4 pts) Betty also has a job that pays her an hourly wage. Her utility over leisure (Le) and other things (x) is: =260ln()+ Assume for simplicity that =1 a. If the money Betty earns is all she has to spend, solve her utility maximization problem to derive Le and x as functions of w. (Hint: we solved part of this problem in class.) b. How many hours does Betty work if she gets paid an hourly wage w=$20? c. Her grandmother Olga is worried that Betty works too much, so she starts sending her transfers that amount to $100/day. How much will Betty work now? (You can continue to assume w=$20) d. Is there some other (legal) scheme Olga could implement to get Betty to work less? (Assume Olga is able to see how much Betty is getting paid each day.)