1. [70 MARKS] Consider the following simplified version of the paper "Self-Control at Work" by Supreet Kaur, Michael Kremer and Sendhil Mullainathan (2015). In period 1 you will perform a number of data entry task for an employer. The effort cost of completing tasks is given by or , where a > 0. In period 2, you will be paid according to how many task you have done. The (undiscounted) utility for receiving an amount of money y is equal to y. From the point of view of period 1, the utility from completing ar tasks and getting money y is equal to -or + By where BE [0. 1], while from the point of view of period 0 it is -ar +y- Assume that you are not resticted to completing whole number of tasks (so you can solve this problem using derivatives). (a) [15 MARKS] Assume that you get paid $1 for each task (so if you complete r tasks you get y = x). In period 1, you are free to choose how much work to do. Calculate how much you will find optimal to do (as a function of a and A). (b) [15 MARKS] Derive how much work you would choose to do if you could fix in period 0 the number of tasks you would do in period 1 (as a function of a). Call this "(a) (the number of task completed under commitment). Assuming #