Suppose that an individual has unearned income of $V and can choose how many hours she works per week at a wage of $w per hour. Assume that she has a total of 110 hours of time to allocate between work and leisure (i.e., H_{max} = 110). Her utility depends on leisure (H) and available consumption (Y).
a. Draw a diagram representing her budget constraint and illustrating her optimal choice of leisure and consumption. Make sure she chooses to supply a strictly positive amount of labour.
b. Suppose that her employer relocates to a new establishment that is some distance from her residence. As a result, if she works she must spend 5 hours per week commuting to the job, regardless of the number of hours she chooses to work. Commuting time does not affect her utility but it does reduce the time available for work and leisure. Draw a diagram that illustrates how this time cost of working alters her budget constraint. Describe how it will affect her optimal choice.
c. Suppose that her employer had not relocated, but instead required her to rent a uniform and renting that uniform cost $R per week, regardless of how many hours she works. Illustrate how this would affect her budget constraint. What happens to her optimal choice?