?
 
  What will be an ideal response?

[leahchrapun]

Answer to Question 1

a. L = 3x0.2 y0.8 + 15 - x - y
b. The optimality conditions are
Lx = .6x-0.8y0.8 - = 0
Ly = 2.4x0.2y-0.2 - = 0
L = 15  x  y = 0
c. First solve for the MRS = MRT condition using the first two conditions above:
.6x-0.8y0.8 /2.4x0.2y-0.2 = y/4x = 1
or simply y = 4x. Substitute this into the budget constraint
5x = 15
So x = 3 and y = 12. Paul will spend 3 hours on the Internet and 12 hours playing video games. What a day

Answer to Question 2

Firms must choose WHAT goods and services to produce, HOW to produce them (through appropriate choice of resources and technology), and FOR WHOM they will be provided (what segment of the market on which to focus).