In any given week, Mia receives satisfaction only from the consumption of goods and from the consumption of leisure L, which is measured in hours. Obviously, Mia consumes many different types of goods, but for simplicity we aggregate the dollar value of all the goods that she consumes during the week and call it C. Assume that if Mia chooses to work, the hourly wage rate is w =4 and she has to sleep 8 hours per day. Potentially, if she wants, she can work up to 5 days a week. Call L Mia's weekly leisure time, where L is all the hours during the 5-day workweek during which Mia is neither working nor sleeping. Mia's utility is given by u(C, L) = CaL1_", where a = 0.5. Wherever rounding is needed, please round to 3 decimal points. a) (1 point) What is Mia's utility maximising choice of C? b) (2 points) By how many hours does her optimal choice of L increase if the government gives her a weekly unconditional subsidy of $20? c) (2 points) Suppose that a = 0.5 and that instead of giving Mia an unconditional weekly subsidy, the government gives Mia a weekly subsidy of R only if Mia does not earn any income from work at all. If she works a positive amount, no matter how small, she does not receive any subsidy. If Mia is exactly indifferent between not working and working a positive amount, it must be that R is equal to (fill in the blank)