3. Retirement Saving [40 marks] Present bias may induce individuals to save too little for old...

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3. Retirement Saving [40 marks] Present bias may induce individuals to save too little for old age, when they no longer have labour income. Consider the following model to address this concern formally. Assume that an individual lives for three periods, t = 0, 1, 2 and has income w in both periods 0 and 1 but zero income in period 2. In each period t the individual derives utility u(xt) = ln(xt) from consumption. The individual discounts the future. Lifetime utility U, from the perspective of period t = 0, respectively t = 1 is given by: Uo= uo + Bou +38 u and U = + 2, where 0 < 6 1 and 0 < 3 < 1. The individual can borrow and save at an interest rate of 0, so that total consumption expenditure must equal the sum of income. (a) Derive the individual's preferred consumption plan (1, i, ) from a period t = 0 perspective (i.e. maximising Uo). Explain the roles of parameters 3 and 6. (b) Derive the individual's preferred consumption pattern (2, 2) from a period t = 1 perspective (i.e. maximising U) for a given value of zo. Explain the difference, if any, between (z, 2) and (x1, x). (c) Suppose that r > r, but that the individual's preferred consumption r in period 0 when anticipating that later consumption will be (x,x) is the same as , i.e. the individual would prefer to save a higher proportion of their period 1 income from a period 0 point of view than from a period 1 point of view. If the individual is aware of their present bias, could a financial product that prevents borrowing, requires an investment k in period 0 and pays back k in period 2 increase period 0 utility Uo? Argue verbally or compute. (d) Could automatic enrollment in the workplace pension scheme (details for in- stance on www.gov.uk/workplace-pensions) address a self-control problem in- duced by present bias? Explain. 3. Retirement Saving [40 marks] Present bias may induce individuals to save too little for old age, when they no longer have labour income. Consider the following model to address this concern formally. Assume that an individual lives for three periods, t = 0, 1, 2 and has income w in both periods 0 and 1 but zero income in period 2. In each period t the individual derives utility u(xt) = ln(xt) from consumption. The individual discounts the future. Lifetime utility U, from the perspective of period t = 0, respectively t = 1 is given by: Uo= uo + Bou +38 u and U = + 2, where 0 < 6 1 and 0 < 3 < 1. The individual can borrow and save at an interest rate of 0, so that total consumption expenditure must equal the sum of income. (a) Derive the individual's preferred consumption plan (1, i, ) from a period t = 0 perspective (i.e. maximising Uo). Explain the roles of parameters 3 and 6. (b) Derive the individual's preferred consumption pattern (2, 2) from a period t = 1 perspective (i.e. maximising U) for a given value of zo. Explain the difference, if any, between (z, 2) and (x1, x). (c) Suppose that r > r, but that the individual's preferred consumption r in period 0 when anticipating that later consumption will be (x,x) is the same as , i.e. the individual would prefer to save a higher proportion of their period 1 income from a period 0 point of view than from a period 1 point of view. If the individual is aware of their present bias, could a financial product that prevents borrowing, requires an investment k in period 0 and pays back k in period 2 increase period 0 utility Uo? Argue verbally or compute. (d) Could automatic enrollment in the workplace pension scheme (details for in- stance on www.gov.uk/workplace-pensions) address a self-control problem in- duced by present bias? Explain.

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Retirement Saving with Present Bias This model analyzes how present bias affects an individuals saving decisions for retirement a Preferred Consumption Plan from Period 0 t0 Maximizing U0 To find the ... View the full answer