4. Consider a consumer whose utility,r over leisure time (L) and spending money (3) is given by u(L, S] = LEE-9%. All spending money is earned by working at wage to per hour. There are T total hours to be divided between work time and leisure time. {a} Write out the budget constraint. (How much spending money is available if she wants L hours of leisure?) (b) USe the \"magic rule for Cobb-Doublas\" (will be taught in Lecture 4} to argue that this consumer will choose % leisure hours1 regardless of the wage. (e) Explain why these preferences are the same as those represented by v[L,S) = logL + 4 log .9. ((1) Using the utility,r function in {c}, nd the optimal demand bundle (L, S] as a function of n: and T. USe either a Lagrangian1 or the method of substitution, or the \"bang-perbuck\" method to do this. 1