We can write the standard T-period saving-consumption model as: Choose (C1, C2,..., CT) to maximize subject...

 

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We can write the standard T-period saving-consumption model as: Choose (C1, C2,..., CT) to maximize subject to U(C, C2,..., CT) = u(c) + Su(c)+...+87-u(CT) c+ C2 1+r +...+ CT (1+r)T-1 W. In this model, there are three motivations that influence the allocation of consumption across periods: "impatience", "future consumption is cheaper", and "consumption smoothing". (a) For each of these motivations, (i) describe in words how the motivation impacts the allocation of consumption across periods (i.e., how c compares to c2, C3, and forth), (ii) describe math- ematically how it enters the problem above, and (iii) describe mathematically the special case of the problem above when the motivation is absent. [Note: You should have a total of 9 responses for part a] 3 (b) Suppose that T = 2 and u(c) = a + bc. Derive the optimal consumption path as a function of 8 and r. Hint: Use the substitution method in part (b). Hint: Your answer to part (b) might provide insight that helps you to answer part (a). We can write the standard T-period saving-consumption model as: Choose (C1, C2,..., CT) to maximize subject to U(C, C2,..., CT) = u(c) + Su(c)+...+87-u(CT) c+ C2 1+r +...+ CT (1+r)T-1 W. In this model, there are three motivations that influence the allocation of consumption across periods: "impatience", "future consumption is cheaper", and "consumption smoothing". (a) For each of these motivations, (i) describe in words how the motivation impacts the allocation of consumption across periods (i.e., how c compares to c2, C3, and forth), (ii) describe math- ematically how it enters the problem above, and (iii) describe mathematically the special case of the problem above when the motivation is absent. [Note: You should have a total of 9 responses for part a] 3 (b) Suppose that T = 2 and u(c) = a + bc. Derive the optimal consumption path as a function of 8 and r. Hint: Use the substitution method in part (b). Hint: Your answer to part (b) might provide insight that helps you to answer part (a).