The setup is the same as the one studied in Lectures 9 and 10. Suppose Jack has 2860 apples. His instantaneous utility function is logarithmic. The net interest rate is zero. There are two equally likely taste shocks: l = 1, h = 3. The present-bias factor is = 1/4. (i) Find the optimal plan g l := (c g 1 (l), c g 2 (l)) and g h := (c g 1 (h), c g 2 (h)) (ii) Find what 'bad Jack' will actually do in period t = 1 if there is no commitment device in place. (iii) Suppose Jack tries the commitment device B := { g l , g h }. What is bad Jack going to choose in either of the states? Can the commitment device B implement the optimal plan? (iv) Can any other commitment device implement the optimal plan? (v) If 'good Jack' has access to an IRA in period t = 0, how many apples will he lock in? (vi) How many apples will 'good Jack' be willing to pay to get access to the IRA? (vii) How high does have to be for the optimal plan of 'good Jack' to be implementable?