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1. (20 Marks) A Discrete-time Consumption Model with Labour Incomes Suppose you estimate your remaining life Span to be T > 0 more years and have NON tradable labour income y (t) > 0 for all times t = 0,1,...,T 1. You need to consume your wealth at beginning of each year, t = 0, 1, 2, . . . ,T 1, during the coming T years and want to leave a bequest B (T) 2 0 at terminal time T in a way that maximizes your total T years utility of consumption and bequest. Build your dynamic utility maximization problem. (Hint: Though you can save the unconsurned wealth for future consumption at in- terest rate r > 0, however, you cannot use your future labour income for current consumption. In other words, you can consume your future labour income 9 (s) only at future time s! The key is to determine how much total income W (t) to be available at each time t. Please reference example 1 in Lecture note 11.)