. a - J. Barney earns $6 an hour and his utilit function is 11(C,1') : c132, where c is dollar worth of consumption and I is hours of leisure. Assume that Barney has 108 hours a week for either labor (h) or leisure (I) a) Write down the equation for Barney's budget constraint. b) How many hours per week does he work? Let his optimal hours of labor supplied be denoted by 11*. c) What is the dollar value of his optimal consumption per week? Suppose now that Barney's employer decides to implement an overtime wage policy. Ac cordingly, Barney will be paid $9 for every hour he works in addition to 11* (Le, W : 6 for the first h* hours and W = 9 for all additional hours). d) Write down the equation for Barney's new budget constraint. e) Draw his new budget constraint. Make sure to label both axes and indicate the relevant points on the budget line. f) Calculate how many hours does Barney work? g) How does the policy affect Barney's optimal consumption level