1. (50 pts) Enforcement of ROSCAS Rotating Savings and Credit Associations are a com- mon way for the poor to save and get big lump sums. But ROSCAs have many of the same problems that plague credit in general. Suppose 10 women come together, each of them put in $20 a month, and they pick the first person to get the $200. All of them can invest in a goat whose milk they will sell. The goat provides an income of $30 a month. Income from other sources is $60 a month. They consume all income that they are not saving, or putting into the ROSCA. (a) (5 pts) First, let's suppose each woman saves separately. Each woman saves $20 a month for 10 months, and then after these 10 months each buys a goat which adds to her income (buying the goat does not count as consumption). What is the average consumption of each woman in the group over the 10 months that they are saving, and after each owns a goat? (b) (10 pts) Now suppose that these 10 women form a ROSCA and give the $200 the first month to one member, and so on until they have all received $200, and each bought a goat. Calculate average consumption of the group for each month. Remember that the person who gets the money first must keep on contributing afterwards, but has a higher income. Did the ROSCA help the group on average? [Hint: To answer this question, you need to think about what happens each month. You can do the calculations by hand, or use Excel if you find it easier.] (c) (10 pts) The last member of the group only gets the $200 after 10 periods. Once she learns that she is last, does she prefer saving by herself or being in the group, or is she indifferent? Before they hold the lottery and find out who goes first and last, are any of the women indifferent about joining? (d) (10 pts) Now consider the incentives of the first person to get the payout. She has to show up for the next nine months and pay $20, otherwise the scheme falls apart. Suppose the only threat the group has is that they will kick her out if she does not pay into the group, and she will not be eligible for the next round of the ROSCA. (Assume these women don't know each other outside of the ROSCA). If she is kicked out of the group, she can still save $20 dollars for the next 10 months. Given her outside option, is being kicked out bad for her? Will she take the $200 and run? Can the group form under such incentives