Verifying Karim's Maximum Utility at t=17 using the Second Derivative Test

An individual has 24 hours available each day to allocate between free time and work. After analyzing their preferences and constraints, it is determined that their optimal amount of free time is 16 hours per day. If this individual earns a wage of $25 per hour, what is their optimal level of daily consumption?

Calculating Daily Consumption from Time Allocation

Calculating Optimal Daily Consumption

An individual allocates their 24-hour day between work and free time. Suppose this person's hourly wage increases, but their optimal choice of free time remains the same. In this scenario, their optimal daily consumption level will increase by the same percentage as their wage.

An individual has 24 hours per day to allocate between work and free time. Match each scenario of hourly wage and optimal free time to the corresponding optimal daily consumption level.

An individual has 24 hours per day to allocate between work and leisure. They earn an hourly wage of €25. If their optimal daily consumption level is €200, they must be choosing to have ____ hours of free time per day.

Error Analysis in Optimal Consumption Calculation

Evaluating the Relationship Between Wages, Free Time, and Consumption

An individual has 24 hours per day to allocate between work and free time. Initially, they earn €20 per hour and their optimal choice is to have 16 hours of free time. Later, their wage increases to €30 per hour, and they adjust their optimal choice to 19 hours of free time. How does their daily consumption level change as a result of these adjustments?

Evaluating Financial Advice on Consumption Choices

Karim's Optimal Choice at Point E (17, 210): The Balance of MRS and MRT