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Find the optimal plan

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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: θl = 1, θh = 3. The present-bias factor is β = 1/4.

(i) Find the optimal plan θ g l := (c g 1 (θl), c g 2 (θl)) and θ g h := (c g 1 (θh), c g 2 (θh))

(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∗ := {θ g l , θg 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 β have to be for the optimal plan of 'good Jack' to be implementable?

Reference no: EM133082802

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