A person chooses between leisure and consumption. The utility derived from any combination of leisure and consumption is given by the formula: u = LC - 88C where u is utility, L is the number of leisure hours per week, and C is the number of dollars spent on consumption per week. This person can work as many hours as desired each week, at a wage of $4 per hour. There is no other source of income.
a. Suppose the wage increases to $8 per hour. Would this person choose to supply more labor at $8 than at $4? What happened to its utility function?
b. Now, instead of an increase in the straight-time wage, suppose overtime is offered at $8 per hour after working 40 hours at $4 per hour. Will this person accept the overtime, and, if so, for how many hours?