4. Public Goods (7 points) Jamal and Leisha just had their first baby. They are planning on how much time to dedicate to their private leisure activities versus child caring, which can be thought as a common public good to the household. On their leisure times, Jamal appreciates watching sports on TV, while Leisha prefers to do yoga. After working, sleeping and eating, each spouse has 42 hours a month to devote to child caring (C:) or leisure activities (Li). Jamal's utility over the time spent watching sports games and child caring is given by Uj = 21n Ly + InC while Leisha's utility over the time spent doing yoga and child caring is given by Uz = 21n Ly + 2In C, where C is the total amount of time spent by both on child caring, given by the sum of each individual's contribution: C = Cy + Cz. For this problem we are assuming that both Jamal and Leisha benefit from the increases in the total amount of time they both spend on child caring C but they don't derive utility from the time the other spends on their own leisure activities. (a) Write down Jamal's utility maximization problem.(b) Find Jamal's optimal number of hours devoted to child caring (C,) as a function of the time on the same task spent by Leisha (CL).{C} Now, write down Leisha's utility maximization problem. {:1} Find Leishu's optimal number of hours devoted to child eating [CL] as a function of the time on the same task Spent by Jamal {Cur}. (e) Use the response functions found in (b) and (d) to find the amount of time Jamal and Leisha spend on child caring and on leisure if they optimize their own functions.(f) From a utilitarian perspective (maximizing aggregate utility), what is the socially optimal amount of time they should spend on each task?(g) Is the answer for (f) different than (e)? If so, why? If not, why not