Suppose Paul's Utility Depends on the Amount of Time Spent

question 24

Essay

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)= 3x^0.2 y^0.8
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?

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Definitions:

Shortage of Strawberries

A situation where the demand for strawberries exceeds the supply available in the market, often leading to increased prices and unmet consumer demand.

Competitive Market

A market structure characterized by many buyers and sellers, free entry and exit, and products that are similar enough to be considered substitutes.

Shortage

A market condition where the demand for a product exceeds the supply of that product, often leading to higher prices.

Effective Price Ceiling

A government-imposed limit on how high the price of a product can be charged, set below the market equilibrium to be effective.