David has to work in order to earn a living. He is paid an hourly wage.He use his income to purchase various neccessities of life. For the sake of simplicity, suppose that David’s consumption needs are fulfilled by one “composite” good called”c“ . He has to divide his time between work and leisure, but he dislikes work and enjoys leisure. He can devote at most 24 hours a day to leisure. Therefore, if he wants to enjoy leisure for L hours,he can work for only 24-L hours. Suppose that David’s preferences for consumption and leisure are given by the utility function U=(C,L)such that he derives positive marginal utility from both commodities. Also suppose that the price of ”c“ is $1 per unit and the wage rate is $w per hour. Further suppose that David’s wage rate of $ w per hour is for the first eight hours a day and he receives an overtime wage of $w‘ per hour for extra time he works, such that w’>w . The relevant budget constraints are shown in the figure.
a. If David’s preferences are represented by an indifference curve like U1 , would he choose to work for more than eight hours? Explain your answer.b. If, instead, David’s preferences are represented by an indifference curve like U2, would he choose to work over time? Explain your answer?